JU
-,
.'~
.'
;~
:
1/
;~JJ
:
L~r~
THEORETICAL STUDIES OF SOME THIRD ROW
TRANSITION METAL COMPLEXES
by
Charles Bonner Harris
B.S. in Chemistry
University of Michigan
(1963)
SUBMITTED IN PARTIAL FULFITLENT
OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May, 1966
Signature of Author
-
-
.
.
Department of Chemistry, May 23, 1966
by ...................
Certified
. . ..
Thesis Supervisor
Accepted by . .
.
Chairman, Dept
- . . . . . . . . . .
ental Committee on Graduate Students
i
.
-
/
038
ii
This thesis has been examined by:
Professor Alan Davison, Chairman
,
'
-x,,- - -,,,
Professor F. Albert Cotton,
Thesis Supervisor
Professor Dietmar Seyferth//
_-
iii
THEORETICAL STUDIES OF SOME TIRD
ROW
TRANSITION METAL COMPLEXES
by
Charles Bonner Harris
Submitted to the Department of Chemistry on May 23, 1966, in
partial fulfillment of the requirements for the degree of
Doctor of Philosophy
ABSTRACT
The electronic ground state of PtC14 2 - calculated by semiempirical
molecular orbital theory is a Alg with a Pt d orbital order and
occupation of (dz2 )2 (dxzdyz) 2 (dxy)2 (dxa2.e) 0 . This result was obtained
over a wide range of variations in the Pt valence state ionization
potentials, the Pt wavefunctions, and the Wolfsberg-Helmholz factor in
both the Mulliken-Wolfsberg-Helmholz and the Ballhausen-Gray approximation. The numerical dependence of the Pt-Cl bond order and the
one-electron molecular orbitals of PtC14 2 - have been examined as
functions of variations in the Pt 6s, 6p and d wavefunctions, the
and the weight given
potentials,
corresponding valence stateionization
to the off diagonal terms in the Hamiltonian matrix.
Finally
a
method is outlined for computingSTOoverlap integrals that accurately
approximate SCF overlap integrals.
A three-dimensional, single crystal X-ray diffraction study of
the structure of K2[Re 2 Cl8]2EH2 0 is reported.0 The crystals are triwith a = 6.75, b = 7.86, and c = 7.61 A, and a = 102.00,
clinic
0 = 108.90, nd y = 107.8 °. There i one formula unit in the cell,
The [Re2 Cl8]2 ion therefore has a center
and the space group is P.
of symmetry; its idealized point symmetry is 4/mmm (D4h). The mean
angle is 104° , the mean
Re-Cl distance is 2.29 A, the mean Re-Re-Cl
Cl-Re-Cl angle is 870, and the Re-Re distance is 2.24 A. The water
molecules are coordinated to K + ions.
The metal-metal and metal-chloride bonding in [Re2Cl 8 ]2 - is
treated by "extended" Hickel Molecular Orbital Theory. The calculation suggests that the pi(TT)bonding contribution to the Re-Re bond
is four times that of the delta(8) bonding and almost twice that of
the sigma(a) bonding. The Re-Re bond stabilization and the 6-bond
rotational (D4h to D4d) barrier in [Re2 Cl8 ]2 - are calculated as
iv
250 kcal and 50 kcal respectively by comparing a hypothetical
2
anion (D4h). The ordering
[ReC14]1- anion (C4v) with the [ReCl 8 ]
of the molecular orbitals is discussed with respect to the magnetic
properties and the observed and calculated spectral properties.
A molecular orbital interpretation of nqr coupling constants is
derived in a general manner. It is simplified by judicious assumptions
and applied to some third row transition metal chlorides.
The bonding, charge distributions, spin densities and spectra
'2
(M = Re(IV), Os(IV), Ir(IV), and Pt(IV))
of the third row MC1e
series is treatedby molecular orbital theory. Specifically, the
calculated nqr coupling constants, the t2g spin densities and the
charge transfer spectra are shown to be in good agreement with
experimental results.
Thesis Supervisor:
Title:
F. Albert Cotton
Professor of Chemistry
V
TABLE OF CONTENTS
Chapter I
General Background and Development of Molecular
......
Orbital Theories .........
General Molecular Theory .........
Self-Consistent Field Theory ......
HUckel Theory ..................... .........
*......
Synthesis of LCAO-MO-SCF and Huckel Method - Moffitt 's
, . ..
...
Atoms in Molecules Method ....
, . ..
...
LCAO-SCCC Method ..................
t s c·
Extended Huckel Theory ............
, . ..
...
Modified SCF Method ...............
Future Improvements in Molecular OrIbital Theory ...., . .. ...
...............
,
......
......
. ..
eeeeee
1
2
4
...
7
eeeeee
eeeeet
.eoeee
.eeeee
Thnesis Goals
...............................
...........
References
..................
.........
The Effects of Various Parameters on Semiempirical
Molecular Orbital Theory of Metal Complexes.
Molecular Orbital Theory of PtC14 2 -.............
Introduction .............................................
.
.............
Method of Calculation
Choice of Atomic Orbitals and the Evaluation
. .......................
of Overlap Integrals
Evaluation of the Diagonal Matrix Elements, Hii ....
Evaluation of the Off-Diagonal Matrix
9
12
!4
16
17
18
19
Chapter II
............................ * ....
Elements,
Hij
Calculations ................................... o
.......
Results
........................
Variation of the Metal Shielding Parameters, yi ..
Variation of the Pt Diagonal Matrix Elements,
Hiits
..................
...............
Spectra
..........................
.......
...
......
Nature of the Pt-Cl Bond ..............,............
...........................................
Tables
Figures
.........................
Chapter III
..................
22
23
24
25
27
30
31
31
33
34
35
36
39
58
The Crystal and Molecular Structure of Dipotassium Octachlorodirhenate(III) Dihydrate,
.................................
2H20O
K2I[Re
2C18]
........
................................
Introduction
Experimental
..............................
Determinationof Structure ..................
..................... 9.................
Discussion
The (Re2 Cl8)2
Ion ...........
.
...........
*.....
72
73
73
74
76
76
vi
Crystal Packing .....................................
77
Comparison with Previous Work ..
..................
78
Tables ...................................................
80
Figures ...
...............................................
83
References ...............................................
85
Chapter
IV
Molecular
Orbital
Theory
of Re 2 Cle8 2
8...
87
88
.......
Introduction .....................
......................
Choice of the Basis Set ..
...........
.........
88
Evaluation of the Overlap Integrals .....
...........89
Evaluation of the Diagonal MatrixElements, Hii
.....
90
Evaluation of the Off-Diagonal Matrix Elements,
Hij
.. .***..*****..........
....
91
Method of Calculation ............
Results
....
*........
.......,
91
..............................................
92
Interpretation of Spectra .........................
Nature of the Re-Re Bond ............................
Nature of the Re-C1 Bond .........................*.
92
94
97
Tables ............ ................
..........
Figures ....................................... 11~
99
117
References
121
........
.......
,....................
Chapter V
Correlation of Nuclear Quadrupole Coupling
Constants with Molecular Electron Structure
Using Molecular Orbital Theory .......
.......... 123
Derivation of eqQ ..................
......................
124
Table
.. .............
a...
131
References ................................
132
Molecular Orbital Calculations on MCle2'
(M = Re(IV), Os(IV), Ir(IV), Pt(IV)) .
............ 133
Introduction ............
......................
*...
134
Orbital Basis Set .........................
.............. 134
Diagonal Matrix Elements, Hii ............................
135
Chapter VI
e...
Calculations ....
.
........... ,......
.........
135
Electron Spectra ...............
.
.............
Charge Distributions and Metal-Chloride Bond Orders ......
Spin Densities
.......
..
,.......
Nuclear Quadrupole Resonance Coupling Constants ...,.....
Tables ...................................
...
References
......
.
.......................
..
136
138
139
140
142
181
Acknowledgements ............................................
183
Biographical Sketch ...........................................
184
vii
LIST OF TABLES
Chapter
II
39
39
5.
Ratio of STO:SCF Overlap Integrals ................
Orbital Shielding Parameters, i ..................-.
PtC14 2 - Overlap Integral Matrix .....................
Cu-Cl Overlap Integral Ratios Over Charge and
Configuration........................................
Pt States and Processes Averaged to Obtain Aii.......
6.
Pt Hii's as a Function
4
7.
8.
Molecular Properties vs. K and K'
9.
Calculated Transition Energies from Fig. 3 ..........
PtC14 2- One-Electron MO Eigenvalues ...............
Pt-C1 Bond Order Contributions ..........
.......
Atomic Orbital Occupation ............
.............
PtC14 2 - MO Input Parameters .......................
PtC14 2- Eigenvectors .........
..............
Reduced Overlap Population Matrix .................
PtC14 2 - Mulliken Overlap Populations .
...............
PtC14 2' MO Charge Matrix .....................
1.
2.
3.
4.
10.
11.
12.
13.
14.
15.
16.
17.
Pt Shielding
Parameters
of Charge
....................
for Points
42
43
.
.........
45
in Fig.
5 ......
46
Chapter III
1. Fobs. and Fcalc ...................................
2. Final Positional and Isotropic Temperature
Parameters
............... .......
3.
40
46
47
48
48
49
51
53
54
56
80
..........
Crystallographically Independent Distances and
Angles in [Re2C1-8 ]2 . ..................
............ 82
Chapter IV
1. Atomic Orbital Shielding Parameters, i .............
99
2. States Averaged to Obtain Re Aii's ........
.
99
100
3. A. Possible Allowed Transition in Re 2 Cl 8 2
........
100
B. Forbidden Transitions ...........................
2
100
C. Spectra of Re2 Cl8
.......
......
... *...........
2
101
4. Re 2 Cl 8
One-ElectronMO Energies ,..............
102
5. Orbital Contributions to the Re-Re and Re-Cl Bond
....
.....................
103
6. Molecular Orbital Energies
103
...................
..
7. Re-Re Bond Energies in Re 2 Cl 8
104
8. Re 2 Cl 8 2 - MO Input Parameters ........................
9. Re2 C18 2 MO Eigenvectors
.......................
107
109
10. Re 2 C1 8 2 - Mulliken Overlap Populations ...............
111
11. Re 2 C1 8 2- Orbital and Atomic Charges .............
112
12. Reduced Overlap Population Matrix ...................
.... ,
.....
13. Re 2 C1 82 - Overlap Integral Matrix ....
113
115
14. Re 2 Cl 8 2 MO Charge Matrix ......
.....................
viii
Chapter V
1. Comparison with Experiment
........
.................. 131
Chapter VI
1.
MC16' 2
2.
5.
6.
ReCl e 2 OsC1 6 2 IrCl6 -2
PtC16 2ReCl6 2'
7.
OsC1,6 2
3.
8.
9.
10.
-1.
MO Input Parameters.....
Overlap Integral Matrix ;ions
Overlap Integral Matrix *. . . .
Overlap Integral Matrix
Overlap Integral Matrix
Eigenvectors ...........
e·e·e
eeeee
13.
14.
15.
16.
17.
18.
19.
20.
.
..
.
.
.
..
.
.
.
.
..
.
. . .. .
.
.
..
.
eeeee
el··
.
.
.
e·eee
.
.
.
.
..
.
.
..
.
.
..
.
.
..
.
.
..
.
.
..
...........
ee·®
.
.
.
.
ele·e
.
.
.
.
. . ..
. ..
. . ..
. ..
142
144
146
148
150
152
154
.
IrC 2' Eigenvectors ...........
156
.
PtCl 2- Eigenvectors ..........., ..
.
158
MCe -' MO Energies and Occupati
60
.
ReCle2 - Mulliken Overlap Populations and Bond
Order Matrix ....................... and Bond................
162
OsC16 2 - Mulliken Overlap Populations and Bond
Order Matrix ............,......
164
....................
IrCl6 2 - Mulliken Overlap Populations and Bond
Order Matrix ........................................
166
PtCl6 2- Mulliken Overlap Populations and Bond
OrderMatrix..............
168
ReC,2- MO Charge Matrix ............................
170
OsCl6
MO Charge Matrix ...........................
172
IrCl6 2' MO Charge Matrix ..........
................. 174
PtC1 2 - MO Charge Matrix ............................
176
MC.1 - Orbital Occupation and Atomic Charges ........
178
MC16 2' Molecular Properties ................
180
Eigenvectors
.
12.
....
....
. .. .
. .. .
ix
LIST OF FIGURES
Chapter II
1. PtC14 2- Molecular Coordinate System ..............
2. One-Electron MO's vs. K
..
..
........
3. Partial One-Electron MO Diagram of PtC14 2
4. Total Electron Energy of PtC14 2 - VS. Pt Orbital
Exponents ...................................
58
60
62
One-Electron MO's vs. Pt Orbital Exponents ..........
One-Electron MO's vs. Hii ...................
*.
64
66
68
Chapter III
1. Sketch of the Re2 C18 2- Ion ..........................
83
5.
6.
Chapter IV
1. Molecular Coordinate System
.
..................
2. Partial One-Electron MO Diagram for Re2 C 8 2
O.......
117
119
-1-
CHAPTERI
GENERAL BACKIROUND AND DEVELOPMENT
OF MOLECULAR ORBITAL
THEORIES
-2-
General Molecular Theory
The problems of molecular physics were solved in principle with
the advent of quantum mechanics in the 1920's when Schrodinger'
presented his time-independent differential equation.
H
= E
(1)
This equation accounted quantitatively for a multitude of atomic
state phenomena.
Exact solutions of Eq. (1) have been obtained only
for H and its isoelectronic ions (e.g., He+, Li
, etc.) because of
the mathematical difficulties inherent in the solution of the threebody problem.
As a result, the solution of Eq. (1) can be arrived
at for molecules only by a method of successive approximations, that
is, a trial function,
,i'
is used to calculate an energy, E ; the
function is changed and a new energy is calculated.
This process of
iteration is repeated until a minimum energy, Em, the expectation
value of the energy of the system in the state %,m is obtained.
This
procedure defines the variational method and as such is subject to
the limitation of the variational theorem2 which states that the
expectation energy, Em, of the system in the state
m
m is always greater
m
than the actual ground-state energy, E, of the system, e.g.,
Em -E
(2)
The difference between Em and E is termed the correlation energy
and is inherent in all molecular calculations.
-3-
Equation (1) can be simplified owing to the smallness of the ratio
of the mass of an electron to that of any nucleus.
The Born and
Oppenheimer approximationS allows the wavefunction,
, to be separated
n respectively.
e and
into its electronic and nuclear coordinates
Thus, the total energy, E, is simply the sum of the electronic energy,
Ee, associated with the electronic states,
e' plus the energy of
the nucleus, E n , associated with the nuclear states,
n.
The deter-
e is our central concern; the rest is the familiar problem
mination of
of translation-vibrational-rotational motion associated with the
nuclei.
The validity of the Born and Oppenheimer approximation has
been substantiated4 in the case of H2 insofar as the Born-Oppenheimer
correction amounts to only 0.014 ev. of a total H2 dissociation energy
of 4.7466 ev.
Equation (3) restates the variational equivalent of our problem
for electron wavefunctions,
e',assuming fixed nuclear coordinates.
ge()
Ee= I e* HeedS J $e Sed
The solution of Eq. (3), strictly speaking, is only a mathematical
problem.
As such, the challenge of its solution has produced a
dichotomy involving purely theoretical methods on the one hand, and
semiempirical methods on the other.
Although purely theoretical
methods play .a fundamental role in our understanding of "small"
molecular systems, they cannot, as yet, be applied to many molecules
aside from diatomics and a few H-triatomics.
Thus semiempirical methods
-4-
are a necessary and essential tool for applying molecular quantum
mechanics to larger molecules.
Carefully used and properly "calibrated"
they have great value and utility for predicting unknown
olecular
properties.
Since our interest centers around calculations of transition
metals and therefore not small compounds, we will restrict this discussion to semiempirical methods.
In particular the following dis-
cussion will be devoted almost entirely to the various Hckel-type5
approaches.
However, an understanding of the approximations made in
Huckel theory prerequisites a rudimentary understanding of the molecular
Hartree-Fock or self-consistent-field (SCF) method. 6 '7
Self-Consistent Field Theory (SCF).
The Hamiltonian operator for an n-electron problem has the form
l/2Vi 2 -
He =
i
Z (Z /ri,)
i cri
Pi
where the indicies run from 1 to n, the terms -1/27i
energy components, the terms (z lra)
2
are the kinetic
are the nuclear attraction com-
is the charge on the a nucleus, and the terms
ponents where z
(j
(4)
(/j j/ri)
+
j/rij) represent the electron-electron repulsions.
The first two terms in Eq. (4) are customarily called Hcore;
the latter being either the coulomb operator Ji or the exchange
operator Ki where
Ji
=
(1)i()/rij
(5)
-5-
Ki =
The
(6)
i(l)$i(2)/rij
i(l) notation refers to electron 1 in orbital i.
For molecules
the LCAO-MO-SCF method is ordinarily employed to solve Schrodinger's
equation using the Hamiltonian operator given by Eq. (4).
A linear
combination of atomic orbitals (LCAO)8 is used to construct solutions
of Molecular Orbitals (MO),
e.g.,
Xi
i' to Eq. (1):
=
' Ci
where the Xj are the atomic orbitals.
Xj
no error is introduced.
X's
(7)
If enough X's
are included
However, one usually restricts the number of
used arriving at a final solution which contains a margin of
error, otherwise known as the LCAO "approximation".
If we insert Eq. (7) into Eq. (1) using Eq. (4), multiply on the
left by X i, and integrate we obtain a set of equations
cE
l
Ci (Hij
- SijEj) =O
(8)
where in the notations of Eqs. (5) and (6)
Hij =
ijre +
[2 Jj
- Kij]
(9)
and
Sij =
XiX
(10)
-6-
Equations (8) are simultaneous linear equations for unknowns, Cij,
and a non-trivial solution exists if
determinant
IHej - SijEi
ij
iji
=
()
Knowing the X 's molecular orbitals, i., can be determined by guessing
the Cits,
computing the integrals in Eq. (9); solving Eq. (1);
determining the Cij's from Eq. (8); comparing the original Cij's with
the final Cij's, and repeating the cycle until the Cij's do not change
from cycle to cycle.
This procedure defines the LCAO-MO-SCF method.
The energy of the MO's are Ei.
The total energy9 of the molecule in
a closed shell configuration, Etotal' is not twice the sum of the orbital
energies, E,
but
E
Etotal
-Hcore
= 2
i
1/2(Ei +
(12)
ire
In principle, the above procedure can be applied to any molecule.
In practice, however, the difficulty in evaluating the Jij and Kij
integrals and the sheer number of integrals involved has restricted
the LCAO-MO-SCF method to small molecules.
As a result many MO
theories evolved l° - 13 which attempted to semiempirically approximate
the Jij's and Kij's (Eq. (9)).
They have to date been applied pri-
marily to pi-electron systems in organic molecules, and as yet have no
significant utility for transition metal complexes.
-7-
Huckel Theory.
An MO theory that has transcended the mathematical difficulties
5
associated with the LCAO-MO-SCF theory is the Huckel Theory.1,"
In this theory the n-electron Hamiltonian is not of the form in Eq. (4).
A much simpler form,
He
(13)
Heff(i)
=
i
is used where Heff(i) is some operator that incorporates in an average
way the electron-repulsion terms of Eq. (4).
Invoking the LCAO
approximation (Eq. (7)) and applying the variational theorem to
Eq. (1) using Eq. (13) as the Hamiltonian operator we obtain, as
earlier,
E
eff
Cj
Ci (Hij - SijEi) =
Thus the problem is simply to determine the matrix elements H
which the cases i
eff
Hij
(14)
(14)
in
j and i = j are distinguished.
=ii
=
Xi
Hexid r
(15)
is called the coulomb integral and is an empirical property of an atom;
eff
Hij
=
ij
j
=
xi*
ex.d,~
Xi
Xjd
(16)
(6)
is called the resonance integral and is an empirical property of the
bond.
Sij is again the overlap integral between the ith and jth atomic
orbitals.
-8-
A critical simplifying assumption in the theory is that
Si
(17)
= 0
when i and j orbitals are not on neighboring atoms.
It has been
shown16 that this is not a bad assumption provided that
O.. =0
when Eq. (18) is satisfied.
(18)
Thus for simple homonuclear pi-systems
(ethylene, benzene, naphthalene) the problem reduces to two parameters,
aii and
ij.
Molecular orbitals for literally hundreds of molecules
have been calculated using Hckel
the theory is its simplicity.
theory.
The greatest advantage of
We need not enumerate in detail the
Streitiewer'sl6 book
successes of the theory in organic chemistry.
gives a truly superb treatment of this subject.
In spite of the
simplicity and limited success of the theory, several major criticisms
can be leveled against it.
parameters,
ii and
First, from a practical standpoint, the
ijrequired
to fit one property usually differ
from those required to fit another.
Thus it is impossible to describe
simultaneously the spectra and charge distribution of a given molecule.
Furthermore, there is no finite bond order between non-adjacent atoms
in a molecule in the framework of Huckel theory.
This is erroneous
and results from the neglect of non-neighboring interactions.
From
a theoretical point of view, it is simply not valid to write Eq. (13).
-9-
For such a one-electron operator the total electronic energy for a
closed shell configuration is given by
Etota
1
= 2
(19)
E
and not by Eq. (12). Even if He (Eq. (12)) is interpreted as the
Hartree-Fock operator (Eq. (4)) it invariably counts electronic
repulsion twice.l7
Method - Moffitt's Atoms in
Synthesis of LCAO-MO-SCF and Hckel
Molecules Method.
Moffitt's attempt'8 to calculate thr rich electronic spectrum of
molecular oxygen using LCAO-MO-SCF theory failed insofar as his results
contradicted experimental facts.
This prompted him to formulate his
atoms-in-molecules methodl 9 in which atomic-spectroscopic data was
empirically incorporated into molecular orbital theory.
The precise
logic and mathematics employed in the original argument will not be
presented since an excellent discussion of the method has been given
by Parr.2 0
Instead, we will present a descriptive formulation of
the theory relying on "intuition" rather than formal mathematics.
The basic idea is qualitatively very simple - atoms in a molecular
field behave similarly to free atoms, but there is an interatomic
correlation effect in molecules which vanishes at infinite internuclear distance.
In other words, the Hamiltonian matrix elements of
the atomic orbitals on an atom in a molecule, Hii , represent the
energy of an electron in a specific atomic orbital i, moving in the
field of shielded atomic nuclei.
Thus, the Hamiltonian operator
for the ith electron can be written as
Hi = -1
/2i2
1
Z/ri
+ E,
i i
a
+ Z p.k/rik
B/riB
k
(20)
and the n-electron Hamiltonian can be written as
eff =
Hie
i
(21)
The symbols in Eq. (20) are defined in the same fashion as in Eq. (4):
however, the sum over
refers to atoms in the molecule on which i
is not centered and the sum over k is to imply electrons on the
atoms.
f
The first three terms in Eq. (20) are therefore the free
atom contributions, A,
i
relation terms, Vc.
and the last two terms are the molecular cor-
Thus the diagonal matrix elements of Eq. (21)
can be expressed as:
Heff
Hii=
c
= A ii + Vc
(22)
The key to the solution of Schrodinger's equation for this method in
the LCAO approximation then is simply the separation of the matrix
elements of the molecular Hamiltonian into intra-atomic and interatomic elements.
The former are estimated from atomic-spectroscopic
data and the latter are approximated or calculated from some orbital
-11-
theory. 21 ,2 2
The methods that have evolved in the past few years to
treat transition metal complexes differ only in the procedure used to
obtain these elements.
Before discussing these methods a word should
be said about the evaulation of the off-diagonal matrix elements,
Hej (i/j), that arise.
By similar arguments, i.e., separation of atomic and molecular
contributions in the Hamiltonian, Moffit 2 2 proposed that the offdiagonal matrix elements, Hj,
could be reduced to diagonal elements,
e
Hei. and HHjj,
plus Vcj, the correlation energy between them, i.e.,
Hej
where Vji
(1/2)SiJ{Hii + Hj
+ 1/2[Vij
+j
(23)
is the complex conjugate transpose of Vij. In this fashion
only the correlation energies need be calculated since the H. 's are
in principle known.
Unfortunately, correlation energies are extremely
difficult to calculate; consequently, they must be approximated.
One such approximation was suggested by Wolfsberg and Helmholz.2 3 ,2 4
In effect they incorporated the correlation terms, V
e
atomic terms, Hii
into the
by the following equation
H.
Hej
= = KS.[ee
K Sij(Hii +H/2
+ H/2
(24)
(24)
where the parameter K is varied to fit some physical observable
(e.g., electronic spectra) associated with the molecular orbitals,
-12-
This approximation, however, was patterned after Mulliken's2 5
approximation for potential energy integrals, Vij.
e.g.,
(25)
Vij=Si(Vii + Vj)/2
Equation (24) is therefore frequently called the Mulliken-WolfsbergHelmholz (MWH) approximation. 28
Utilizing Eq. (24), the MWH approximation, the application of
semiempirical molecular orbital theory to inorganic complexes reduced
(1) to the evaluation of the overlap integrals, Sij, and (2) the
estimation of diagonal energy matrix elements, H.
It is the various
approaches used to estimate the latter that further distinguishes
the types of molecular orbital theories employed in transition metal
chemistry.
These will now be discussed.
LCAO-SCCC Method.
The LCAO-SCCC method, the linear combination of atomic orbitals
self-consistent in charge and configuration, was suggested by Gray2 7
and has been applied to many transition complexes2 8 with little or
no experimental confirmation of the results.
The method attempts to
calculate a linear relationship for the His
in Eq. (22), in terms
of the configurations of the ith orbital.
For instance, in a trans-
ition metal, e.g., Mn2+, the d orbital may be in one of several configurations:
5
dS
, d 4 s, d 3 sp, d 2 s2 p, d 2 sp2 , etc.,
-13-
each having a different energy as obtained from spectroscopic tables2 9
of the ion.
Moreover, in a complex the metal may not have a formal
valence state of +2 in this case, but may instead be +1; thus,
giving rise to a new series of configurations;
de, d5s, d 4 sp, d 3 s2p, d 3 sp2 , etc.
each again having a different energy.
In order to accommodate
these possibilities the method initially assumes a given charge and
configuration on the atoms and uses the H
states.
's corresponding to these
If a Mulliken
The molecular orbitals are then calculated.
population analysis3 0 '3 l is performed on the MO's a new charge and
configuration for the atoms can be determined.
New H ii's corresii
ponding to these new states are then used in the next cycle.
In
cases where the charges or configurations are non-integral, extrapolated
values are used.
The procedure is reiterated until the charges and
configurations do not change from cycle to cycle,
At this point the
calculation is said to be self-consistent.
The method as described is an elegant way of obtaining the Aii
terms in Eq. (22).
However, a basic fallacy of the method is that
it neglects entirely the molecular interaction (interatomic correlation) terms, Vi
(Eq. (22)).
This is equivalent to saying that
the interatomic electron repulsion terms are exactly equal to the
negative of the interatomic nuclear attraction terms.
This is certainly
not the case, nor should one naively expect it to be so.
Using a
-14-
point charge approximation, one can to the first order show that
these terms can be as much as +5 to +15 ev.3 2
The ultimate result
of such an error is that the metal orbital Hi's
are much too stable.
That is, their dependence on charge is about -10 to -15 ev. per
metal charge unit (e.g., M
to M+1) rather than about -1 to -3 ev.
which would result from the incorporation of the molecular terms.
This is illustrated in the following way.
Suppose a Pt atom were
in the environment of four C1 atoms (e.g., PtCl4 2 -) and the charge
on the Pt in this environment was +1.
The H i for the
it were a free ion would be about -20 ev.
d orbital if
In the C1 environment,
however, the 5d electrons see an effective minus field due to the
-0.75 charge on each C1; thus, the 5d electrons are "destabilized"
by about 10 ev. by electron-charge repulsions.
that is neglected in the LCAO-SCCC method,
It is this repulsion
As a consequence the
calculated metal-to-ligand covalency is too great and the calculated
This has been verified in
metal effective charge is too low.
several cases by Nuclear Quadrupole Resonance studies of transition
metal halides
33 - 35
Extended Huckel Theory.
Extended Hckel
Theory (EET) assumes a Hamiltonian operator
of the form given by Eq. (22); the V
term, however, is replaced by
the point charge approximation given by Pople.36
Vii =
c
Z
eff/r
(26)
(26
-15-
The
eff
represents atoms on which i is not centered and zef is the
effective nuclear charge of atom
In order to evaluate Hii
.
it becomes necessary (1) to evaluate Aii using the procedure outeff
CAO-SCCC method, and (2) to determine Zff .
lined in the
If we
assume, as does the ICAO-SCCC method, that the ith electron on the
a atom is perfectly screened from the
the
would be zero.
atoms, then Z
nuclei by electrons on
This is usually not the case.
eff
What ultimately determines the value of Z
is the penetration of
electron core.
This can be illustrated
the ith orbital into the
by the following two examples.
molecule A-B.
Assume that we have a diatomic
If the radial portion of the A wavefunctions are
very contracted (e.g., E) they do not penetrate very far into the
positive field of the B core; consequently, it sees an effective
negative charge on atom B.
On the other hand, if the A wave-
functions are diffuse, they penetrate more into the positive field
on B.
Furthermore, if this penetration is great enough, the A
wavefunction may see an
effective" positive charge on atom B.
Thus,
the "diffuseness" of the orbitals (a property of only the radial
part of the wavefunctions) determines (1) the sign of Ze f f and (2)
its magnitude.
If one defines the potential field around atom B as v(r) (where
v functionally defines the charge density around B), then
Z,/rB
,
eZR
ff/=
< XilV(r)l i>
(27)
-16-
Since it is difficult to compute the integrals in Eq. (27),
several approximations have been suggested.
Pohl, Rein, and
Appel 3 7 obtained the penetration correction for hydrogen halides by
the use of coulomb repulsion integrals.
Ros3 8 has devised a method
for estimating these terms by assuming the electron density contributions from individual orbitals on B are localized between
concentric spherical shells.
In other words, the integrals are
practically zero for high and low values of r in v(r).
Finally, the Z
empirically into Hi
ff
can in certain cases be incorporated semi-
by systematically varying the Hi's
to calibrate them with some observed molecular property.
in order
A descrip-
tion of this procedure is given in Chap. II.
Modified SCF Method.
Recently, there has been an attempt to do molecular orbital
calculations on transition metal complexes in the framework of a more
theoretical approach.
Fenske3 9 formulated an approach similar to
the SCF approach insofar as all diagonal matrix elements are calculated from first principles.
It, however, differs from SCF theory
in that the Mulliken approximations 2 5 are used to simplify
one
center coulomb and exchange integrals and the Shulman and Sugano 4 °
electrostatic interatomic integrals have been approximated by point
charge crystal field integrals.4 1
The Hamiltonian operator
for this
method incorporates interatomic correlation and therefore closely resembles
-17-
the SCF Hamiltonian.
The method has, however, not been tested in
its ability to predict molecular properties such as charge or bond
covalency,but it seems to calculate reasonable 10 Dq values for the
first row hexafluorides.4 2
Furthermore, it is apparently consistent4 2
with the nephelauxetic effect4 3 which has been attributed4 3 '44 to
the reduction of the effective metal charge resulting from electron
donation via chemical bonding.
All in all the theory outwardly appears "promising".
However,
as yet it has not been used to predict or verify the molecular
properties of charge distributions and bond orders.
Future Improvements in Molecular Orbital Theory.
There are two areas where substantial improvement in semiempirical MO theory could be made.
First, new methods for the evaluation of the diagonal terms,
Hii, must be found.
A theoretical method must include the inter-
atomic correlation or penetration terms.
For closed shell systems
Ros 4 5 is developing a computer program to analytically compute these
terms.
An empiricalmethodisdeveloped in this thesis (Chapters II and
V) in which these terms are "calibrated" by certain molecular
properties.
Specifically, a molecular orbital interpretation of
nuclear quadrupole resonance is developed (Chapter V) and is applied
to transition metal complexes (Chapters II and VI) as a means of
evaluating (1) the parameters used in MO theory and (2) the results
derived from MO theory.
-18-
The second area where improvement is needed is in the evaluation
of the off-diagonal matrix elements, Hij.
Specifically, the kinetic
energy contributions to Hij should be calculated explicitly and the
MWH approximation should be used for the potential terms only.
8
64
"
This has been done for some simple organic molecules48 but has not
been used for transition metal complexes.
Thesis Goals.
The goals of this thesis are:
(1)
To evaluate the variable parameters in extended Huckel theory
in order to obtain the best fix values for a series of molecules.
(Chapter II)
(2)
To apply MO theory to the metal-metal and metal-ligand bond
to determine what specific interactions are important in each.
(Chapters II and IV)
(3)
To apply nuclear quadrupole resonance results to verify molecular
orbital calculations,
(Chapters V and VI)
-19-
I
CHAPIER
REFERENCES
1.
P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed.,
Oxford Univ. Press, London, 1958.
2. R. Daudel, R. Lefebvreand C. Moser, Quantum Chemistry:
Methods and Applications, Interscience, N.Y., 1959.
3. A. Frbman, J.Chem. Phys., 36, 1490 (1962);
J. 0. Hirschfelder, J. Chem. Phys., 32,
D. W. Jepsen and
1323
(1960).
and C. C. J. Roothaan, Revs. Mod. Phys., 32, 219 (1960).
4.
W. Kolos
5.
Y. I'Haya, Advances in Quantum Chemistry, Vol. I,
Lowdin,
Per-Olov
Ed., Academic Press, N.Y., 1964.
6.
D. R. Hartree, The Calculation of Atomic Structures, Wiley,
N.Y., 1957.
7.
C. C. J. Roothaan, Revs. Mod. Phys., 23, 69 (1951).
8.
J. H. van Vleck, J. Chem. Phys., 2, 22 (1934).
9.
B. J. Ransil, Revs. Mod. Phys., 32, 245 (1960).
10.
R. Pariser and R. G. Parr, J. Chem. Phys., 21, 466
11.
R. G. Parr, J. Chem. Phys., 20, 1499 (1952).
12.
J. A. Pople, Trans.Faraday Soc., 43, 1375 (1953).
1.
C. M. Moser, J. Chem. Soc., 3455
14.
J. D. Roberts, Notes on Molecular Orbital Calculations,
(1954).
Benjamin, N.Y., 1961.
15.
r-
(1953).
G. Del Re, Nuovo Cimento, 17, 644 (1960).
16.
A. Streitwieser, Jr., Molecular Orbital Theory for Organic
Chemists, Wiley, N.Y., 1961.
17.
R. G. Parr, J. Chem. Phys., 19, 799 (1951).
18.
W. Moffitt, Proc. Roy. Soc.(London), A210, 224 (1951).
19.
Ibid., A210, 245 (1951).
20.
R. G. Parr, Quantum Theory of Molecular Electronic Structure,
Benjamin, N.Y., 1964.
21.
M. Kotani, K. Ohno and K. Kayama, Handbuch der Physik, 37/2,
1 (1961).
22.
J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 1,
McGraw-Hill, N.Y., 1963.
23.
M. Wolfsberg and L. Helmholz, J. Chem. Phys., 20, 837
24.
See Chapter II of this thesis for a discussion.
25.
R. Mulliken, J. chim. phys., 46,
26.
See Chapter II and IV of this thesis.
27.
H. Basch, A. Viste and H. B. Gray, J. Chem. Phys., 44, 10 (1966)o
28.
C. J. Ballhausen and H. B. Gray, Molecular Orbital Theory,
Benjamin,
29.
497
(1952),
(1949).
N.Y., 1964.
C. E. Moore, Atomic Energy Levels, U. S. National Bureau of
Standards Circular 467, 1949 and 1952.
L
30.
R. S. Mulliken, J. Chem. Phys., 23, 1833 (1955).
31.
Ibid., 23, 1841 (1955).
32.
For specifics, see Chapter II of this thesis.
33.
R. Barnes and S. Segel, Phys. Rev. Letters,
, 462 (1959).
-21-
34.
R. Barnes and R. Engardt, J. Chem. Phys., 29, 248 (1958).
55.
G. K. Semin and E. I. Fedin, Zhurnal Strukturnoi
Khimii,
1, 252, 464 (1960).
36.
J. A. Pople, Trans. Faraday Soc., 49, 1375
(1953).
37.
H. Pohl, R. Rein and K. Appel, J. Chem. Phys., 41, 3385 (1964).
38.
P. Ros, Thesis, Eindhoven, Holland (1964).
39.
R. Fenske, private communication.
40.
R. G. Shulman
and S. Sugano, Phys. Rev., 130, 517 (1963).
41. C. J. Ballhausen, Introduction to Ligand Field Theory,
McGraw-Hill,
N.Y., 1962, p. 57.
42.
R. Fenske, private
Inorg.
43.
communication.
Chem., 5, July,
To be published
in
1966.
C. J. Jorgensen, Absorption Spectra and Chemical Bonding in
Complexes, Pergamon Press,
Oxford, 1962, p. 134.
44. Idem., Progress in Inorganic Chemistry, Vol.4, F. A. Cotton, Ed.,
Interscience,
N.Y., 1963, p. 73.
45.
P. Ros, private
communication.
46.
R. S. Mulliken,
J. chim. pys.,
47. K. Ruedenberg,
48.
J. Chem. Phys.,
46, 497 (1949); 46, 675 (1949).
34, 1861 (1961).
M. Newton, F. Boer, W. Palke and W.Lipscomb, Proc. Natl. Acad.
Sci.,
553,1089 (1965).
-22-
CHAPTER
II
THE EFFECTS
OF VARIOUS
AMEERS
MOLECUIAR ORBITAL THEORY
MOLECUAR
ON SEMIEMP/fICAL
F METAL COMPIEXES.
ORBITAL THEORY
F PtC1
4
2
-
r
-23-
INTRODUCTION
Previous studies of the electronic structure of PtC14 2 - have led
to several ambiguities concerning the splitting of the Pt 5d orbitals.
Ballhausen and Grayl on the basis of an MO treatment using hybrid
orbitals have proposed a Pt 5d orbital order of (dxz;dyz), (dz2),
(dxy), (dx2.y2).
Fenske, Rudenberg and Martin 2 proposed the same
order by considering the problem in terms of electrostatic crystal field
theory.
Chatt, Orgel and Gamben3 and more recently Martin4 ' 5 proposed
a (dZ2), (dxz;dyz), (dxy), (dx2_y2) orbital order.
electronic spectrum of K2 PtC1
4
Unfortunately, the
both in the solid state5 6'7 and in
various solvents3 can be interpreted using either splitting scheme.
In an attempt to resolve these ambiguities, Martin 5 has studied the
vibrational fine structure of the polarized spectrum at low temperatures
and has suggested the latter assignment to be more probable.
The results of the various semiempirical MO theories are too
qualitative to accurately calculate one-electron transition energies
necessary for the unambiguous assignment of the electronic spectrum.
We feel, however, that the original Pt 5d orbital splitting scheme
proposed by Chatt, Orgel and Gamben3 is correct within the limitations
of a semiempirical MO theory which neglects spin.
We must assume,
however, that the solvent does not interact appreciably with PtCl4 2
along the C4 axis.
'
The validity of such an assumption is indicated by
the lack of substantial changes of the electronic spectrum in various
polar solvents3 and by the fact that the solvent is not found coordinated
to the Pt in the solid state.8
It is not the main purpose of this section to accurately correlate
the electronic spectrum but to discuss the effects of variations of
the parameters in semiempirical LCAO-MO theory on the estimation of
the one-electron ground state energy levels of PtC14 2- and to use
Mulliken population analysis9 "o
on the eigenvectors of the ground
state MO's to determine the electron distribution in the Pt-Cl bond.
METHOD OF CALCULATION
The LCAO-MO theory used is a modification of the extended Hckel
MO theory.
The modification is a stringent but necessary restriction
on the values of the "molecular" valence state ionization potentials,*
Hii
of the basis set orbitals.
Sij
are evaluated.
In every calculation all overlaps,
No assumption is made as to the extent of hybrid-
ization of the ligand and/or metal wavefunctions.
the variational principle, l l
This ensures that
E/8c i = O, where ci is the MO coefficient
and E is the MO eigenvalue, is satisfied for all atomic orbitals in the
basis set.
ii =
These conditions and the LCAO assumption, 12 i.e.,
c'i i where yi is the jth MO and Xi is the ith atomic orbital
leads directly to the familar condition for the secular determinant,
The distinction between molecular valence state ionization potentials,
Hii, and atomic valence state ionization potentials, Aii, is made
in order to discuss the energy of the ith atomic orbital in a molecular
and free ion field respectively.
r
-25-
i.e.,
detlHij - ESij
= 0,
where HiJ are the usual Hamiltonian matrix elements between the Jith
and jith atomic orbitals.
Choice of Atomic Orbitals and the Evaluation of Overlap Integrals.
A basis set of 25 orbitals, the Pt 6s, 6p,
d and the C1 3s, and
We
3p atomic orbitals were used to construct the molecular orbitals.
assumed that the non-valence electrons do not participate in bonding
and these, together with the nuclei, form a core potential that was
unchanged by interactions between the valence shell electrons,
The atomic orbitals were expressed as nodeless Slaterl3 (STO)
orbitals of the form:
t(n,l,m) = Nrn -l exp(-ir)(')
where N is the normalization coefficient,
meter, and Ym(e,)
(2)
. is the shielding para1
is the usual real spherical harmonic.
The shielding parameters,
ij,were chosen in the following fashion
to best approximate overlaps between self-consistent wavefunctions
(SCF).*
First an interpolated numerical radial wavefunction for C11/2
was obtained from SCF wavefunctions of C1 ° and Cll-. 1 4 ' 15
Numerical
Herman-Skillman wavefunctions for the Pto 6s and 5d orbitals were
used; the 6p wavefunction was approximated by assuming a slightly
smaller a than the 6s. The Hartree-Fock wavefunctions of Watson
and Freeman were used for C1 ° and C1 l- .
-26-
overlap integrals between the SCF
's for "cis" C1 3s-3s, 3P-3p, and
3s-3p orbitals were then calculated.
's in Eq. (2) were varied
The
so that the overlap integrals between the STO wavefunctions were
nearly the same as those obtained from SCF wavefunctions.
way the C1 3s and 3p shielding parameters were fixed.
cedure was followed for
tO-C1/2-
In this
The same pro-
overlap integrals of the type 6s-3s,
6s-3p, 5d-3s and 5d-3p; however, only the Pt
a.'sl 6 needed to be
varied.
The ratios of overlap integrals between STO and SCF wavefunctions
Table II gives the final oi's
are given in Table I.
used to calculate
the overlap integrals which are given in Table III using the molecular
coordinate system shown in Fig. 1.
We assumed that the overlap integrals did not change with
variation of the charge distribution in the course of self-consistent
The error inherent in such an assumption can be
charge refinement.
estimated if we assume that the Pt wavefunctions have a similar
dependence on charge and configuration as some other known wavefunctions.
The wavefunctions of Pt are not available for configuration and charge
states other than the Pto state 5d9 6sL.
Ros 1 7 has already given simple
diatomic overlap integrals for a limited number of charge distributions
and configurations of CuC14 2 .
listed for Cu d'l°s and d°p
I
parison to Cu 4s and
4
Since the 3d to C1 overlaps were not
configurations, we restricted the com-
p to C1 overlap integrals.
Table IV lists the
-27-
overlap integral ratios Cu°-C1
Cu0O
44
0
_Cl
O.6-
-5
and Cu 0 -C1 0' 5:_
:CUl+_ClO.75
for the orbitals and configurations listed.
Since a Pt charge of +0.439 was obtained after full charge
refinement, we concluded that although an 9% error is introduced in
certain cases (6 p-3s; 6s-3s) by neglecting to recalculate overlap
integrals as a function of charge, the average error is only 5% to 6%.
Evaluation of the Diagonal Matrix Elements, Hii.
Hii is the energy of an electron in the ith atomic orbital moving
in the field of the nuclei and other electrons in the molecule.
In
terms of the Hamiltonian operator and orthogonal wavefunctions, Xi;
these matrix elements can be expressed in the Dirac notation as:
Hii = <Xi1-1/2 V712Xi>- <Xi IZ/r lxi> + <Xi l j>iXjj/rij
X i
(3)
<xii
Z/r$lxi> + <Xi l
XkXIriklXi>
k>i
k/j
where -1/2 V 1 2 is the kinetic energy operator, Zra
is the nuclear
attraction operation of the oathnucleus on which the ith atomic orbital
is centered and
Xjxj/rij are the electron repulsion operators where
the jth atomic orbital is on the
centered on the
nucleus.
k designates atomic orbitals
nuclei.
If we define the free ion-contributions to Hii, namely the first
three terms in Eq. (3), as Aii and the remaining terms as Mii which
-28-
are the contributions to Hii from other atoms in the molecule, we can
re-express
Hii as:
Hii
(4)
Aii +Mii
For specific free ion electron configurations the Aii's can be
explicitly evaluated.
They have, however, been traditionally estimated
by the valence state ionization potentials (VSIPii).
+l
+ e- were estimated as the
The Aii's for the process Cl°OCl
1 8
for the 3s and 5p orbitals in the
VSIP's given by Hinze and Jaffe
2 2 2
configurations sp 2 p 2 p 2 and s p p p
respectively.
l
The Aii'S for the process PtO°Pt + + e- were estimated by averaging
19
for the conthe spectral states and multiplicities given by Moore
figurations and processes listed in Table V.
Since the spectral states
of Pt2 + have not been recorded, we have estimated the Aii's for the
process Ptl+
_pt2+
+ e.
Zerner and Gouterman20 have obtained VSIP's for many of the first
row transition metals, M.
+
They found that the VSIP's for M' were
about 10 ev. higher than the M° for 4s and 3d electrons and about 7 ev.
higher for 3p electrons.
+
Since the ionization potentials'l for Nil ,
Pdl+, and Ptl+ are 10.52, 11.09 and 9.56 ev. higher than the ionization
°
potentials for Ni° , Pd° and Pt , we felt that it is reasonable to
expect that the behavior of the VSIP's of the Pt states are similar to
the metals of the first row.
Therefore, the approximation was made
that the Aii's for Ptl + were 10 ev. higher than the Aii 's of Pt° for
the 6s and
d atomic orbitals and 7 ev. higher for the 6p atomic
orbitals.
In principle the multicenter integrals of Mii can be calculated.
This would be a formidable calculation requiring an unjustifiable
amount of computer time.
They can, however, in part be estimated by
the point charge approximation:
Mii
i
E
Zeffr
(5)
where Zef f is the effective point charge of the
nucleus.
The sum
is over all nuclei except the nucleus on which the ith atomic orbital
is centered.
The inner nuclear distance between the a and
in Bohr radii
is r.
nuclei
Table VI lists the values of Aii and Mii resulting from such an
approximation for the Pt 6s, 6p and 5d atomic orbitals.
in Table VI, is significant in two respects:
ii, defined
(1) it is larger for the
more covalent Pt-Cl bonds (i.e., Pt charge closer to zero); (2) it is
larger for the more diffuse 6p orbitals.
These results suggest that
Aii is in some way related to the penetration of the Pt wavefunction
to the C
inner core, an effect which is neglected in the point charge
approximation of Mii.
The potential field around the C1 atom changes
from negative to positive at some point approaching the C
nucleus;
therefore, the larger the amplitude of the Pt wavefunction, the greater
will be the stabilization of the M.. from the positive portion of the
C1 potential field.
Thus, the Pt 6p atomic orbital should be stabilized
more by this effect than the 6s and 5d orbitals.
Rather than neglect this penetration correction, the
assumed to be functionally related to it.
ii was
The molecular terms Hii
corresponding to the Ptl+ states were therefore restricted to values
one ev. higher than the corresponding Pto states.
values were obtained by interpolation.
on the Hii's.
All intermediate
This is a stringent constraint
However, in a later section of this paper it will be
shown that the one-electron molecular orbitals can only be justified
experimentally if one does in fact impose such a constraint.
This is
only an empirical test but non-the-less a fact which we feel is
significant.
Evaluation of the Off-Diagonal Matrix Elements, Hi.
The Hij's are the usual Hamiltonian matrix elements between the
ith and jth atomic orbitals.
They have been evaluated semiempirically
by the Mulliken-Wolfsberg-Helmholtz (MWH)21 approximation, Eq. 6.
Hij f KSij(Hii + Hjj)/2
K is the Wolfsberg-Helmholtz
(6)
factor and Sij is the overlap integral
between the ith and jth atomic orbital.
This approximation was used for all calculations.
In addition,
23
however, the MWH approximation was compared to the Ballhausen-Gray
-31-
(BG) approximation (Eq. 7) for various values of K and K'.
a/2
(7)
K Sij(HiiHjj)
Hi
The results of this variation are listed in Table VII for several
molecular properties.
Calculations.
Using the wavefunctions and Hii listed earlier the secular
determinant (Eq. 1) was solved* for a full basis set of orbitals.
The eigenvalues and eigenvectors were obtained and a Mulliken population
analysis of the eigenvectors yielded the reduced overlap populations
(bond orders) and charge distributions.
The calculations were cycled
n times such that the differences between the Pt charge at the n-lth
cycle was less than 0.001 charge unit from the nth cycle.
All calcu-
lations were performed at the M.I.T. Computation Center on the I.B.M.
7094 .
RESULTS
K can be considered as a parameter that artificially controls
the extent of charge flow from the ligand to the metal in the bonding
Its value directly effects the calculated covalent character
region.
A modified Fortran program*written by R. Hoffman was used.
Orbital il'swere calculated by a Mad program 'WAVWF" written by
C. B. Harris.
_
_
_ _ __
__
r
-32-
of the metal ligand bond.
Thus, the calculated molecular charge
densities, bond orders, and electron transition energies are very
sensitive to one's choice of K.
Table VII lists the metal charge, metal-ligand bond order, and
the lb2g
lblg transition for various values of K in the MWH approxi-
mation and K' in the BG approximation.
It is unlikely that Pt has
a charge less than +0.1; therefore, an upperlimit to K = 2.0 and
K' = 2.2 can be assigned.
ascertain.
The lower limits are more difficult to
If Pauling's electroneutrality principle2 4 is qualitatively
correct, the Pt charge should be lowered to at least +1.0.
This would
then place a lower limit on K and K' at 1.5 and 1.6 respectively.
Figure 2 is a partial plot of the energy level diagram as a
function of K.
Several features are apparent from this diagram.
First, there
is a strong K-dependence of the energy of the first non-occupied
antibonding orbital (big*). The observed lb2g*-
big* transition
energy, however, falls nicely within the above limits of K at a value
of about 1.7 to 1.8.
Secondly, there is no 5d orbital inversion over large ranges of Ko
Specifically, the alg* (5dz2) orbital is lower in energy than the
The dependence on K' is the same as on K except that energies are
slightly shifted down (o.5 ev.) for K' = K.
__________
eg* (5d)
orbital at all values of K from 1.4 to 28.
The Ballhausen
and Gray calculation gave the orbital energies eg· > alg*.
Finally, we find the first orbital above the big* (5 da) is an
a2u* (6pn) orbital.
alg* (6s) orbital.
Ballhausen and Gray, however, proposed the
Intuitively, one would expect the metal 6p
orbital to be very nearly non-bonding; consequently, the energy of
the au*
would be very near that of the atomic 6p orbitals.
in fact clearly the case.
This is
The atomic 6s orbital mixes significantly
with the ligand a orbitals resulting in a much higher energy for the
molecular alg* orbital.
Since the metal 5d orbitals transform under different irreducible
representations in D4h symmetry, one could choose a different value
of K for each orbital (5 da, 5di, 5d).
be governed
by the
This choice should, however,
character of the overlap integrals (Pt-C1)2 5
such that the rr interactions have larger K's than the a interactions,
This would result in a lowering of the ag*
e.
energy relative to the
However, no inversion of the eg* and b2g* levels would occuro
Figure 3 is a partial one-electron molecular orbital diagram in which
K(a) = 1.75 and K(n) = 2.00.
Variation of the Metal Shielding parameters, ai.
The Pt 5d, 6s and 6p shielding parameters were varied over the
ranges listed in Table VIII.
I
of PtC14 2
A plot of the total electronic energy
revealed an energy minimum extremely near the values of
the shielding parameter determined by our method,
Furthermore, this
energy minimum corresponded to a reduced overlap population (bond
order) maximum between Pt and C1 (Fig. 4).
The dependence of the 5d orbital splittings are extremely
sensitive to the radial part of the Pt wavefunctions as shown in
Fig. 5.
Note also that there is no inversion of any of the occupied
5d-type molecular orbitals and that the first non-occupied antibonding
molecular orbital (big*) is especially sensitive to the choice of the
values of the
i's.
Variation of the Pt Diagonal Matrix Elements
Hii's.
The hardest parameters to estimate are the diagonal matrix elements,
Hii
In most first row transition metals the free ion contribution,
19
Aii (Eq. 4) to Hii can be easily calculated from "Moore's Tables"
for integral charge distributions,
Analytic calculation of the multi-
center integrals, Mii,(Eq. 4) is a formidable problem requiring an
unjustifiable amount of computer time,
In lieu of any approximations,
of the Pt were systematically varied in an attempt to arrive
the H.'s
at a simple empirical method of estimating these terms,
Figure 6 is a partial plot of the one-electron molecular orbitals
versus assumed HI 's for Pt.o
If one were to assume that the Ptl+
Hii's were 10 ev. higher than the corresponding matrix elements for
Pto, then region I would be where the calculation is self-consistent
in charge.
The molecular orbital diagram is erroneous at this point for
the following reasons:
-35-
(1)
The lb2g* - lblg* transition energy is much too large.
(2)
The alu* molecular orbital has a lower energy than the
b2g* orbital.
(3)
The ligand big molecular orbital is muchtoo high in energy.
(4)
The energy difference between the t'
and eg* molecular
orbitals is too large.
The above conclusions are substantiated by spectral studies.
A more reasonable interpretation of the spectra can be made in
region II (Fig. 6).
This is, in fact, the region where we feel the
Hii's would be most nearly correct based on our earlier arguments.
In region II the Ptl + H..'s are only
to 2 ev. above the Pt° H.ii's
This is consistent with the behavior of carbon and boron as pointed
out by Lipscomb2 6 and with that of copper as shown by Ros. 7
Furthermore, the energy minimum in Fig. 4 in effect says that the
final Hi..'s, obtained after charge refinement, are the "best" values
l1
for the wavefunctions used.
Spectra.
We wish to emphasize that it is not the purpose of this section
to make accurate computations of the positions of absorption bands in
PtCl4 -,as we feel that the present status of semiempirical molecular
orbital theory does not lend itself well to this end.
One can, however,
obtain qualitative information from MO theory that may be of some
assistance in spectral assignments.
The calculated transition energies
-36are listed in Table IX.
These are calculated from Fig. 3.
The
eigenvalues and eigenvectors for K = 1.80 are listed in Tables X
and XIV respectively.
The relative energies of the e * vs, alg
and alg
vs. a2
are opposite to those proposed by Ballhausen and Gray.l
This is
presumably a result of their method of obtaining hybrid orbitals2 7
via the minimization of the VSIP/Sij(G) of atomic orbital.
The
variational principle is not rigidly satisfied in their method for
orbitals that mix in the same irreducible representation,
As a result,
the energy of the alg* MO is higher in their MO diagram than in ours.
All wavefunctions in our calculation at least rigidly satisfy the
variational principle for all atomic orbitals in the basis set,
Nature of the Pt-C1 Bond.
The Pt-Cl bond is, classically, a two-centered electron pair
bond.
It is, however, more appropriate to discuss the ionicity or
covalency of the Pt-Cl bond in the framework of MO theory,
The amount
of covalency or bond order, as defined by Mulliken,9 can be calculated
from the overlap integrals and the
orbitals.
eigenvectors of the molecular
Table XI lists the various contributions to the Pt-Cl bond
covalency.
Several things are apparent from Table XI:
(1)
The main contributions to the Pt-Cl bond order are from the
interaction of the Pt 6s, 6p: and 5d
orbitals respectively.
L
to C
3po atomic
'F
-37-
(2)
The interactions of 6p
6p -5d
to C1 3sa are approximately
equal but only contribute 1/3 that of (1) to the covalency.
(3)
The interactions of Pt 5d
and Pt 6p
to C1 3pT atomic
orbitals are slightly antibonding and constitute at best a
weak TTfield.
By summing all the above contributions to the covalency, one
obtains a total Pt-Cl bond order.
a in character.
This is 0.403 and is almost entirely
It should be emphasized, however, that the number
0.403 represents the covalency of the Pt-Cl bond.
One minus this co-
valency is, then, the ionicity.
The covalency of the Pt-Cl bond in PtC14 2 - has been measured by
nuclear quadrupole resonance (NQR).2 8
Marrom, McNiff, and Ragle2 9
found a covalency of 0.39 and a Pt charge of +0.44.
We calculated* at a
Pt charge of +0.439.
The close agreement between MO results and NQR results suggests
that a MO treatment of NQR would be far more useful since it would
tie in with the general picture of the electronic structure of complexes.
Such a theory has been derived and will be presented in a later section
of this thesis.3 0
Both the Pt charge and Pt-Cl covalency were calculated from the
parameter listed in Tables II and V with a K = 1.8.
?L__________
-38-
Table XII gives the occupation of the atomic orbital after final
refinement.
From the occupation of the p orbitals of the C
we can
predict a NQR asymmetry parameter of about 0.025 for K2 PtC14.
(To
be discussed later in detail.)
The complete bond order matrix is given in Table XV calculated
from the Mulliken population analysis given in Table XVI.
charge matrix is given in Table XVII.
The MO
T-
-59-
TABLE
I
Ratio of STO:SCF Overlap Integrals
C1 3s
,,,,
*CiSn
C1 3s
0.99
3P
Pt 5d
6s
.98
o.96
tcis A
0.97
".cis
Cl 3p
1,00
o.98
TABLE II
Orbital Shielding
I.
arameters,
i
Cl 3s
Cl 3p
Pt
d
Pt 6s
Pt 6p*
2.245
1.850
2,150
2.600
2.450
II
Illl
*
Pt
6
p - approximated as described in the text.
-4o-
TABLE III
PtC14 2
'
Overlap Integral Matrix:
Atomic
Orbitals Correspond to the Order Listed
in Table XIII
r
0
o
-4
0
oo
o
0o
'0
0
o
o0
oC
0
0-40 0C)
00
0
00000;C;
444O
-
0I
o
I
I
I
0
I
t
I
O
.1N
t-
0
''O0
0
*
I
0
cr
0
0
O
0
000000000
Q
I
'0
I
0O
N
I I
i
99999~u~
0' cN
04Q00
'la
NV m - N
4
0
00
I
t
0
O
l
o
0
o
0
o
O
0
0
r-
Q
0
0
N
C)
00
0-r-
I
9
Nu
OD
0
0
C
I
N
o
00
9
00 000
I I
999
0
00
0
I
00
-
I
0
Q
Nm
--o 0r
000
00
t
09.
It
NlN
NN
f*
I
fl
*
M1
C0
o
(n
I0
0
0_
00
19.
I
0#
I
Q
0
I
I
0C
C
O
o
o
t I
!
N N
00o'otis
0
0
-r
0 o0
0 o 000 00
oo
000
0000
0
00000000
oo8 .11
C;(; 80,18 C;8 (
1
0t
L1
4
f-
or-
A
9
I
N
I
0o
I
4
0000000
44*
o
o
0
I
0000
99
'0
'0
4
I
00
00
4'
C; 4
O
O
x
_
O
O
0
O
co
a'
0
O
0
0.
0
O
O
0
.-
0
9'-
0
.
0I
O!4
I
001
O
I
p-
mrF.
rni
-4
I
10
P-
Ch
'0
0
4
I
000-0
4
.
0
-
0
r-
'0
'3
r-
-
**
9
9o
!
1
0
'0
en
N
9
O -_
9
*
I
N
oF
co
0N
Ln
000
8(~8~ pl.
m 0 800
JJJJJJJJ~~~~~~~~~~~~
'0
'0 0
'0
N
m
00000000
I9
9
ol
I I
r
0
0
o
0
'0
N
_
88 0
0 P-
0
'0
'0
000
9;;1
-
-
- -
-
-
-
-4
N
N
NO
N
0
lo
N
N N
0
0
N
p-
00
0o
c0
'0
N
I
9
0
co
-4
.-
000
I
I
-O.
.
0
00O
4 444
00
0
000000
99
_-O
N
t-C
00- 00 0
00
0
O0
0-'0 000
I
O
O
0
ON
oc0
Oo
0-
0
O
c000
c0 '..
0-, -oo0
8 ( 000
I
r-
00
0
I
m
99I
LA
,0
99
N
o
0
co
0.0
I
ar
O0-4 N f4 L 4 - CO O- N n -4
o
0
o0
-4
I
0
0Q
000 NF
00
9 99
I
000
I
I
LrA
r
Nf4,04
99 I9
0
4 .-
999;
o0
'0
N -
o0
4e o
1
f
c(J mN
00
...
0000
N
4...d
N_
I
f
-
0
00
t- ol
000 0000Q 00
9
000
,ogo
8
- N I t
9
I
9t
0
0000000000000000
-
m
__ _
N
J'JJJJJJJJJ**JJJJJJJJ
O-O
M N
o
I
N
rj
r-
-
0
f'.LA
Nj
0000
I1
N
-'F'.3
0
00
-4
0000t
0
M N
Fc
co
00
*I.
o N
rP
9.-
LA o0
0
000
)
r
IUn 0
N1l
0
0
o0o
0
0
0000000000
00000
000000 Ioo0
!1 II9I
I
000
0000000000000000
888889
98888*
99*
8
OOCOOOOOOOOOOOO
000'00
0
00
l
0 000
N
F.Ln
co c
U.P-
-4N
_
0
0
0
'0LkmA
rn o
N -
0
0
N N o00
r
O0
0
co
r
I
O0
0
I
N9l9
09'-
0
O
0
0
9
4
O - -0
I
8
00
9 I
00
00
I
o--
ct *
,
4
0
0oo
Pr
'0
I
o0
NO
~o
N
1 l
N4
0'
00
PIt I-
(7V
11 1
8
0
It
00
.. a
I
**
O
fq)
'4'
011 C; 8 88 8
0
0
0u
0
9-
I9
9r-
Q
0 19 o
000
000000000000000000
NI
o0
L0
0- o.
9
('4
00
a
r
99>
'0 _
NI
r- 0
-'0
I
00000000 0000
!oo
I
n000000000000000000000- 00
0
00000000000j
I
0
rCo0
000 000
0
'0
0
?L
0
-4
0
o0Ny
r-go
N
O0
0 00 0 00 0 0
t
e
_'
I
r
O
0
-
r-
O
.4
44
O
I
.0
9
0o
0
o
000
4.4
4.4d
0
0
0
0'
N
0
co
I
0
00
0.0
00O N0
0
0
0o
OQ 0 00
000
0000000 0 O 000 JJJJO
44
_1
I
-
99l
I
O- te N '
--..
O~ O
-4
LAU
~N
0
.4
-4
N
00 0
-4-4
N
N
NPM4 LA
NN N
N
T
-42-
TABLE IV
Cu-Cl Overlap Integral Ratios Over
Charge and Configuration
Configuration
CUOC1lO 50-/Cul+_ClO
75-
CUO.Cl. 50-/CuO °44-CC1061
I*
' i-/;
3d 9 4s 2
3d9 4p2
4s-3s
1.16
1.09
4s-3p,
o.96
o.98
4p-3s
1.07
1.04
4p-3p
0.83
0.91
9%
4pfl3Pr
0.93
0.96
4%
_
_
.
*
IA
= I(R 2 - 1) X 1OQI
All values calculated from Ref. 17.
i
9%
r-
TABLE V
Pt States and Processes Averaged* to Obtain Aii
for PtO
-
Ptl+ + e
PtO
i
6s
6
p
-.
5d9
+
6s
5d86s2
-
5d6s
+
6s
5d8 6 s6 p
-
5d8 6p
+
6s
ev
5d8 6s6p
-
5d86s
+
6p
-5.35
5d9 6 p
-.
5d9
+
6p
ev
5d10
-.
5d9
+
5a
5d96s
-
5d86s
+ 5d
5d86s2
-.
5d76s2 +
5d9 6p
-
5d860o +
-9.80
-10.61
ev
5d
-
All states were averaged over multiplicities and were
obtained from Ref. 19.
L
<Aii>
5d9 6s1
-
*
Final State I + Orbital
Initial State
w
-44-
TABLE VI
Pt Hii's (in ev) as a Function of Charge
Pt Charge
q
0
0.5
1.0
1.5
2.0
C1 Charge
-0.500
-0.625
-0.750
-0.875
-1.0
Point Charge
Approximation
for Mii
12.3
15.4
18.5
21.7
24.7
-15.61
-20.61
-25.61
-30.61
-10.35
-15.35
-20.35
-25.35
-10.4
-8.5
-6.7
-13.4
-11.5
-9.7
i
5d
6p
-5.35
4ii*
d6
6p
*
-12.3
t q ) - Mii
= Aii (Pt) - Aii (P
Aii
-7.7
T'r"
-45-
TABLE VII
Molecular Properties
I
vs. K and K' (Eqs. 6 and 7)
lb2g*- blg*
Tran. Energy
K
Pt Charge
1.6
0.813
0.293
2.70
1.8
0.439
0.403
3.74
2.0
0.138
0.476
4.80
2.2
-0.116
0.529
5.90
Pt-C1 Bond Order
Pt-C1 BondOrder
(ev)
lb 2g* - big*
Tran. Energy
K'
Pt Charge
1.5
1.23
0.057
2.14
1.7
0.849
0.220
3.11
2.0
0.397
0.371
4.62
2.2
0.157
0.436
5.68
-46-
TABLE VIII
Pt Shielding Parameter for Points in Fig. 5
S1
S2
S3
2.60
2.20
1.95
1.70
2.95
2.45
2.05
1.80
1.55
3.65
3.15
2.75
2.50
2.25
L2
L1
6s
3.60
3.10
6
p
3.45
d
4.15
0
TABLE
X
Calculated Transition Energies from Fig. 3
Transition
lblg*
lbzg*
2.5
lb jg*
2.7
:alg* - big*
3.6
la2u*
5.0
e
g
*
lb 2 g*-
I
Energy (ev.)
1* la2U*
5.2
lalg*
6.1
la2*
-47-
TABLE X
PtC14 2 - One-Electron MO Eigenvalues
MO
Energy(ev.)
1
8.51
8.51
4.24
-4.70
-6.76
-10.49
-10.68
-10.68
-10.98
-13.49
-13.83
-13.83
-14.18
-14.58
-14.58
-14.71
-14.82
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-15.09
-15.09
-15.41
-16.10
-23.29
-23.50
-23.50
-24.o4
Sum = -625.73
i
Occupation
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
T-
-48-
TABLE XI
Pt-Cl Bond Order Contributions
Pt
3p(a)
3s
6s
0.023
0.112
6p(a)
o.o~o
0.132
3Pz
3py
-0.005
0.022
6pz
5d11,z2
0.011
0.094
0.002
o.oo8
-0o.o018
I-xz
-0.017
TABLE XII
Atomic Orbital Occupation
H
Pt
Pn
6 pz
6s
Pa
6 Px
_~~~~~~1
Numberof
electrons
6 py
,
0.581 0.061 0.215 0.215
Cl
Number of
electrons
L
5dz2
_
,
3s
3p(a)
3px
3Pz
1.94
1.68
2.00
1.98
_,
,
5dn
,
5dxy
_
1.893 3.97
5dx2_y2
,
1.99
,
0.50
i1 ,
-49-
TABLE XIII
PtC1 4
2
MO Input
Parameters:
N = principle
quantum number; L = angular momentun quantum
number: The orbital
· :L
correspondence is:
M
Sigma
0
O
0
1
1
0
1
x
y
0
1
0
0
Z2
XZ
2
0
2
x 2 -y
1
1
2
yz
1
xy
Orbitals
z
A
p
d
d
7-r-
-50-
TABLE XIII
0
Orbital
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Atom
1
1
1
1
1
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
Hij = 1. 8 0(Sij
Coordinates A.
N
L
M
Sigma
6
6
6
6
5
5
5
5
5
0
1
1
1
2
2
2
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
)(Hi + Hjj)/2.
X
0
0
0
0
0
0
0
0
0
2.33
2.33
2.33
2.33
-2.33
-2.33
-2.33
-2.33
0
0
0
0
0
0
0
0
Y
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2.33
2.33
2.33
2.33
-2.33
-2.33
-2.33
-2.33
Orbital
Z
Exp.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o
0
0
0
0
0
0
0
0
0
2.600
2.450
2.450
2.450
3.150
3.150
3.150
3.150
3.'50
2.245
1.850
1.850
1.850
2.245
1.850
1.850o
1.850
2.245
1.850
1.850
1.850
2.245
1.850
1.850
1.850
Hii
-9.79
-5.35
-5.35
-5.35
-10.61
-10.61
-10.61
-10.61
-10.61
-24.00
-15.10
-15.10
-1510
-24.00
-15.10
-15010
-15,10
-24.00
-15.10
-15.10
-15.10
-24.00
-15.10
-15.10
-15.10
-51-
TABLE XIV
PtC14 2
Eigenvectors for the Eigenvalues
Listed in Table X:
MO's
Across and AO's Down
-S
o
o
0-
0
9O
O
o 0II
_"4
O
O
C0
I t 0
0o
0oO oo
I
0
I9
t
I
O
O
0I
0
woo
0
9
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TABLE XV
Reduced Overlap Population Matrix Atom by Atom
1
2
3
4
5
1
17.5085
0.4032
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F
-54-
TABLE XVI
PtC142
Mulliken Overlap Populations:
AO's Across and Down
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TABLE XVII
PtC14 2' MO Charge Matrix:
and AO's Down
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Fig. 1 -
PtC142
molecular coordinate system used to
calculate the overlap integrals listed in
Table III.
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2.0
2.2
2.4
-62-
Fig. 3 -
Partial one-electron MO diagram of PtC14 2-:
K(a) = 1.75; K(rr)= 2.00.
I
-4
-5
A2u
0)
Cl7
.)
1
0--9-I0
U)
oo -13
-
0
D
~_
C)
I
C
"
_
r
U
Q
L
t
-1
O
t
-14
Molecular Orbitals
-64-
i
1
r
i
I
i
i
j
F~ig.4 - Total electronic energy of PtCl2
~
~~~epnns
r~
vs. Pt orbital
___
-610
a)
i
-612
o -614
L_
o -616
c -618
._
W
o -620
4a-
w -622
4--
0
I
6 24
-624
~- CZ9Q
I
I
I
I
I
I
I
L2
LI
0
SI
S2
S3
S4
Metal Wavefunction Exponents listed in Table 8
i,
T
-66-
Fig. 5 - One-electron M0's vs. Pt orbital
exponents.
en
a)
ca)
-6
o
L-
L.
0
3
a)
i
I
0
L
i
I
I
II I
i
I
c
-
l
i
i
I
-I
i'
t
I
-I
VIera
Wavefunction
_
4
.~
Exponents listed
in Table 8
-68-
Fig. 6 *
i
I
l
I
3
I
I
ne-electron MO'svs. the diagonal matrix elements,
TS~~~~~Hi
ai
T
-4
-5
-6
An
-7
C
-8
:):
a,
!
-
0
0
-9
-10
C)
0
Z>
-II
0
C
-12
0 -13
-14
-15
0
-3
-6
Hii +Q
-12
-15
-70-
Chapter II
REFERENCES
1.
H. B. Gray and C. J. Ballhausen,
J. Am. Chem.
Soc.,
85, 260
(1963).
2.
R. F. Fenske, D. S. Martin and K. Ruedenberg, Inorg. Chem., 1,
441 (1962).
3.
J. Chatt, G. A. Gamlen and L. E. Orgel, J. Chem. Soc., 486 (1958).
4.
D. S. Martin, M. A. Tucker and Allen J. Kassman, Inorg. Chem., 4,
1682 (1965).
5.
D. S. Martin and C. A. Lenhardt, Inorg. Chem., 3,
6.
S. Yamada, J. Am. Chem. Sc.,
7a.
73,
1368 (1964).
1182 (1951).
P. Day, H. F. Orchard, H. F. Thompson and R. J. R. Williams,
J. Chem. Phys., 42, 1973 (1965).
7b.
O. S. Mortensen, Acta Chemica. Scan., 19, 1500 (1965).
8.
R. G. Dickinson, J.Am. Chem. Soc., 44,
9.
R. S. Mulliken, J. Chem. Phys., 23, 1833 (1955).
2404 (1922).
10.
Ibid., 23, 1841 (1955).
11.
R. Daudel, R. Lefebure and C. Moser, Quantum Chemistry:
Methods
and Applications, Interscience, N.Y., 1959.
12.
1
J. H. Van Vleck, J. Chem. Phys.,
2,
.T b
A
P f%1
zo
-%tLf
Av
1 n+--
ore
xe-r
22 (1934).
14-
R. E. Watson and A. J. Freeman, Phys. Rev.,
14.
R. E. Watson and A. J. Freeman, Phys. Rev., 123,
15.
R. E. Watson and A. J. Freeman,
123,
521
(1961)
121
(1961).
Phys. Rev., 120, 1125 (1960).
-71-
16.
F. Herman and S. Skillman, Atomic Structure Calculations, PrenticeHall, Englewood Cliffs, N.J., 1963.
17.
P. Ros, Thesis (Chemistry), Eindhoven, Holland, 1964.
18.
J. Hinze and H. H. Jaffe, J. Am. Chem.Soc., 84,
19a.
540 (1962).
C. E. Moore, Atomic Energy Levels, U.S. National Bureau of
Standards Circular,467, 1949 and 1952.
l9b.
J. A. Pople, Trans.Faraday Soc., 49, 1375 (1953).
20.
M. Zerner and M. Gouterman, Theoret. Chim. Acta, 4,
44 (1966).
21. R. Mulliken, J. Chem. Phys., 46, 497 (1949).
22.
M. Wolfsberg and L. Helmholz, J. Chem. Phys., 20, 837
(1952).
23.
C. J. Ballhausen and H. B. Gray, Inorg. Chem., 1, 111
(1962).
24.
L. Pauling, Nature of the Chemical Bond, Cornell University Press,
N.Y., 1960.
25.
L. C. Cusachs, Sur L'Approximation de Wolfsberg-Helmholz, Battelle
Memorial Institute, Geneva (1964).
26a.
M.D. Newton, F. P. Boer, W. E. Palke, and W. N. Lipscomb, P.N.A.S.,
53,
26b.
1089 (1965).
W. N. Lipscomb, private communication.
27.
C. J. Ballhausen and H. B. Gray, Inorg. Chem., 1, 111 (1962).
28.
T. P. Das and E. L. Hann, Nuclear Quadrupole Resonance Spectroscopy,
Academic Press, N.Y., 1958.
29,
E. P. Marrom, E. J. McNiff and J. L. Ragle, J. Phys. Chem., 67,
1719 (1963).
'.-I-0 .
rhanter
V
- --. r , fchests.z
- . R.'
- 0 --L.1 L.--
f1
-·JVVI
-72-
C HAFER III
THE CRYSTAL AND MOLECULAR STRUCTURE OF
DIPOTASSIUM
OCTACH RODIRHENATE(III)
K [Re 2 C1 8 ] 2H2 0
DIHYDRATE,
-73-
INTRODUCTION
The preparation and characterization of compounds containing the
octachlorodirhenate(III) and octabromodirhenate(III) ions,
Re 2 Cl8 ]2
and [Re2 Br8 ]2 - has been reported.l'3 The full characterization of
these species requires both chemical and X-ray evidence.
The chemistry
and certain physical properties2 of various compounds have been described.
This section reports an X-ray diffraction study of the crystal
and molecular structure of one such compound, namely, K2 [Re2 Cls].2H
8
2 0,
of sufficient accuracy to show unambiguously the structure of the
[Re2 Cl 8 ]2
ion.
EXERIMENTAL
The crystals of K2[ReCl
8 ]'2H2 0
were obtained from a sample of
the compound prepared in a manner described elsewhere.3
The crystal class and unit cell dimensions were established from
zero layer Weissenberg photographs.
+hcaA-tmana<rb.
0
_7a.
w .A
>
°.
B = 108.9°; 7 = 104.80
>
*
The crystals are triclinic with
7 AR
2
0
A *
41
0
A
ey -
In
(o
The calculated density assuming one formula
weight per unit cell is 3.66 g. cm.
3;
the approximate density,
estimated by flotation in CH 2 I2 ,is 3.5 g. cm. '3 , thus establishing
that Z = 1.
Intensity data were collected by the equi-inclination Weissenberg
method with Cu K
radiation using a crystal with approximate dimensions
0.02 x 0.02 X 0.05 mm.
within half a sphere (h
I
The levels 0kl-4kl were recorded; 579 reflections
0) with sin 9/A
'
450 were recorded.
-74-
Intensities were estimated visually using an intensity wedge
prepared by timed exposures of one reflection from the same crystal.
On upper layers
the elongated spots
rected for elongation.
that
were
read
were cor-
Lorentz and polarization corrections were
made, but in view of the small size of the crystal, absorption
corrections were omitted (
= 480 cm.'l;
tmax = 2.5).
DETERMINATION OF STRUCTURE
Using the corrected intensities, a Patterson synthesis was
computed.4
The Re-Re vector was immediately obvious.
Placing one
Re atom at the origin, coordinates for the other were derived.
Fourier synthesis was then computed4 using phases
A
determined by Re
atoms alone and assuming the acentric space group P1.
The eight
chlorine atoms and two potassium atoms were found in this Fourier
map.
The positional parameters for these atoms as well as five scale
factors (one for each level) were subjected to one cycle of full matrix
least squares refinement.5
The atomic scattering factors used here
and subsequently were taken from the International Tables.8
of Table 3.3.1A were used for K+ , C1- and 0°
were taken from Table 3.3.1B.
dispersion.
Those
while those for Re °
No corrections were made for anomalous
The set of calculated structure factors now at hand were
used to compute a three-dimensional difference Fourier function from
which all Re, K
and C1 atoms were removed.
Only two significant peaks
appeared; these were assigned to the oxygen atoms.
-75-
The positional parameters of all 14 atoms as well as a scale
factor for each level were now subjected to two cycles of full matrix
least squares refinement.
In these cycles, temperature parameters
of 1.0 for Re, 2.0 for K, and C1 and 4.0 for 0 were assigned and kept
fixed.
The calculated structure factors obtained from the second of
these cycles were used to compute a three-dimensional Fourier map,
which showed no significant unexplained peaks and which also showed
an essentially centric distrIbutionof atoms about the mid-point of the
Re-Re line.
It was therefore concluded that the correct space group
is P1.
Using P
and assigning the above-mentioned initial temperature
factors and using the average values of the pairs of atomic coordinates
for the 21 coordinates now required, eight cycles of full-matrix least
squares refinement were now executed.
The scale factors were not varied,
Following this, one cycle was run in which the 21 positional parameters
and the five scale factors were varied, but not the temperature factors.
Finally, one cycle was run varying positional parameters and temperature parameters, but not the scale factors.
The residual 7 was now
0.168 and the changes in positional parameters were less than the
estimated standard deviations.
As a final check on the correctness
of the structure a three-dimensional difference Fourier map was computed.
It showed no peaks of significant magnitude.
atr+,lr
f'asct+.or~ t'
\
%
~V~UC~LJ~ruu~
The final set of calculated
A \ t.nether with the observed absolute values of
v I
C11·r -r
-76-
The atom coordinates
the structure factors are listed in Table I.
and isotropic temperature factors are listed in Table II.
The
standard deviations, a, were obtained from the least squares formula
a 2 (j)
where a
=
a
(wA
2
)/(m n)
is a diagonal element in the matrix inverse to the normal
equation matrix.
DISCUSSION
m
Il-r _1 12- Tj
The two ReC14 halves of the ion are related by a crystallographic
This fact requires that the rotomeric configuration
center of symmetry.
of the
Re2 Cl8 ]2
ion be the eclipsed one.
of the ion are listed in Table III.
The principal dimensions
From these, it can be seen that
the symmetry of the ion is D4h (4/mmm) within the significance of the
individual dimensions.
0
Thus all Re-Cl bonds have lengths in the range
2.29 i 0.03 A., all Cl-Re-Cl angles are in the range 87 * 2°9 and all
Re-Re-Cl angles are in the range 103.7i 2.10. Figure 1 is a sketch
of the
[Re 2 C18 ] 2
ion showing the
numbering system for the atoms and
giving the meanvalues for each type of principal dimension together
with the meandeviation of the individual dimensions of each type from
their meanvalue.
The eight chlorine atoms lie approximately at the
o
corners of a cube with edges ca. 3.2 A. in length.
-77-
The dimensions of the [ReaCl8]2
ion may be compared with those
of the Re3 C1 9 group which has been found in Re(III) compounds derived
directly from Re(III) chloride,8 -11 and in Re(III) chloride itself.l2
The average Re-Re distance in the triangular Re 3 cluster which occurs
0
in these compounds is 2.48 A.
Since
the order of the Re-Re bond is
found to be 2.0 by a molecular orbital treatment,l3,1
4
it is evident
that the Re-Re bond order in [Re2 Cl 8 ]2 - must be quite high indeed,
0
since the bond is some 0.24 A. shorter.
in fact, a quadruple bond.
?.29
i
It was shown l4 that it is,
The Re-Cl distance in [Re2 Cl8 ]2 - ,
0.02 A., is approximately the same as those for Re to non-
bridging C1 atoms in the Re 3 C19 derivatives.
we have 8 2.36
i
Thus, for [ResCl 2 1]3
0.03, and for Re 3 C1 9 [(C2 H 5 )2 C86HP139
the crystallo-
graphically independent distancesll of this kind are 2.32
0.02
0o
and 2.31 ·* 0.02 A.
Crystal Packing.
The crystal of K2 [Re2 Cl8 ]2H
ions and H.,Omolecules_
2
0 is an array of K+ and [Re2 Cl 8 ] 2'
The rran,-nmr. nf npas
n,hh
r
arn
the potassium ions (both of which are crystallographically equivalent)
is quite irregular.
i
i
The K
ion lies approximately above the center
of the square set of four C1 atoms, C11, C
[Re2Cls]
J
ion.
4,
C122, C133 of one
These four chlorine atoms lie at distances of 3.52,
3.21, 3.41, and 3.63 A. respectively from K +, each distance having a
standard deviation of 0.03 - 0.04 A.
In other directions about the K+
-78-
ion there are C1 atoms of other [Re2 C1]8
2
ions at distances of 3.31,
0
3.38, 3.40, 3.50, 4.52, 4.98 A.; at least the first four of these are
to be considered coordinated.
2.66
o
o.o8 A. from K+ .
Finally, the oxygen atom is
The 0 atom has six C1 atoms at distances of
0
3.3 - 3.7 A. from it, in directions such that O-Ho..Cl bonds might
exist; however, these distances are all somewhat greater than those
considered typical of HOH
*
The eight K+-C1 distances
C1- bonds.
O
O
in the range 3.21 - 3.63 A. and the K+-O distance of 2.66 A are all
reasonable.
0
The closest Re..C1
non-bonded contacts are 3.58, 4.66,
and 484
A,,
O
all with standard deviations of 0.03 A.
None of these closest non-bonded
C1 atoms lie at all close to the extended Re-Re line.
Thus, each Re
atoms
atom can be considered to be coordinated by only the four C
to which it is bound in its own [ReCl
2
8] '
ion.
Comparison with Previous Work.
As was shown in preceding work, 3 K2[Re2 Cl 8].2H20
is the correct
formula for a compound previously reportedle as KH[ReCl4]'H20
as a compound of Re(II).
on the corresnondin
..
_.._
....
__
__
_
that is,
An X-ray study has recently been carried out
nvridinium compound, written by the Russian workers 16
...
--
_,
X
as (C5 HN)H[ReC14], by Kuznetsov and Kos'min.
17
They found it to
contain a dimeric group, but the formula they assigned to it was
[Re2 Cl 8 ]4 .' Some of the dimensions they report disagree rather markedly
with those we found in K2 [ReCl18]'2H2 0; thus they give the Re-Re
-79-
distance as 2.22
i
0
0.03 A.
0
0.02 A. and the Re-C1 distance as 2.435
Their method of refinement was described simply as "trial and error,"
however, and on subjecting their intensity data to full-matrix least
squares refinement, we 1 8 have effected marked changes in atom co2ordinates such as to bring the dimensions of the [Re2 Cl8 ]
their compound into good agreement with those of Fig. 1.
ion in
Our re-
investigation of the structure of (C5 HeN)2 [Re2 Cl 8 ] as well as an
investigationis of the corresponding collidinium compound, (C8 H12 N)2 [Re2 Cl8], which has the advantage over the pyridinium salt that it
does not form twinned crystals, will be reported in detail elsewhere.
V1
TABLE I
1. FOR 9081.
88k
0
I102
163
1
001930
0099 17
306
3 02
122
96 13
0116
336
no'
19
19
06
0 -3
I 0 0 5
003
706
$3 11
69 -32
0 7 -32
69
00-837-36
7
-"
A
0
I3
0-
17
17
673
16:
1I
6
6
-1
81
0I 1
0
o
1 0
36766
n- I
o
o
236102
2 -34
0-23
7
3
66141
72
AZ
37
'3
1
7
63
3
~
°3 3130
32
1
6 07
0-331
34 107
'3 .3
7912
6
3 2
l 3-6
016
18
0
0-'6 79
37~~~
0
0-73
1
Ol *.9*6
9
19
3
466-339
1 -
1
1
1
n
9
21
92
9
-9
7
1
31
1
1
6
-6 -
13
1
3
37
-98
2
15
31-0
3
1
1
991111-6
677
8'
9,
-
776
66
163
10
1-66
37-63_
-7423
130
III
316
3-3-1~~~~~~~~~~~~_
3068
13
6
72
33
1-16
21
10
6'
86
76
19317±)83
3-37
3-60676
1-13
36
i-2-
7
7
1
!
67
0'
73 -76
71 -76
60
-56
1
1-613
62
6
1 -212
10
I
6
66, 0
3 2 1
69
39
3-2
80
2 2 107
93
91
1-2-7
30 -32
1 2 2
1-2
-3 1160
12-3 -2-199
1
1
,7
3-23
36-6
2 - 1 "6 339
5
''263
i
7S
5 T5
126
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2
12
338
I-2
6
3
69
37-3~~~~~~~~~~
1235
31-39
1 2
1 2
1--
3
-
66
63
31
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8 67
36
31,
83
6
31
S47-
2
2 0203
0206
20-3101n
i
1
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201
2 0
26
7-5
13
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33 -3R
122 - 6
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:
0
691
7
79
69-7 3
79
0 -631102
066
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3
2
62
83
33
128 136
91 -98
2-1-6
21-69
31
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±
0
IZ16 32
09
79
36.
17
62
8
39
381-6
133-61
9
6
63
21 -782
2 -2 - 71
2 -7
2
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27
17
19
66
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70 -70
4' -4
37
3-636
81
6
-7
19 -21
6 -206
19
6
3-63-4
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1
so
go0-113
39-119
73-:90
6 -3
3-3
7 3 0
313
1I
3 -3-1
1 3 1
60-93
83 -37
90 -96
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2
2
6-
1
37
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0
3
0
6
1
,
0
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301
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312
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6
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3
66
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3
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36
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95
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108
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62
578-7
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387
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-66
2 6
2
3
-2
2-671
26
3
77
89
83
2 -4 -.
2
267
;'
_38
2
62
7-60
2677
56
66-5
3
23
2-33
2-3S6
2
0
5
673 -9
0~
6l
73
77
1
2
- 1 -3
-325
1
0-
3-
73
2
16
7 -61
161I
3-62
I- I 3642
-'
753
1 2
63
2-
-96
2
0
3 80
117 2d9106 -il
2
0-6
|
723-73
223~~~~~~~~~~~~~~~~~~~)6
0102-19
0 76-39
'6
f) :54 - 0
0-3761-t
91
0- 010
60103
91
"63
-1
169..
0 2 138 123
062
66I30
8o
063
3
29
3(
1
2 :2 -7'
2
I
2
0
63 -87
1 9
2
47-51
12-2
38*3~~~~~49-15 22-3
176 3 22 161
1
' 8 4C _S
"
'I I
1
32
603
9,
993
i21616
127
212
'68 -71
1-27
53
9
3310
16
12
6
2-1-2
8
3-3-3
89 76
78
69
37
213
69
.
-.
21
I
21-3
12
3
1
3 -Il
61
32
I
96
III
13
-8
13
87-98
92-86
1-321
6S
3
2-:13
1-3
-
-91
120
87 -83
8-82
l
1 38-122
10I9
3 8-1 _j
2 -61
7-67
2-62
2-3 &
2113
2-6
2 :7 30
3123 _60
31
~~~~~~~~~~~~~~~666
7-9
9-66--62
- z zazz
e
3-6-2
96 102
I 1 -6
6
I -61
23
9
6
6 .36
1-6
37 -42
1 -63
-66
1-16
66
6.
I -7
0
1 -787
7
1 -71
38
39
33
3
1-7
2
173
1 -7
31-70
1.-0
5
13
91
1
39
6
3
-
30
32
33
771661
32
31
68-93
5
1
56 -61
2 -2
96
93
2 2 1
2
n
9
2-2 1 1-1
7
3
6
21
2263292
4
2 2
22399-36"
2 -2-1
2
93
3
70
36
6-6
63-6
-e
6
2-16
.39
9
1-1-3
18
133
'1
1
?
5
-6
72-1
2 1 -66
31-so
6 -7
76
3-6
1~~~~~~~~
8'
¶ I 6
60-68
36
47-67
3 -3 2
3
-3
1-3-3
1-16
11
1-7
13
1-~1
2 1
2 -5
2-36
1-33
-1 -3 13
1I6
1' 1
06
3I
6 13833
126 100
1-1-6
-16I
1
6
'
6
3
13
61
37
0 2 3
61
29
92
67
n90
6
n-26
2- *
26
1
5
0 2
5
SY1
n-23
39
262
61
3
0-26
5
3
02-6
326S
66 -30
0 2 7
96
2 .1
30-27
0 17
16
3?017917
13617
3
:P 15
U II 11±9 Yi
33
II
'3
1
.
11
53
0 -3 2
3
7
0
3
a -6
0
0~~~~~~~(-7
0
039
46
1
3
0-~121
,.~~~~~~~t
3 01
1
O 28-22
3
1
634
601
1
6
6
139 161
6-6
61
76
Is
6
-9
56
2 -96
1 -3
1 -3 -
51
R?
17
2
-72
31-23~~~'4
6l20
9
11
320
96121
39
66
-19
0 5 S O' *1
(
-1
10 2
1
3
~~~~~~
I ~~
2
1~0131-66
O3-7
637
7
3-6
2I1 2
1131
6
31
16
0-~~~~~~~~1 003 26
11
-1
620 1
33 3
27
3-139
I1
7
01-3 63
¶3~~~~~~~1
01-6'6
631-1-3
01
60-33
11
I131
01
136I
I
t
78
36
2
3
0 -46
0-6
4
5
1
7
62
62" 6
39
61
12
2 21
6
1
11
20
7
8.7
360
7
61
98
76-66
92
6-66
-7
6-71
-7
0
2
78
9
*7 -56
2J-20
22 -22
-81-
TABLE II
FINAL POSITIONALAND ISOTROPIC
TE
ATURE
a
ARAMETERS
Atom
x/a
y/b
z/c
B
Re
0.8193(8)
0o.9854(5)
0.9504(5)
0.91(7)
C1,
0.754(5)
0.046(3)
0.226(3)
1.3(4)
Cl2
0.826(6)
0.279(4)
0.957(3)
2.1(5)
Cl3
0.709(5)
0.909(3)
o.615(3)
1.5(5)
Cl4
0.639(5)
0.675(4)
0.892(3)
1.7(5)
K
0.878(5)
0.659(4)
0.326(3)
2.7(5)
0
0.78(2)
0.46(1)
0.56(1)
3(2)
_ ___ _ _ _ ___
(a)
Numbers in parentheses are standard deviations occurring
in the last significant figure for each parameter.
III
II
i
-
L
--(--.----C------. ;
-II--
-82TABLEIII
CRYSTALLOGRAPHICALLY INDEP:NDENT
AND ANGLES
DISTANCES
2
(Re2C12e]
IN
Distances, A
,
m
m
m
ar
Rel-Re,,
2.241(7)
Rel-C11
2.26(2)
Rel-C12
2.29(3)
Rel-Cl3
2.31(2)
Rel-C14
2.31*3)
3.31(5)
i
3.33(4)
Cl1-C1l1
Angles,
Degrees
Cl.-Rel-C12
85.4(8)
C12 -Rel-C1 3
88 (1)
C13-Rel-C14
86.0(9)
C1l4 -Re -C1 1
87.9(8)
Rell-Re x-Cl
105.8(6)
Rell-Rel-C1 2
103.4(7)
Rell-Rel-C13
101.7(6)
103.6(6)
RL.-Re -C14
IA.\ IhFa
r
4n rv
?m
n+h
A
t-.mnarl.
+.
tvAA]4at+n nm-
in
irrin'the
last significant figure of each dimension. They were calculated from
the standard deviations in Table II by the method of D.W.J. Cruickshank
and A. P. Robertson,Acta Cryst.,6, 698 (1949),
using a molecular
geometry program for the IBM709/7090/7094 computer, written by
Dr. J. S. Wood.
~~--p---~-·-
l -C-I-C.·----~~~~---C---r--··CI----*-·~~~.---·
--1
;:= - -.
i
-83-
Figure 1. A sketch of the [RezCle]2
ion in K[ReCle]2RH 2 0.
The
numberingof atoms with single subscripts corresponds with
that in Tables II and III.
An atom with a double sub-
script is related to the atomwith the correspondingsingle
subscript by the center of inversion. The distances and
angles are the averages of those in Table II, with the
intervals representing meanderivations of the individual
dimensions from these averages.
l
l
1~~~~~~~~~~~~~~~~~~~~~--
:. . ^ .: . ----
t
.
-4
p84-
-85-
Chapter III
REFERENCES
S. J. Lippard,
M.I.T.
(1965).
1.
Thesis,
2.
Thesis, W. R. Robinson, M.I.T. (1966).
3.
F. A. Cotton, N. F. Curtis, B. F. G. Johnson, and W. R. Robinson,
326 (1965).
Inorg. Chem.,
4.
Using ERFE-2, a two- and three-dimensional Fourier program for the
I.B.M. 709/7090, 1962, by W. G. Sly, D. P. Shoemaker, and
J. H. Van den Hende.
5.
Using a full matrix least squares refinement program for the
I.B.M. 709/7090, 1962, by C. T. Prewitt.
6.
International Tables for X-ray Crystallography, Vol.
II,
Kynock
Press, Birmingham, Englanda, 962.
7.
Residual
minimizes
8.
is EIFol
El
IFO -
-
Fc[Il/EIFoI;the refinement
IFc11
2
/EIFo
program,
however,
12 .
J. A. Bertrand, F. A. Cotton, and W. A. Dollase, J. Am. Chemo Soc.,
85, 1349 (1963); Inorg. Chem., 2, 1166 (1963).
9.
W. T. Robinson, J. E. Fergusson, and B. R. Penfold, Proc. Chem.
Soc., 116 (19653).
10.
J. E. Fergusson, B. R. Penfold, and W. T. Robinson, Nature, 201,
181 (1964).
11.
F. A. Cotton and J. T. Mague, Inorg. Chem., 3, 1094 (1964).
12.
Idem., ibid.,
3, 1402 (1964).
-86-
13.
F. A. Cotton and T. E. Haas, ibid., 3, 10 (1964).
14.
F. A. Cotton, ibid., 4, 334 (1965).
15.
See for example data summarized by G. C. Pimentel and
A. L. McClellan, The Hydrogen Bond., Freeman, San Francisco,
1960, Table 9-XXV, p. 290.
16.
A. S. Kotel'nikov and V. G. Tronev, Zhur. Neorg. Khim., 3, 1008
(1958).
I
I
:1I
and P. A. Koz'min, Zhur. Struk. Khim., 4, 55 (1963).
17.
B. G. Kznetozov
18.
F. A. Cotton and W. R. Robinson, to be published.
-7-T
-87-
CHAPER
IV
i
l
MOLECULAR ORBITAL
THEORY OF Re
2
C1 8 2
-
-88-
INTRODUCTION
The preparation1 and structure2 of the [Re2 Cl 8 ]2- anion has been
discussed.
Its chemistry3 ,4 appears to be consistent with the proposed
quadrupole metal-metal bond.
As such, it provides an excellent example
of a molecule in which to study the effects of the various factors
contributing to the metal-metal bonding.
This approach, however,
requires a detailed knowledge of the individual orbital contributions
to the metal-metal bond; therefore, an extensive molecular orbital
calculation for [Re2Cl 8 ]2 ' has been undertaken.
All Re-Re, Re-C1,
and Cl-Cl interactions have been considered in a semiempirical approach.
Choice of the Basis Set.
A basis set of fifty atomic orbitals, X i (i = 1,50), was used
to construct the molecular orbitals YJ
(j = 1,50), in the LCAO-MO
approximation s (Eq. 1).
=
C
(1)
This basis set included the Re 6s, 5d, and the C1 3s and 3p atomic
orbitals.
It was assumed that the non-valence atomic orbitals on both
Re atoms and the eight C1 atoms did not participate in bonding, but
formed a core potential that was unaltered by interactions of the
valence electrons.
The atomic orbitals, Xi's, were expressed as single
term Slater Orbitals8 (STO) as given in Eq. 2 where ai is the shielding
parameter, Ni is the normalization coefficient, ni is the principle
T
-89-
quantum number, and Y 1 (9,c) is the usual real spherical harmonic.
Xi = Nir ni
exp(-air)Y 1m (eCp)
(2)
All atomic orbitals were expressed in a right-handed coordinate system
as shown in Fig.
1.
Evaluation of the Overlap Integrals.
The shielding parameters, a. 's, for the Re orbitals were determined by adjusting yi to fit the overlap integrals between STO orbitals
IJ
centered on Re and Re' (Fig. 1) to a numerical overlap integral between
Self-Consistent Field (SCF)7 Re wavefunctions,
discussed more fully earlier.s
The
This method has been
i's for the Re 5d and 6s orbitals
were obtained in this fashion from the overlap integrals of the type
Re-Re' 5d-5d and 6s-6s respectively.
Since the SCF Re
6
p wavefunction
was not available, the Re 6p radial wavefunction distribution was
assumed to be equal to that of an Re 6s.
The C1 ai's were determined by numerically integrating the SCF
1
Re orbital with an SCF9 - 10
C1 orbital and fitting the resultant overlap
with an overlap integral between STO Re and C1 wavefunctions.
The Re
ai's had already been fixed by the Re-Re' overlaps; thus, only the
C1
i's needed to be varied.
Re
.ei's in
The C1 3s and 3p
i 's listed with the
Table 1 were obtained by averaging the
5d-3s, 6s-3s, 5d-3p and 6s-3p overlaps.
i 's from Re-Cl
In this fashion all Re-Re'
go-
and Re-Cl overlap integrals are essentially the same as overlap
Only the very small Cl-Cl over-
integrals between SCF wavefunctions.
laps are in error.
We assumed that the shielding parameters did not
change with charge configuration changes.
The error in such an
assumption has been discussed earlier. 8
Evaluation of the Diagonal Matrix Elements, Hii.
As noted earlier,8 Hii, the energy of an electron of the ith
atomic orbital moving in tne irela o
tne nuclei ana otner electrons
of the molecule can be expressed in terms of the one-center atomic
energy integrals, Aii, and the multicentered molecular energy integrals,
Mii.
This is expressed in Eq. 3.
Hii = Aii + Mii
(3)
The Aii's are estimated by the Valence State Ionization Potentials
(VSIPii) of the ith atomic orbital.
The Mii's can be approximated by
a point charge expression and an additional penetration correction.
The same dependence on charge was assumed here for Mii as was assumed
in the PtCl4 2 - molecular orbital calculation.8
Table 2 lists the
spectral states and processesll averaged to obtain the Aii's listed
for the Re 6s,
6
p and 5d orbitals.
The C1 3s and 3p Aii's used were
those calculated by Hinze and Jaffei2 for s2 p2 p 2 p and sp2 p2p2 states
respectively.
-g-91-
Contrary to expectation the Re 6s atomic orbital appears to be
more stable than the Re
d in Table 2.
Rather than average the 6s
states (Table 2)for lower energy configurations to invert the 6s and 5d
Hii's, we used the values as shown.
The rational for this being that
the radial portion of the 6s orbital is much more diffuse than the
5d, thus, it is stabilized more by the nuclear attraction to adjacent
Re positive core in this molecule.
Intuitively, one might expect
this type of behavior.
Evaluation of the Off-Diagonal Matrix Elements, h.
The Hij's
the Hamiltonian matrix elements between the ith and
jth atomic orbitals, were evaluated by the Mulliken-Wolfsberg approxi-
mation
th14
(Eq. 4).
Hij
KSIj)Hii
+
Hj)/2
(4)
K is the Wolfsberg-Helmholtz factor and Sij is the overlap integral
between the ith and jth atomic orbitals.
A K equal to 1.80 was used for all Hij s. This value is the same
as the optimum value determined from previous calculations8 and is
close to the
best fit" value for small molecules.15',16
Method of Calculation.
The extended Huckel molecular orbital theory was employed in
which all overlap integrals were evaluated.
No assumption was made
to the extent of hybridization of the ligand and/or metal wavefunctions.
I
I
-92-
These conditions and the LCAO-MO assumption lead directly to the
familiar constraint on the secular determinant:
det
Hij - ESijI
= O
(5)
The calculation was refined on charge to a self-consistency1 7 of
100th of a charge unit on Re.
RESULTS
Interpretation of Spectra.
A partial one electron molecular orbital diagram is given in
The calculated energies for the allowed electric-dipole
Fig. 2.
transitions are listed in Table 3A.
The calculated energies for the
forbidden transitions are listed in Table 3B.
modes
Vibrational
contribute intensity to these transitions via a vibronic
can
coupLing mecnanism.
Tne experlmensal
Drani;lon
energes-----
anu
corresponding approximate oscillator strengths are listed in Table 3C.
The eigenvalues and vectors for Fig. 2 are listed in Table IV and Table IX.
The two low energy electric-dipole forbidden transitions 20,600 cm. 'l
and 19,500 cm.
'l
are assigned to the
itions respectively.
b2g
laz
and lb2g 'ag
trans-
Further evidence for the correctness of such an
assignment is provided by the [Re2(RCOO)4 X 2 ] systems°
Presumably the
halide ions (X) are coordinated on the axial positions of the four
fold axis.
utilized.
I
In order to bond the halides the Re 6pa orbitals must be
Thus, the lb2g -la2U
and lb2g -* lalg transitions should
-93-
The
Such is the case experimentally.
be absent in these molecules.
differences in the experimental minus the calculated transition
energies are in part due to the fact that the Re 6p shielding parameter, a, was chosen equal to the Re 6s where as in reality it would
be somewhat smaller.
The assignment of the lb2 g
the previous assignment.2 0
-
la2u transition is consistent with
'l
(lb2 g
The transition at 20,600 cm.
la2g) was undetected in the earlier study but has since been confirmed.
The two transitions at 32,800 cm. - l and 39,200 cm. l have oscillator
strengths20 approaching unity.
dipole allowed transitions.
as a lb2g -
Iblu (6 - 6*).
As such, they should be electric-
The 32,800 cm. -l transition was assigned
Although the agreement between the
calculated and observed transition energy for this assignment is poor,
Both the lb2g - leu and
no other reasonable assignment is possible.
the leg -
blu assignments can be ruled out as possibilities.
Such
assignments would require an inversion of the b2g and eg (6 and r)
molecular orbitals.
In other words, the interaction of the Re 6
orbitals would be greater than that of the Re
orbitals.
Clearly
this is unreasonable.
Assigning this transition as a lalg -. lau
would mean that the
a to non-bonding a separation would be less than the 6 - 6* separation.
This is possible but highly unlikely in view of the very large overlap
difference between a and 6 orbitals.
-94-
The only other possible assignment for this transition would be
a leg
-a2u.
If this were, in fact, the case one would expect this
transition to be absent, which it is not, in the Re 2 (RCOO)4 X 2 molecules,
would be greatly shifted by the interaction
since thean's (Fig. 2)
with the X's in such molecules,
In any case polarized spectra will
certainly distinguish between the lb2g
-
1
blu and leg - la2
possible
while the latter
assignments insofar as the former is z polarized
is x, y polarized.
Nature of the Re-Re Bond.
The Re 5d molecular orbitals have an occupation of (alg)2 (eg)4 -
,n.
IkU2g)
\2
*.
ml,'len
1
LX4L Q
Clg
_, av-inA
fAiCVI
+en+.
Q
WA
A_ 4vn
4nnemnrn+
L%D
J..
.r4+h +ha
.
Y. .&IL
E
n
raI
4..A
diamagnetism of [Re2 Cl 8 ]2 .
Within the framework of the electron pair definition of a single
bond, the Re-Re bond is a quadrupole bond.
It is perhaps more
appropriate to describe the Re-Re bond in terms of the molecular
orbital description.
Bond order, as defined by Mulliken,2 1 is given in Eq. 6.
BO~
= E
ii
N(i)Ci C Si0
(6)
N(i) is the number of electrons in the ith molecular orbital, C i
and Co. are the eigenvectors of the ith and jth atomic orbital in
the ith molecular orbital, Sij
L~~~~~~~~~i
'A
is the overlap between the ith and
T
-95-
jth atomic orbital,and the sum over i and j is restricted to orbitals
on the
and B atoms.
Thus the Re-Re bond order can be expressed
as:
BOReRe= a +
(7)
+
a, r, and 6 are the designations for sigma, pi, and delta contributions.
Table 5 lists the various contributions to the Re-Re bond.
Tn
n annjlcnam
w
thp
h
hbond
Ra n
deri hpde in r
IPh1i
It is apparent that the major portion of the Re-Re'bond is the
n bond.
Furthermore, it is about four times as strong as the 6 bond
and twice that of the a bond.
The BORe,Re; BORe-
1
ratio of 4.7 is
the Re-Re electron pair bond order assuming a Re-Cl single bond,
It
is interesting to note that this ratio is consistent with the chemical
conversion of
Re2 Cl8 ]'2
to Re 2 (RCO0) 4 C1 2.
This ratio suggests a
simple ligand displacement reaction mechanism in which the Re-Re
bond remains intact throughout the reaction despite the severe
reaction conditions.
I
Because the Re-Re'
and a bonds are symmetric about the four
fold rotation axis in [Re2 C18 -]2
they should not preferentially stabilize*
Since the C-Cl' overlap integrals would change under a C4 rotation,
there could be a very slight stabilization in one or the other
symmetry. However, these effects would be energetically small
compared to the energy differences between the 6 bond in the two
symmetries.
__
_ -- ___.
-96-
the molecule in D4h as opposed to D 4 d symmetry.
Only the 6 bond has
the proper symmetry characteristics to stabilize the molecule in an
eclipised D4h symmetry.
However, the Cl-Cl' repulsions would be
higher for a D4 h (as opposed to D4d) configuration.
Therefore, the
ultimate stabilization of the molecule in D4 h requires that the 6
bonding stabilization energy be greater than the Cl-Cl' repulsion
energy.
In order to calculate the 6 bond stabilization energy, either
the energy of the 6 molecular orbital in a staggered D4d [Re2 C18 ]2
configuration must be known or the energy of the 6 molecular orbital
in a hypothetical [ReCl4 ]
-
molecule must be known.
The latter
approach was preferred because it not only gives the 6 bond stabilization energy but) in fact, gives the total Re-Re' bond energy.
The one electron molecular orbitals were calculated* for a
+
2 )
l'
molecule. The correlation
P
(1/2 of [Re2 Cl
hypothetical [ReC14
8]
and [ReaCl4 ]2
between the [ReC14]
Table VI for the 6,
for
ReCl4
TT
'
molecular orbitals is given in
and a orbitals.
Assuming a high spin d4 system
], Eq, 8 is the Re-Re' bond stabilization
individual orbital interactions (i = a,
energy
for
and 6).
Stabilization energyi = [2N(i)Ei(ReC14 )1' - EiN(i)(Re2Cl 8 )2-]
The same parameters were used in this calculation as were used in
the [Re2 C18]2 - calculation.
(8)
+
ReC14*- ha
_ _ __ _ __ _
C
syrret-rr.
-97-
N(i) is the number of electrons in the ith molecular orbital and the
Eils are the molecular orbital energies of the ith orbital for the
The sum of these stabilization energies is the
species indicated.
total Re-Re' bond energy,
These results are listed in Table VII.
If we assume that the four-fold rotation barrier
the C-Cl'
repulsions in [Re2 C18]2 - is of the same order of magnitude
as the three-fold rotation barrier in C 2 C1 6 (
t
arising from
7 kcal./mole), then
the 6 bond stabilization is seven times the energy of the four-fold
rotational barrier.
Thus, the
in excess of the Cl-C1
6
bond provides a potential well far
barrier to rotation and the molecule is
stabilized in an eclipsed D4h rather than a staggered D4 d configuration.
The difference between twice the total electronic energy of
[ReCl4 ]l- and that of [Re2Cl 8 ]2 - is only 255 kcal./mole yet the
Re-Re' bond energy is 366 kcal./mole.
The difference,
ll kcal./mole,
when:
can be attributed to the Cl-Cl' repulsion energy that occurs
2[ReC14
1
-
[Re 2 Cl8 ]2.
Nature of the Re-Cl Bond.
It is apparent from Table V
that the a contribution to the
Re-Cl bond order is about four times that of the
,. Since the
Rel (Fig. 1) is not in the plane of the 4C1 (C11, C12, C3s
C1 4 ),
the a and rr contributions to the Re-Cl bonds are not rigorously
separable by molecular symmetry,
bonds in Table V
Ii
i
i
I
L
Thus, the values of a and
TT Re-Cl
are accurate only insofar as they represent an
T
-98-
upper limit of
bonding and lower limit of a bonding within the
framework of rigorous a-Trseparability.
The total Re-Cl bond order,
0.47, is, of course, not subject to the separability of a and
systems.
All input parameters are summarized in Table VIII.
The eigen-
vectors for the energies listed in Table IV are tabulated in Table IX.
The Mulliken overlap populations are given in Table X; the orbital
charges and bond order or reduced overlap population matrix are given
in Tables XI and XII respectively.
The overlap integrals are listed
in Table XIII and the MO charge matrix is listed in Table XIV,
T
-99-
I
TABLE
Atomic Orbital Shielding Parameters,
i
I
Re
C1
6s
1.56
6p
1.56
5d
2.11
3s
3.37
3P
2.46
TABLE II
States Averaged* to Obtain Re Aii's
6s
5d5 6s2
5d66s
- 5d5 6s + 6s
5d5 6s6p
- 5d5 6p + 6s
5d4 6s2 6p
-
5d4 6s6p + 6s
5d5 6s6p
-
5d5 6s + 6p
- 5de + 6s
5d4 6s2 6p 5d
-5.45 ev.
5d4 6S2 + d
-
5d66s
- 5d5 6s + 5d
5d4 6s2 6p-
-9.88 ev.
d4 6s2 + 6p
5d5 6s 2
5d5 6s6p
*
Average Aii
Process
Re Orbital
4
- 5d 6s6p + 5d
5d36S26p + 5d
All configurations obtained from Ref. 11.
-6.98 ev.
T
-100-
TABIE III
2
Possible Allowed Transitions in Re2 C18
A.
Polarization
Transition
1b2g
1'blu
leg
laz
leg
-
18,600 cm.
z
blu
x,y
29,700 cm. 'I
x,y
35,860 cm.-
z
53,270 cm.'-
x,y
54,530 cm.'z
laig - lazu
'b2g -
Calculated Transition
Energies
eu
B.
Forbidden Transitions
Energy
Transition
(calculated)
lb2g- lalg
10,800 cm.-
lb2g
- lau
12,400
leg
- lag
lalg - lalg
C.
cm.- l
28,000 cm.'37,700 cm.'
Spectra of Re2 C18 2
'
Oscillator Strength
Energy
14,500 cm.- l
0.023
20,600 cm.
'l
32,800 cm.
'l
0.31
39,200 cm.-1
0.65
<< 0.01
T
-101-
TABLE IV
ReC1 8'2
MO
{
Energy(ev.)
1
77.39
2
3
23.47
23.47
4
2.17
5
6
7
-0.76
-0.76
-1.33
8
-1.33
9
10
11
12
13
-1.86
-1.86
-2.03
-6.31
-7.08
14
-7.28
15
16
17
18
19
20
-8.62
-10.76
-10.76
-11.95
-13.68
-13.69
21
-13.72
22
-13.73
23
-13.73
24
-13.74
25
-13.74
One-Electron MO Energies
Occupation
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
MO
Energy(ev.)
Occupation
26
27
28
29
30
31
-13.82
-13.82
-13.84
-14.16
-14.25
-14.25
2
2
32
-14.26
2
33
34
35
-14.32
-14.32
-14.46
2
2
36
-14.46
37
-14.46
2
2
38
-14.47
2
39
-14.53
2
40
-14.62
41
42
43
-14.70
-15.31
-23.27
44
45
-23.27
-23.27
46
-23.27
47
48
-23.31
-23,31
49
-23.62
50
-24.20
2
2
2
2
2
2
2
2
2
2
2
Sum = -1139.40 ev.
2
2
2
2
2
i
-102-
it
Ii
I
i
TABLE
i
V
II
II
I
Orbital Contributions to the Re-Re and
I
Re-Cl Bond
Re-Re Bond
Re, Re
a
a
o.684
rr
--__-
6
m
Re-Re
1.345
= 2.264
0.235
6
Re-Cl Bond
Re, C1
ax
a
y
BORe
Re-Cl
0.062
z
y = in plane nrbonding
0.029
- --
---
z = out of the plane
I
yTT
0.387
1T
r
y
Tr
z
x
T
bonding
=
0,478
T
-103-
TABLE VI
Molecular Orbital Energies (ev.)
Re 2 Cl8 2'
ReC14
TT
J
Total
Electronic
-7.52
-8.61
-8.24
-10.75
-10.07
-11.95
-13, 015(kcal/mole)
-26, 286(kcal/mole)
Energy
TABLE VII
Re-Re Bond Energies
Energy (kcal/mole)
..
16
-51
IT
-230
a
-85
in Re2 Cl 8 2
-104-
TABLE VIII
Re2 Cl e 2 - MO Input Parameters:
N = principle
quantum number; L = angular momentum quantum
number:
i
o
I
I
I
"-
The orbital correspondence is:
M
Sigma
O
0
z
1
0
x
O
02
1
0
2
0
1
1
x2-y 2
xz
2
1
xy
Orbital
p
z
XZ
d
T
-105-
TABLEVIII
Orbital
Orbital
Atom
N
1
2
3
4
1
1
1
1
5
1
5
6
7
1
1
521
52
i
i
1
i
r
i
i
i
d
M
Sigma
6
0
610
611
611
o0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1522
y
X
0
0
2 1
8
9
L
-9.88
-5.45
0
0
0
0
0
1.12
1.12
1.56
1.56
-5.45
1.56
-5.45
1.12
1.12
1,12
1.12
1.12
2.11
-6.98
2.11
-6.98
2.11
-6.98
2.11
-6.98
2.11
-6.98
-1.12
-1.12
1.56
-9.88
1.56
-5.45
-1.12
-1.12
-1.12
1.56
-5.45
1.56
-5.45
2.11
-6.98
-1.12
-1,12
2.11
2.11
-6.98
-6.98
-1.12
2.11
2.11
3.37
-6.98
-6.98
-23.45
2.46
2.46
2.46
3.37
2,46
2.46
-14.38
-14.38
-14.58
-23.48
-14.38
-14.38
2.46
-14.58
3.37
2.46
2.46
2.46
3.37
2.46
2.46
2.46
-23.45
-14.38
-14.38
-14,38
-23.45
-14.38
-14.38
-14,38
337
-23.45
2.46
2.46
-14.38
-14,38
3.37
-23.45
0
0
0
0
0
11
2
6 1
12
13
2
2
6 11
6 11
0
1
0
0
14
15
16
17
2
2
2
2
5 20
521
5 22
521
0
0
0
1
0
0
0
0
0
0
0
0
0
18
2
522
1
0
-1.12
19
20
333 00
00
1
0
3
21
3
3
0
0
1.66
22
23
3
4
3 1
3 00
1
0
0
0
24
4
3
1
25
4
3
11
0
0
26
27
4
5
3
30
1
0
1
0
0
0
28
5
3
1 0
0
0
29
5
3
1
0
0
30
5
3
1
0
31
32
33
6
6
6
3 00
3 1 0
3
1
0
0
0
0
0
0
1.66
-1.66
-1.66
-1.66
-1.66
1.66
1.66
1.66
1.66
-1.66
-1.66
34
6
3
1 1
1
0
35
36
37
38
39
7
7
7
7
8
3
3
3
3
3
0
1
1
1
0
0
0
0
1
0
2.22
2.22
2.22
2.22
2.22
1 1
1
1
0
1
0
0
1
1
0
*
ii
1.56
6 00
00
H
H
1.12
1.12
2
0
Exp.
0
10
0
z
1.66
1.66
0
2.22
-2.22
-2.22
-2.22
-2.22
-2.22
-2.22
-2.22
O
-22
-2.22
-22
-1.66
0
-1.66
1.66
1.66
1.66
1.66
0
-1.66
-2*2
2,46
-14.38
T
TABLE VIII
(continued)
Orbital
Orbital Atom N
L M
Sigma
X
2.22
2.22
2.22
41
42
8
8
8
3
3
3
1
1
1
0
1
1
0
0
1
43
9
3
0
0
0
-2.22
44
45
9
9
9
10
3
3
3
3
1
1
1
0
0
1
1
0
0
0
1
0
-2.22
-2.22
-2.22
-2.22
40
46
47
48
49
50
Hij
10
10
10
3
3
3
1
1
1
0
1
1
0
0
1
= 1.80 (Sij)(Hi + jj)/2
-2.22
-2.22
-2.22
Hii
Z
Exp.
o
o
o
-1.66
-1.66
-1.66
-14.38
-14.38
-14.38
0
0
0
0
1.66
1.66
1.66
1.66
2.46
2.46
2.46
3.37
2.46
2.46
2.46
o
-1.66
-14.38
-14.38
-14.38
-23.45
o
-1.66
0
o
-1.66
-1.66
Y
3.37
2.46
2.46
2.46
-23.45
-14.38
-14.38
-14.38
T
-107-
TABLE IX
Re 2 Cl
' 2
8
MO Eigenvectors:
and AO's Down
MO's Across
00
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0
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I
i
-109-
AO's Across and Down
i
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TABLE X
ReaCl82
II
i
i
Mulliken Overlap Populations:
r
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0
0
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iiiiiI
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j
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IT
-111-
TABLE XI
Re 2 Cl8 2
Orbital and Atomic Charges
Orbitals
Orbital Charges
Orbitals
Orbital Charges
1
2
0.745
41
42
43
44
45
1.802
1.945
1.857
1.904
1.802
46
1.945
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
0.276
0.327
0.327
0.716
0.993
o.458
0.993
1.132
0.745
0.276
0.327
0.327
0.716
0.993
o.458
0.993
1.132
1.857
1.904
1.945
1.802
1.857
1.904
1.945
1.802
1.857
1.904
30
1.945
1.802
31
1.857
32
1.904
33
1.945
34
1.802
35
36
1.857,
37
38
39
40
1.904
1.802
1.945
1.857
1.904
47
48
49
o50
Atom
1
2
3
4
5
6
7
8
9
10
1.857
-1.904
1.802
1.945
Net Charges
1.03
1.03
-0.51
-0.51
-0.51
-0.51
-0.51
-0.51
-0.51
-0.51
-112-
TABLE XII
Reduced Overlap Population Matrix Atom by Atom
1
7.81
2.26
2
2.26
7.81
3
o.48
4
oo
5
0.48
6
-o.ol
7
o.48
8
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9
0.48
lo-1l
0.48
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0.48
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0.48
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0.48
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o.48
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o.48
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o.48
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o.48
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14.56
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14.56 -0.00
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o.48
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14.56
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14.56
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14.56
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14.56
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.k
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4.56
-113-
TABLE XIII
Re2C18 2
Overlap Integral Matrix:
AO's Correspond to the Order
Listed in Table VIII
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.0000000.0
.00
9
.-.
c0 0
0o00
.0
iii
0
o
..00~
Oooo000000000000
o
0..0o00*0o000*00
i
i ii
0.
~~-
o.o.o.o.oo.o.ooo.o...oo.
Ii
Ii
. . . . . . . . .
oO
iii
11
0 100 00
0000
0
00
0
0 0
.
.
0
*I .. .
o
0000
0000000..00
liit
i i
iI
0
I
.i
..
*000..
.00*0*0
000
.
0
0000
1.0
0
*
o
o
ooo0
00000
0000
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00000
oo0
oo0000*
o
0
0
o0o
0000000000000
00000000000000
0000000000000
00000
0
.00
0
0000
00000
0000
0000
F
-115-
TABLE XIV
Re2 Cl 8 2
MOCharge Matrix:
and AO's Down
MO's Across
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i
'I
-117..
Fig. 1 - Molecular coordinate system used to calculate
the overlap integrals listed in Table XIII.
i
I
I
-1
I
-1
I
0
CM
I
CM
C)
C)
+1
+
N__
OD
CM
0
0o
311
C)
-
C)
-
__·_
____I_________
__
_
_··__
_______
___·(__·
___
_·____IX_____
___
T
-119-
I
I
Fig. 2 - Partial one-electron MOdiagram for Re2 C182 .
L
T
E (*)
-2
BIg
-3
-4
l-
w
-5
0)
t.,
-6
0
I0
- Blu(8')
-7
A 2u
,,,-%
0
AIg (n)
-8
0
c
n(o-')
.-- 0-
-9
B2g (8)
0
LLI
4-
-10
u
a)
0
-II
-0>o-o-o- Eg (7r)
-12
--o--- Aig (r)
-13
-o-- Blu (Ligond)
1
-121-
CHAPTER IV
REFERENCES
1.
F. A. Cotton, N. F. Curtis, B. F. G. Johnson and
W. R. Robinson, Inorg. Chem., 4,
326 (1965).
2.
Chapter III of this thesis.
3.
F. A. Cotton, N. F. Curtis and W. R. Robinson, Inorg. Chem.,
4, 1696 (1965).
4.
F. A. Cotton and W. R. Robinson, unpublished work.
5.
J. H. van Vleck, J. Chem. Phys., 2, 22 (1934).
6.
J. C. Slater, Phys. Rev., 36,
7.
F. Herman and S. Skillman,
57 (1930).
Atomic Structure Calculations,
Prentice-Hall, Englewood Cliffs, N.J., 1963.
8,
Chapter II of this thesis.
-
.
n..
f
.
watson anC A. J.
.
. ..
i--
reeman, enys.
ev., Le), 9~
J.
(gbl).
10.
R. E. Watson and A. J. Freeman, Phys. Rev., 120, 1125 (1960).
11.
C. E. Moore, Atomic Energy Levels, U. S. National Bureau of
Standards Circular, 467, 1949 and 1952.
12.
J. Hinze and H. H. Jaffe, J. Am. Chem. Soc., 84, 540 (1962).
13.
R. Mulliken, J. Chem. Phys., 46, 497 (1949).
14.
M. Wolfsberg and L. Helmholz, J. Chem. Phys., 20, 837
15.
M. D. Newton, F. P. Boer, W. E. Palke and W. N. Lipscomb,
Proc. Natl. Acad. Sci., 53, 1089 (1965).
16.
W. N. Lipscomb, private communication.
17.
Same method utilized in Chapter II.
(1952).
-122-
18.
W. R. Robinson, Ph.D. thesis, M.I.T. (1966).
19.
F. A. Cotton, C. B. Harris and W. R. Robinson, unpublished
work.
k.
I
20.
F. A. Cotton, Inorg. Chem.I, 4,
21.
R. W. Mulliken, J. Chem. Phys., 23, 1833
334 (1965).
(1955).
T
-123-
CHAER
CORREIATION
V
OF NUCLEAR QUADRUPOIE COUPLING
WITH MOLECULAR ELECTRONIC
USING MOLECUIAR
RBITAL
STRUCTURE
THEORY
CONSTANTS
~~~T~~~~~-124-
Derivation of eqQ.
Direct quadrupole spectroscopy is potentially a more useful
tool for the chemist than the relatively limited literature to date
might suggest.'
Although experimental problems have been trouble-
some in the past, recent work2 has considerably advanced the "state
of the art".
From the theoretical or interpretative side, chemists
have depended almost exclusively upon the basic considerations
and relationships concerning the connection between chemical bonding
and quadrupole resonance frequencies put forward by Townes and
Dailey.3
It is the purpose of this chapter to derive, in a very general
way, an expression for the nuclear quadrupole coupling constant,
eq. Q., for a given atom, a, possessing a nuclear quadrupole
moment,
a.
%,
in a molecular field gradient of magnitude q
at nucleus
The chief features of the derivation of eqO Qa, which leads to
a result which is more general than the Townes and Dailey relationship,3 are the following.
is assumed.
K
First, no hybridization of s and p orbitals
Secondly, a basis set of orthogonal molecular orbitals,
that span all atoms in the molecule is used.
The expression
derived does, however, reduce to the Townes and Dailey relationship
under appropriate limiting conditions.
The desirability of an expression giving eq
LCAO-MO expressions for
a in terms of the
occupation numbers of a set of molecular
1I25orbitals for the entire molecule is, in general terms, selfevident.
Such
an expression should be of particular utility in the case of many transition
metal complexes, for which LCAO-MO treatments of the electronic structure
are becoming increasingly of interest, since a means of evaluating such
treatments in terms of their ability to predict physical observables
other than electronic energy differences is
Let
'.n) be the atomic orbitals used to construct the
i(i =
molecular orbitals,
I
conspicuously needed.
K (K = 1-..n)
in the LCAO-MO approximation, Eq. (1),
in which
n
K
=
-
KI
.16
i
.
-
.
.
-
-
-
- -
-
.
- .
-
is tne coericient
(1)
C
i=l
I .
.
.
.
I
- I
.
.
I
or the itn atomic orobitalin te
-
-
I
I
-
-
nam molecular
orbital and the i's span all atomic orbitals of the atoms in the molecule.
It is convenient to require that all atomic orbitals on the same atom be
orthogonal.
the field gradient existing at the location of a nucleus
q,
a (or at any other point in the molecule), is now a property of only (1)
the distribution of electrons in the molecule and (2) the distribution of
the other nuclei in the molecule.
It can, therefore, be expressed as a
K
sum of components, q K, due to the electrons in each of the molecular
orbitals,
orbitals,
*K
nuclq n
of the
the charges
crges
of the
the nuclei,
plus aa resultant
resultant of
plus
of
c
sA K +
NKqK
=
viz,
., viz.,
2
(2)
Snucl.
nucl.
K
K
in which N
,K
is the number of electrons in *K.
the form' (3),
The term q
K
must have
T
-126-
K~
ee
|
where r
K* 3~cos2e-1)
=
(3)
l)KdT
cos
K*
"
represents a distance measured from nucleus a and the angle
is
measured relative to a fixed direction, usually along a bond or along the
bisector of a bond angle, but, in general along the Z axis of a molecular
coordinate system.
and (2) we obtain (4):
By combining ()
K
KKqij
S NiC
q Z
i
nucl.
J
where
$
i =e
(3 Cos2 -l)
(5)
d
r3x
The terms in the summation (4) are of four types, as shown explicitly
in (6).
The
,ii
j
The
integrals.
in which i refers to orbitals on atom a, are one-center
where
and qJJ
are two-center integrals,
The
denotes an orbital not on atom a,
jk
k in which J and k denote orbitals on
different atoms, neither of which is atom a, are tbree-center integrals.
IC K12g ii
NK
qe
K
'kj
t~~~~~~~~~~~~~~~.
s
J
K1ai
J
i
j~
'C
K kj
+ E C ~~
Cic
+
+
<
iJ,
nucl.
+ qOncl
(6)
W27-
Up to this point no approximations (other than the LCAO-MO approximation itself) have been made.
However, the evaluation of all ('N3,
for N atomic orbitals in the basis set) integrals in (4) and (6) would be
impractical for all but the simplest molecules.
Moreover, these expres-
sions would be applicable only to those few small molecules in which MO
calculations have been carried out using as a basis set the core orbitals4
as well as the valence shell orbitals of all atoms.
It is therefore
virtually a necessity to simplify (4) and (6), without, however, sacrificing
too much in generality or accuracy.
The following simplifications appear suitable:
(1)
The sum over all core orbitals on atom a will be designated P.
For unperturbed core orbitals there would be spherical symmetry and hence
no contribution to q,
but because the core suffers polarization, an effect
well known as the Sternheimer correction
s
P has a finite value, the dis-
position of which will be considered later.
(2)
The sum over all the two-center integrals
which J refers to a core orbital, plus qnucl.
q
in (6), for
will be approximated by
core
, a resultant of the contributions of the cores of all atoms in the
molecule except atom a, the charge on each core being taken as the charge
on that atom when its valence-shell electrons are removed.
compactness of cores, nucleus
Due to
the
can be taken to lie entirely outside the
electron density of all of them to a high degree of accuracy; thus we are
essentially invoking Gauss'theorem.
-1.28
(3)
1/2
E
The sum over all non-core two-center terms, q,
CKi
is assumed to be equal to the
Kq
i,J
plus
negative of qore
ji
defined above.
This is equivalent to assuming that the non-core electrons
of all atoms but atom a together with half the overlap populations of
all bonds formed by atom
exactly screen the nucleus of a from the
potential due to the cores of all other atoms in the molecule.
This
will not, of course, be precisely true, but the error arising from this
assumption can be shown to be of the order of only a few percent.
error was estimated by computing the field gradient at one C
This
atom due
to the net effective charges on all other atoms of PtC14 2 , the effective
charges being those provided by a population analysis and charge distribul
tion computation using the eigenvectors provided by an LCAO-MO calculation
-P-JAJJ.
4 Ls-4UH
In-sumac L'B3LL@i
4-64
P--- mlv -WEALD
L
I.AAMfiJ.L^A.
4nql
-I
---- bl4.LQ.
b-h~jiai.
S
e
tow--.--U
Web
nS~
AUU4L.
C
r-d
U
V
the total field gradient.
(4)
All three-center integrals are neglected entirely, since they
are inherently small and decrease as a function of r 3
'
With these four simplifications, we now write (4) and (6) in the
following way:
|q%=
S
K
|CjK12
C-
ii +
i
KKija
+ P
i(j
where the bar indicates that i and
are summed only over non-core orbitals.
We now introduce a Mulliken-type e relationship, namely,
qi
%X
=
(8)
..i
1I
1'~~~~~~~1
-129-
which permits (7) to be written as:
qa= S-
+ P
i
(9)
where
if
and
fi
E
is N
K 1 2 + CK
(i)~
E s C'~
iptJ
aooi
s aif
and fi is simply a molecular orbital expression for the occupation of
when (9) is multiplied by eQ. and terms rearranged slightly, (10) is
obtained.
(eqQ =
i
fi
e%
i
+ (eQaP/fi)}.
(10)
If we assume, following Townes and Dailey,3 that the polarization term,
P/Afi , though inherently large, varies negligibly from molecule to molecule,
and is incorporated in the experimental value for the free atom, then the
(3
brackets in (10) may be replaced by the known quantity for
free atom.
For C13 5 , for example, the value 109.7 mc/sec is used for
term in the
the
p electrons, NK being simultaneously replaced by
one hole in a p shell.
2 -NK
since the atom has
Thus, for C1 3 5 we finally arrive at (11).
eqQ = 109.7 S
(2-NK)tICiK12+
i K
(i
CiJij3
(11)
The expression (11) is the molecular orbital analog to the valence
bond
theory
Fm exeRinni
---------- T'-'
…
CU_
V
111
J
_____ - _
n
pni.z
nf UPI-uAdTo1qv.
IIJ?
W4__
--- ----
_-
nd
--
n nnwrw.+.a
ehi
V
I
IIV-P
-Y
-·
OUY
-150-
basic approximations, except, of course, for those which stem directly
from the valence bond formalism itself.
advantages to Eq. (11), however.
There are some important
First, no assumption is, or need be,
made as to s-p hybridization.
Second, no assumption is, or need be,
made concerning the extent of
-bonding.
,can be predicted along with eqQ.
Third, the asymmetry parameter,
Of course, more computation than
in the Townes and Dailey treatment is required in order to realize these
potential advantages.
In order to illustrate the applicability of the expressions derived
here in utilizing measured nuclear quadrupole coupling constants to
evaluate or monitor the results of LCAO-MO calculations for transition
metal complexes, some relevant figures are presented in Table 1.
I
--1
- .1s of - % r 4 I - '
LILVJX~LtSlU
V.lDU.l*~.L ¶.A
VI.
-- 1- S l -1 a-LCU . .LV113
L6DL6bC.LVUb
.'
Oreo
at
' 'Ina Truc
.r%1
W.LlL U
IUJ.Ly
The
13 -2 -7
1o-^s1O AetSS
ed
IUtb%.r.LUq:. U I gwp.
Someresults not directly connected with the problem of the
quadrupole coupling constants are presented to indicate the general nature
of the results.
It may be seen that in these cases, the observed and calculated values
of eqQ for C1 3
5
as a ligand agree fairly well.
The trend through the
series of hexachlorometallate(IV) complexes is particularly well represented.
r
0
0
I
-t'
I
I
0
I
I
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U.\
bO
I
0
H, 0
I
-~~~~+
'. 0*
Ct.
,
0'.
0
44
S Y
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H
i(n
I
H
0
tc\
C
H
0
U'-
to
0
co
.
c
c;
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-
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co
-~~~~~~~
H
OI
0
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UO
C,
H
IC
0(\
I
K.
* * .·
au
I
C
d
0
h
410
m
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d
D
H
tq
0
10
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0
o
c)
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C)
h~~
cO
tQ
ci
to
C)
I*
0
*
-W
0 CD
I0Hd
d
CH
)0 1
H
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la
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c)*'
4)
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10
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H:
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04
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H
oC t
H
V
C~~~~~H1
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CO .
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0'.Id0s E1Pl4
4)
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4)
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X lb
<
$4q
P )
a5).$
P40
w. @
H~IdI
b
0 ')Oj~ "44
01
44
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cz
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REFERENCES
1.
For general background see Das, T. P., and E. L. Hahn,
Nuclear Quadrupole Resonance Spectroscopy, Academic Press,
N.Y., 1958, and Semin, G. K., and E. I. Fedin, Zhurnal
Strukturnoi Khimii, 1, 252, 464 (1960).
2.
Peterson, G. E., and P. M. Bridenbaugh, Rev. Sci, Instr.,
35, 698 (1964).
3.
Townes, C. H., and B. P. Dailey, J. Chem. FPhys.,17, 782
(1949).
4.
The core is defined to include the nucleus plus all filled
orbitals of lower energy than those of the valence shell.
Thus, the core of Pt includes the orbitals
5s, 5p, and
5.
s, 2s, 2p, .....
d, 6s, and 6p being considered as valence orbitals.
Sternheimer, R. M., Phys. Rev., 84, 244 (1951); 86, 316 (1952);
95, 736 (1954).
6.
Mulliken, R. S., J. Chim. Phys., 46, 497, 675 (1949).
-,~~~~~~~~~~~~~~~~...
A
1
-133-
CHAPER VI
MOLECUIAR ORBITAL
CALCULATION ON
(M =Re(IV), Os(IV), Ir(IV)
I
I
C12-
and Pt(IV))
T
INTRODUCTION
In the preceding chapters (II and IV) a molecular orbital method
was developed and applied to the calculation of molecular properties.
An interpretation of nuclear quadrupole resonance, based on the
principles of molecular orbital theory, was derived in Chapter V
and applied to the series MC18 2
Pt(IV)).
(M = Re(IV),
s(IV), Ir(IV) and
This chapter will deal with the specifics of the MO
calculations of this series and with the application of these MO's
to the verification and prediction of molecular properties associated
with these molecules.
ORBITAL BASIS SET
The metal 6s, 6p and
d atomic orbitals and the C1
s and 3P
atomic orbitals, a total of 33 wavefunctions, were used to construct
molecular orbitals in the LCAO-MO approximation.'
All wavefunctions
were expressed as Slater Nadeless Orbitals (STO).
The functional
form of STO orbitals is given by Eq. (2) in Chapter II.
The shielding
parameters, ri (Eq. (2), Chapter II), for the basis set in this
calculation were determined in precisely the same fashion as in the
PtC14 2 - calculation (Chapter II).
Herman-Skillman radial wavefunctions3 were used for the metal
6s and
d atomic orbitals.
The radial portion of the 6p atomic
orbitals were approximated as a 6s atomic orbital.
wavefunctions were used for the C1
A
Watson-Freeman 4
s and 3p radial wavefunctions.
-135-
0
The metal-to-chloride inter-nuclear distance5 was 2.56A. in
all cases.*
Hii
DIAGONAL MATRIX EEMENTS,
The diagonal Hamiltonian matrix elements,** Hii, for the metal
orbitals were approximated by Valence State Ionization Potentials
(VSIP) listed in Table I.
Since the spectral assignment of the
states listed in Moore's Tables e are incomplete, we assumed that
there was a linear decrease in the VSIP's of 2.5 ev. going from
Re to Pt.$
CALCUIATIONS
I
All overlap integrals, Sij, were calculated and all off-diagonal
matrix elements, Hi,
were approximated by the
with a Helmholz factor, K, equal to 1.80.
WH
approximation
The secular equations
__________
Although there is a slight variation in this value depending
on the cation of the respective complex, we feel the variation
is too small to appreciably effect the final results.
**
See Chapter II for a complete discussion of these matrix
results.
This somewhat parallels the behavior of the first ionization
potentials of the neutral metals .
See Chapter II for details.
I
__________--
T
-136-
(Chapter II, Eq. (1)) were solved and the MO energies and eigenvectors were determined in each case (ReCle2 -, OsCl2-,
PtCle
2
).
The same dependenceof Hij with charge
IrCle2 -,
was assumed in
these calculations as in the PtC14 2 - and Re 2 Cl8 22- MO calculations
(Chapter II and IV).
For each molecule, the calculation was recycled to a selfconsistency of a 0.G1 charge unit on the metal.
All overlap integrals are tabulated in Tables II-V for the
Re, Os, Ir and Pt cases respectively; all eigenvectors
for the
final cycle are listed in Tables VI-IX; all molecular orbital
energies and orbital occupations are listed in Table X; all Mulliken
overlap populations7 ' 8 and reduced overlap populations or bond orders
are listed in Tables XI-XIV; all MO charge matrix elements are listed
in Tables XV-XVIII; and all orbital
occupations and atomic charges
are listed in Table XIX.
ELECTRONIC SPECTRA
The semiempirical MO theory utilized in these calculations is
not well suited for quantitatively describing electronic spectra
because it does not explicitly include electron repulsion integrals
in the
amiltonian.
However, it can provide useful information about
trends in a given series of related molecules.
Among other things, Table XX lists the energies of the last
occupied
4
MO's,
Et2g ; delta
(A),
the separation between the
t2g
and
I
-137-
e
MO's, and the charge transfer energies, t
-
t2g.
The experimental A for all members of the series is about
4.1 ev.9
l°
In view of the sensitivity'
of the calculated A to the
values of the variable parameters in the theory, it is gratifying
to calculate an average* A equal to 4.2 ev.
Although no apparent trend is evident in either the experimental
or calculated A, there is definitely a trend in the charge transfer
spectra, t
that the t2u
t2g,
-
across the series.
Jorgensen9 has pointed out
t2g transition decreases about 0.75 ev. for each
new electron in the partly filled t2g molecular orbital with metals
of a constant oxidation number.
For the series treated in this
chapter the experimental differences 9 in the tu
-
t2g
transition
for Re(IV) to Os(IV) and Os(IV) to Ir(IV) are about 0.9 ev. and
0.6 ev. respectively.
agreement being
The calculated differences are in close
0.87 ev. and 0.59 ev. respectively.
It is interesting to note that the general decrease in the
charge transfer energies parallels the general decrease in the
calculated t2g MO energies, Et2g .
In the framework of Extended
Huckel Theory, Et2g represents the calculated first ionization
potentials of the molecules.
There are no experimental ionization
8 _ ~------ -Obtained by averaging A's of the four members of the series in
Table XX.
i
__________--
-158-
potentials available for this series.
owever, it would not be
surprising if future experiments paralleled the calculated Et
t2g
12
that the effective charge of the
behavior since it is knownll'
metal decreases from ReCle2
to PtC1e2- resulting in a decrease
of the electron-nuclear attraction energies.
CHARGE DISTRIBUTIONS AND METAL-CHLORIDE BOND ORDERS
An important aspect of the results in Table XX is the uniform
decrease of the effective metal charge in these complexes going
from ReCe1 2
to PtCle2-.
what one would expect.
A general decrease in charge is exactly
Nuclear quadrupole resonance (nqr) datal l l2
provides direct evidence for the validity of this trend.
The similarity of the metal-chloride (M-C1) bond orders or
covalencies (Table XX) is intriguing when juxtaposed with the
The lack of an appreciable
effective metal charge decrease.
increase in the M-C1 bond order with a substantial metal charge
decrease results from the increased occupation of the antibonding
t2g MO going across the series.
sigma (a) and pi ()
When bond order is reduced to its
contributions, one notes (Table XX) a general
increase in a covalency across the series resulting from an electron
flow from the C1 Spa orbitals.
This results in decreasing the
effective metal charge across the series.
However, the antibonding
character of the t2g electron added to each member in the series,
causes a decrease in the M-Cl TT-bondorder.
The inherent symmetry
-139-
of the
orbitals do not provide as effective a mechanism for C1
to metal charge flow as the a orbitals.
Consequently, the effective
metal charge decreases across the series via electron flow from
the C1 pa orbital.
covalency.
This results in a net increase in a bond
Since, however, the
t2g
MO is a antibonding T-type
-bond order across the
orbital, there is an increased negative
series.
This, to a large extent, cancels out the increased a
bond order increase resulting in a more uniform total metal-chloride
bond order for the compounds listed.
Finally, it is interesting to note that the decrease in the
effective metal charge across the series is consistent with the
nephalauxetic effect i3, 4
SPIN DENSITIES
With the exception of PtCl6 2 - which has filled t2g MO's, all
other complexes in Table XX have one or more unpaired electrons,
As such, they are subject to esr studies,
2
available in the series is that for IrCl1
6
The only esr study
i
'"
The C1 3 5 hyperfine
has been interpreted as arising from a spin density of only 70%
on the Ir.
The g value indicates that about 85% of the spin density
is on the Ir.
One can calculate the spin density on the metals by squaring
the t2gMO'sand obtaining the Mulliken overlap population 7 ' s
(Tables
XI-XIV).
The ability to calculate reasonable spin densities
'I
_140-
(Table XX) from the t2g Mo coefficients indicates that this MO
method properly estimates the percent of C1 pTT bonding in the
IrCl6 2
case.
The general trend of increased ligand participation
in the t2g MO across the series (Table XX) could be verified in
the future with esr studies on the ReCl6 2
The verification of C
p
and OsCl6 2 - complexes.
bonding to the metals is provided by
nuclear quadrupole resonance studies.
NUCLEAR QUADRUPOLE RESONANCE (nqr)
COUPLING
CONSTANTS (eqQ)
In nuclear quadrupole resonance one measures transitions
between nuclear spin states which are split by the interaction of
the nucleus with the electric field produced by the electrons.
Consequently, the electron distribution in well-defined atomic and
molecular systems containing quadrupolar nuclei can.be measured.
Because the resonance frequency is dependent upon the local electronic
environment of the nucleus, nqr, like esr, sometimes affords the
only feasible physical method for the elucidation of electronic
structure.
The interpretation of nqr spectra of halide ions has always
been done in terms of a valence bond approach i7 (the well-known
Townes-Dailey treatment), but for complexes in particular
and other
compounds as well, a molecular orbital treatment would be far more
useful since it would tie in with the general picture of electronic
structures of complexes and with the results of other kinds of
sT-
-141-
measurements (e.g., esr, nmr), and would be more flexible.
a theory was developed in Chapter V.
Such
It will now be applied to
the molecules treated in this chapter.
Using Eq. (11) of Chapter V, the nqr relationships i8 between
C1 Pa and p~ electrons, the eigenfunctions or MO coefficients listed
in Tables VI-IX, and the overlap integrals listed in Tables II-V,
we calculated the nqr coupling constants, eqQ, tabulated in
Table XX.
The excellent agreement between calculated and observed eqQ's
substantiates our belief that the MO method employed gives reasonable
predictions and explanations of the bonding properties in these
complexes.
Furthermore, the increase in eqQ across the series
verifies the contention that the effective metal charge decreases
across the series via electron donation through the C
The occupation of the C
C1
orbitals.
orbitals is given in Table XXo
the decrease in the number of C1 3
The C1
3
a
Note
electrons across the series.
s occupation stays constant, presumably because (1) the
s orbital energy is very stable with respect to the 3P, and
(2) the C
function.
3p radial wavefunctions is more diffuse than the
s wave-
-142-
|2
TABLE
I
' MOInput Parameters:
M!s 2-
N = principle
quantum number;
momentumquantum number:
L = angular
The orbital
cor-
respondenceis:
M
Sigma
0
0z
1
1
0
1
0
1
2
1
2
0
0
0
1
1
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x
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yz
xy
d
4.
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TABLEIII
OsC
i
i
2-
Overlap Integral Matrix
OsC142- VXITAPMATRIX
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1.0000
0.
0.
0.
0.
02
0.
0.
0.
0. 1729
-0.
-0.
0.
16
17
0. 2692
0.
1.0C0
0.
0.0189
-0.
0.
0.
1. C000
0.0189
0.
0.
-0.0274
1.0000
0.
O'
C.
0.
0.
0.
0.
0.
0.
C.
0.
0.
1.0CCC
0.
0.
0.
0.
0
120000
0.
O
0,
0
0.
O.
0.
0.
O
0.3235
O2
-C.0414
-03235
0.
-0.
-0.
-C;3663-0;
-C.
0.1431
0.0375 O.
-0.0274 0.
0.
0.0101
32
0.2692 -0.
-0;3E63
0.
0.
-0.
0.
0.1431
0.
0.
0.
0.
0.1431
0.
0.
0.
18
-0.3663 C.0717 -0.
-0.3235 -0.0414 O
0.
0.
0.
0;
0.
0O
0.0829
0.
-0.3663 -0.0717
0.
0.1431 -.
00605
-0.
-0,
-0.
-0;0605
-0.
O
-0.
-0.1242 -0.
0.
0.
-0.
0.
0.
-C.
0.
0.
0.
0.
0,0078 -0.
0.
0.
0.
-0.
-0.
-0.
0.0375 -0.0274
-0.0189 -070189
1.CCO
0.
0.
0.
0.
020004
0.
0.
C.0004
-0.
0
C.
0.1431
C.
0.
0.0101
0.0375
0.
02
0.
0.
C.0101
O2
0.0101 -04
0.0189
-0.0375
-0.0274
-C.0189
0.0375
0.0101 -01
-0.0274
-02
0.
28
29
30
0;
0.
O
0.C004
0.
0.
0.
0.CCC4
O;
31
1.0C0
0.
0.
32
O2
1.0000
O;
33
0.
0.
1.COCO
-0.0274
02
02
O.
O
-0.0718
-0.
-0.
-0.0189
0.0189
0J0101 -C2
-C0274
0J0189
02
0O0375-CJC274 -J
-O
-CJ
02
02
23
24
-02
0.1431
O
OJ
021431
0.
O
0.
0.
0.
-0.0605
-0.
0.0101
0.
-0.
0.0101
0.
Oj
O
O
-0J
-020605
25
-02
26
C2J
27
-023663
0J3235
O
OJ
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0.
0
0.
0
0.
0
-0.
02
C
-0J
021431
-021242
OJ
-0j
02
-02
-02
OJ
O
C
-C2
-0j
02
-02
0J0181 -020274
-0J0315
02
-0J0274
-020274 -OJ
-02
02
020375 -0J
-C2
0J0004
O
02
02
1.0000
0.
02
0
2OOO0 02
J0189-0J0274
O
-CJ
OJO101 02
O
O
02
080101
-O2
0.0189 -0.0274-02
-0.
0.0375 -O
0JO0
-020040 -0J0189
CJ0315 02
02
OJOOT8-CJ0181 -02
020375
C
OJOOIO-CJC040
-OJ
-020274 -OJ
-J
OJOl
0J
0J
02
lC
02
30
021729
-043235
Oj
02
0J0829
-O
02
010078
-01089
-010189
020101-02
00.189 -020214 -020375 02
0.
0.
02
020605 -01
-OJ
O.
020315 020181 -020375 -020274 -'J
-020274 O
CJ
00189 00OO02-JCCO
-0.
OJ
020189 0J0078 -0J0189 -C0189 -OJ
O
0.
-0J0274 -0.0189
OJ
CJC605 -OJ
-0,0274 -0.0189 -0.0379
-0.0189 0.0078 -0.0189
-0J0375
OJ
OJ
-CJ
0.
0.
C.0101 -0.
-C2
J1431
O
0.
-0.
29
-02
-020717 0J0829 -C1434 -CJ
120000 0J0189 -0J0375
020189 IJ0000 C
-020375 02
ICCC
0.
28
022692 0J1729 -C22692 02
02
O
-020189 0.0375
02C0101-OJ
-020274 -020375 -020189 C20375 -C0274 -OJ
-0.0189
02
O2
0M010
OJO0 -010189
0J0189 -020274
020189 -0J0375 -C20274 C2
-0.0189
0.
020375 -020274
OJ
C2
-02
O2C002 -0.
-0O
020010 020078-020189 -02
0.
0.0004
02
OJ
0J0181 -020274
0j
1.0000 -0.0010
-O.0ClO 1.0000
40J
020189 020189 0J0078 -C20189 008JO9 0
02
0M0101
40J0189 -0;0375
ojo01
-0.0609
OJ
402
020375 -0J0189 -0
020189 0J
-020274 -0J0375 '0J0189 02
020189 -O
-0J0315-020274 0J0189 Oa
020078 0J0189 -0j0189 -02
020018 0{0189
-0J0189 -0J0274 C0315 -Cj
-0J0189 -020274
-0.C040 0.
0.
Oj
-0.0189 0.0078 0.0189 0.
020375 -0.0189 -0;0274 -02
C.0101
-0
-020189 -OJ
CJ0371 -CAC274 400189
020078 Oa
-C0189 -0J0189 0JOO8
-Oj
0J0101 C
-02
-Oj
020078 -OJO185-0J0189 -02
020189 -0J0214 -C20375 -0J
-0.
020718 -0,
-40J
-03
02
O
0MOO2 -CZ
O
0.2004
-'020020 oh
-OJ
-02
2I0000 0
O
1jOOO
-C2C04C-02
02
01
-02
0J0004 02
Os
-020189 020189 020078 0
02
Oj
0,0078 -0.
0.
Oj
0.0605 -0O
-0J1242 -
-i0J3235 OJ
OJ
-02
02
02
-02
020605
OJ
C.
1J0000 C2
02
Oj
I2CCOO 0J
O
Ca
120C00
OJ
OC02001-C2
020004 C2
-C2
020605 0J0189 -OJ
-020605
-Oj
0.
-O2
-023E63 -.
-0.
-0.
0.0078 -0.
0.
021431 402
-0.
02
-020414
O
02
-0J
-020605
020718 -02
-02
0J1432
02
-c2
OJ
C0717
0J0605 -C2
OJ
020010 O2
-020605 0
-02
O,
020018 OJ
O.
-02
-0.
j
C
0.3Z35 -02
02
-020414
O.:
0J1729 -0J
-0J2652 -
021431 -C2
07
0.
0.
C.0189 -0.0375 -0.
33
O
-C.0274 -0.0375
O.
C.
-0.
0.
-C.0274 0.0375 -0.0189
0.0101 -0.
0.0189 -0.0274
0.1242
0.0189 -0.0189
0.0189 0.
-0.0375
1.COCO C.
0.
0.
1.0000 0.
-0.
-0.3235
0.0717 -0.0414
-0.
-0.
-0.
0.0605
0.
0.0101 -0.
0.0189-O
-0,3663
22
-0.
0.
0.
0.0189 -0.0189 -0.
0.0375 -0.
0%0010 -0.
-0.0040
0.
-0.
Oj
02
0:
0.0605 -0
-0.
0.1242 -0.
-0.0718 -0o
0.
-0.0605
-O
0.
-0.0274
-0.
-0.1434 -0.
0.1431 0.
0.
0.0829
O
0.1434
0.
-0.
0.
-0.
-0.
0.1431
-0.
25
26
27
0O
0;1242 -0;
O.
0.
-020718 0.
0.1729 -0.
0.0189 0.0189 0.
-0.
Oj
0.
-0.
-0.2692
-0.0274 -0.0375 -0.
-0.0375 -0.0274 C.
-0.0274
0.
21
0.
-C.0605
23
-0.
-0.
0.
-0.
-0.0375 -0.
0.0189 -0.
-0.0717 -02
1.0C00 0.
0O
0.
1.0000
O
02
0.
0.
120000 02
020718 O
O;
120000
-0.
0.
0.
0:
-01242 -0.
-OJ
02
-0.
0.
020605 O
0.0718 -0.
02
020002
-0.
-0.
0.
-02
20
-0.0605 -0;
21
22
-C.0414 -0.
0.
-0,0605
O.
19
-C.
0.0375 -0.0274
OJ
0.0605
-0.
0.
O.
C.1729 -0.
-0.
0.
0.
00717
0.
01
0.3235 -C.0414
-C.
-0.
0.
0;1431
0;
-0.
0.
-07
0.0375 -0.
0.0189 -0.
-0.0274 0.
24
0
0.0375 -0.0274 C.C010 02
0.0078 0.0189
0.0189 0.
-0. 0375 0.
-C0189 -0;0274
-C.
0.
-0.C274 -0.
0.0101 0.0189 0.0375
-0;
0.0078 -0.0189
0.0189 0.
18
19
20
02
-0.0274 -0. 037 5 0,
-0.0375 -0.02 74 0.
0.0189 -0.0189
0,0002
0.
17
0.1729 -OJ
O
-0.0189-02
-0.0040 -0.
0.C004 0.0189 -0.
-0.
0.0078 -0.
0.
O2
9
16
0.
020010 0.
0.
-0.
-0.
15
O,
O
-0.
0.
C.1431
0.
0.
-C.
-0. 3663 -0.
-0.
0.1431 0.3235 -02
-0.0414
.
-0.0717 -0.
0.
0.
0.
-02
-0.0718
0.
0. 1242 0.
0.
0.
0.0605
-0.
-0.0605 0.
-0.
0.
6
14
0.
(1
-0.
0.
0.
C.1431
0.1434
13
0.
02
0.
-0.
0.
021729 -0.32 3 5
0.2692 -0. 3663
-0.
0.
5
11
12
C.
0.
0.
-0.2692 -0.366 3 -0.
0.
0.1431 -0.
-02
-0.
0.
10
0
C
0.
O
C.
1.COCO
C.
-0.
0.
-0d3663 -0.
-C.
0.1431
4
7
8
1.000( 0
0.
0.
0.
0.
0.
0.
0.
0.
0.143 I
-0.2692 -0.
0.
-0.
01729
0.
-0.
0.1431
0.2692 0.
0.
-0.
01729 0.
0.143 I
-0.
-0.
-0.
-0.2692 -0.
0.1729 0.
-0.
0 . 143 1
-0.
0.
0.2692 0.
0A 1729 0.323 5
31
1
2
3
0.
-
010078
-0,0189
010189
0J0101
Oa
00181
00078
OJO318-0{0139
o
02
-0J0274 -010189
400180 0M00T8
40J0311 -020189
oj
O
400274 0J0169
0J
020002
0j
-OJ001
o 02
O
1200eO O
Oj
120000
02
02
O
C
0C04
02
OJ
O
0J
020004 O
TABE IV
2 ' Overlap Integral Matrix
IrCle
IrC14
1
2
3
1.0000
0.
0.
0.
1.0000
0.
0.
4
0.
5
6
7
8
0.
0.
0.
0.
0.
0.
0. 784
0.
0.
0.
9
10
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
-0.
0.2716
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
C.
0.
0.
0. 1784
0.
0.1475
0.
0.
0.1475 0.
-0.
0.1475
-0.
0.
0.
0.2716 0.
0.1784 0. 3334 0.
-0.2716 -0. 3661 -0.
0.1475
-0.
-0.
0.
-0.
-0.
0. 1784 -0.3334 0.
0.2716 -0. 3661 0.
0. 1475
-0.
0.
-0.
0.
0.
16
17
18
0.
0.
0.
0.
O.
O.
0.
0.
1.0000
0.
0.
0.
0.
0.
0.
0.
1.00CC
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
O.
O.
O.
0.
0.
0.
0.
0.
O.
1. 0000
O.
0.
0.
-0.0770
0.1475 -0.
0.3334 -0.0457
-0.
0.
0.
-0.
-0.3661 0.0770
-0.3334 -0.0457
0.
0.
0.
0.
-0.3661 -0.0770
0.
0.0915
0.
-0.1541
-0.
-0.
0.1475
0.
0.
0.0915
0.
0.1541
0.
-0.
0.1475 -0.
19
0.
0. 784 -0.
0.
0.1784 -0.
0.1475
-0.
0.
-0.
-0.3661 -0.
0.
0. 1475 0.3334 -0.
-0.
-0. 0457 0.
-0.0770 -0.
0.
0.
-0.
0.
0.1334
0.
-0.0792 0.
0.0667
0.
0.
-0.
-0.
-0.0667 0.
0.
0.0078 -0.
0.0010 0.
0.
0.0101
-0.
0.
0.2716
0.2716
0.
1.0000
0.
0.
0.
0.
0.
0.0667
0.
-0.0274 -0.0 37 5
-0.
-0.0375 -0.0274
0.0189 -0.0189
0.
0.
0.
0.
1.0000
0.
0.0002
0.
0.
-0.
0.
0.0004
0.0375 -0.
0.
0.
0. 0375 -0.0274 0.0010
0.0078 0.0189
0.0189 0.
-0.0189 -0.0274
-0.0 375 0.
-0.
0.
-0. 0274 -0.
0.0189 0.0375
0.0078 -0.0189
0.0189 -0.0274
-0. 0274 0.
-0.
0.
0.0101 0.0189 -0.0375
O.
0. 0375
31
0.2716
0.0101
0.
0.
32
-0.
33
-0.
-0.3661
0.
0.
0.1475 0.
0.
0.
0.1475
0.
-0.
0.1541 -0.
-0.
-0.0667 -0.
0.
0.
0.
-0.0667
-0.
-0.
0.
0.
0.0189 0.0189
-0.0274 -0.0375
-0.0375 -0.0274
0.
0.
-0.
0.
0.
0.0101
0.0189 -0.0189 -0.
-0.0274 0.0375 0.
0.0375 -0.027 4 0.
0.
0.0101
0.
0.0189
0.0189 -0.
-0.0375
-0.0274 0.
0.0101 -0.
0.
-0. 02 74
-0.0375 -0.
-0. 0189
0.0189 -0.
0. 03 75
-0.0274 -0.
0.0101 -0.
-0.
-0.02
74
0.0375 -0.
-0.
0.0010 -0.
-0.0040 0.
0.
-0.
0.
0.
0.
1.0000
0.
0.
0.000 4
0.
0.
0.
0. 0004
0.
0.
0.
1. 0000
1.0000
0.
0.
0.
0.0792
0. 0792
-0.
0.
0.
-0.1334 -0.
O.
-0.
-0.
0.0792 -0.
-0.0667 -0.
-0.
-0.
0. 1334 -0.
0.
0.
0.
-0.0792 O.
0.
0.0667
0.
0.
-0.
-0.
-0.
-0.
0.1334 -0.
-0.0792 -0.
O.
-0.0667
0.
0.
-0.
0.
O.
-0.1334 -0.
0.
0.
0.
0.
-0.
-0.
0.
-0.
0.0667 0.
-0.
0.0667
-0.
-0.
-0.
0.
-0.
-0.
0.
-0.
-0. 0667 0.
-0.0667
0.
-0.
22
20
21
-0. 2716 0.1784
-0.2716 0.1784
0.
-0.
1.0000
O.
0.
-0.
-0.
0.
1.0000
0.
-0.
-0.
0.1475 0.
0.
-0. 3661
0.0770
-0.
-0.
-0.
0.1334
-0.
-0.
-0.
0.0667 0.
0.0189 -0. 0189
-0.
-0.
-0.0189 -0.
-0.0274 0.03 75
-0.0040 -0.
0.0004 0.0189 -0.
0.0375 -0.0274
-0.
-0.0189 -0. 0189
0.
0.0078 -0.
0.
0.
0.
0.
0.0101 -0.
0.
-0.0274 -0. 03 75
0.0189 -0.
1.0000 0.
-0.0375 -0.0274
1.0000 0.0189 0.
0.
0.
0.
0.0189 0.0189 1.0000 0.
-0.
0.0189
1
0.
OVERAP MATRIX
0.
0.1475 0.
-0.
-0. 3661 -0.
0.
-0.
-0.
-0.2716 -0.
28
29
30
32
33
0.
0.
-0.
-0.
0.
0.
0. 1784 0.
0.1475 -0.
-0.
-0.3274
31
0.
0.
0.
1.0000
-0.0457
0.3334 0.
-0.0457
0.3334 0.
0.1784
0.1475 -0.
0.
0.
-0.
0.0770
-0.3661 -0.
-0.2716 -0.
0.1475
0.
-0.
0.
-0.
-0.0457
-0.3334 -0.
0. 1784 0.
23
24
25
26
27
0.
0.
-
0.
0.
0.
0.
0.
1. 0000
0.
0.
0.
0.
24
-0.
-0.
-0.
-0.
0.
-0.
0.
0.
1.0000 0.
0.
0.
25
0. 2716
0.2716
-0.0667 -0.
-0.
-0.
0.0078 -0.
0.0189 0.0189
-0.
0.0101 0.
0.
-0. 0274 -0.0375
-0. 0189 0.
-0.0375 -0.0274
-0.0189 -0.
-0.0189 0.0189
0.007 8 -0.
0.
0.0101 0.
0.
-0.02 74 0. 03 75
0.0189 0.
0.0375 -0.0274
-0.0189 0.
0.0010
0.0002 -0.
-0.
0.0004 0.
0.
0.
0.0004 0.
0.
0.
0.1784 -0.
0.
-0.0457
0.
0.
1.0000 0.
-0.0010
1.0000 -0.
0.
0.
0.
-0.0010
0.0004
0.
0.
-0.
-0.
-0.
-0.0040 -0.
-0.
0.0004
0.
-0.
-0.0667
0.0792 -0.
-0.
-0.
0.0667
0.
0.
0.
0.1475
-0.3334 0.
-0.
-0.
0.
1.0000 0.
1.0000 0.
0.
0.
0. 1475 0.
0.
0.
-0.3661
0.
-0.3334 0.
0.
-0. 0770
-0. 0457 0.
0.
0.
0.
-0.1334
-0.0792 0.
0.
-0.
-0.0667 -0.
-0.
0.
1.0000 -0.0010 0.
0.
-0.0010 1.0000 0.
1.0000 0.
0.
0.
1.0000
0.
0.
0.13004 0.
0.
0.
0.
-0.0040 0.
0.
-0.0189 0.0078 0.0189 0.
0.0175 -0.0189 -0.0274 -0.
0.
0.0101
-0.
-0.
0.' 0101 0.
0.
-0.02 74 -0.0189 -0.0375 0.
0.
-0.0189 0.0078 -0.0189 0.
0.
-0.0375 0.0189 -0.0274 -0.
-0.
0.0101
-0.
0.;0101 -0.
-0.0274 -0.0189 0.0375 -0.
-0.
0.
0.
0.
-0.
0.
0.0667 0.
0.
U.0002
0.
-0.
C.00o
0.
-0.0667 0.
0.0078
0.
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0.0667 0.0189
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0.
0.0078
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-0.0667 0.0189
0.0189
-0.
0.0078
0.
-0.0189
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0.0189
0.
0.
-0.
0.0078
0.
0.0189
0.
0.0189
0.
23
0.1475
0.1784 -0.
-0.2716 -0.
0.
0.1475 -0.
0.
0. 3334 -0.
-0.3661 -0.
0.
0.
-0.
0.1475
-0.0457 0.
0.0770
0.
0.0667
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0.
0.
0.0792 -0.
-0.1334 -0.
0.
0.
-0.
0.
0.
0.0002 -0.
0.0002 -0.
0.
1.0000
0.
0.
0.
0.0004
0.
-0.
0.
1.0000
0.
0.
-0.
0.0189
-0.
-0.0274 0.0375
0.0375 -0.0274
-0.0189 -0.0189
0.
-0.
-0.0274 -0.0375
-0.0375 -0.0274
-0.0189 -0.
0.0375 -0.
-0.0274 -0.
-0.
0.0101
-0.0189 -0.
-0.0375 -0.
-0.0274 0.
0.
0.0101
0.0078
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0.0078
-0.
-0.0189
0.0189
0.0078
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0.0078
0.0189
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0.
0.0101
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O.
0.
0.0101
0.
0.
0.0189
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0.
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0.0375
0.
26
27
28
29
30
0. 784 -0.2716 -0.
-0.
0. 784
0.
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0.
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O.
-0.
0.
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0.0101 -0.
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0.
0.0101
0.
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0.0189
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0.0375
-0.
-0.0189
-0.0274
-0.0375
0.1784
0.1784 -0.2716 -0.
-0.
-0. 3334
0. 3334 -0. 3661 -0.
0.
-0.
0.1475 -0.
0.
0.
-0.
0.1475 0.
0.
0.
0.0915 -0. 1541 -0.
0.
0.0915
0.0667 -0.
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0.
0.
0.
0.
0.0078
0.0189
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0.0078
0.0189
0.0189
0.
0.0078
0.0189
0.
-0.
0.
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0.066? -0.
-0.0189 0.0 189 0.
-0.0274 0.0375 -0.
0.0375 -0.0274 -0.
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0.0101
-0.0189 -0.0189 -0.
-0.0274 -0. 0375 0.
-0.0375 -0.02 74 -0.
O.o1
0.
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0. 0189
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-0.0274 0.
0.0375
0.
0.0101 0.
0.
0.0078
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0.0078
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0.
0.0078
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0.
-0. 0274 -0.0189
-0.0040 -0.0189 0.0375 0.
0.0078 -0.0189 -0.
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0.
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0.0189 -0.0274 -0.
0.
0.
0.0101 0.
0.
0.
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1.0000 0.0189 -0.0375 0.
0.0002
0.
0.0189 1.0000 0.
O.
-0.0010
O.
1.0000 0.
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0.
1.0000 0.
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1. 0000
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1.0000
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0.0189 0.0002 -0.0010 O.
0.
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0.0 375 0.0010 -0.0040 0.
0.
0.0004 0.
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0.
0. 0004 0.
0.
0.
-0.0274 -0.
T
-150-
TABLE V
PtC162- Overlap Integal
Matrix
ptV102-OVERLAPMATIIX
I
2
1.0000
O.
3
O.
4
5
6
7
8
9
10
11
12
13
14
15
16
0.
1.0000
O.
0.
O
0.
O.
1.0000
0.
O.
0.
O.
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O.
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0.
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0.
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0.
0.
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0.
0.
0.
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0.
0.
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0.0660
0.
0.0784-0.
0.
0.
0.
1.0000 0.
0.
0.
1.0000 0.
0.
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1.0000
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0.
0.
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06600
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0.0765
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0.
0.
10000
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0.
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0.
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0.
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1.0000
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0.
0.
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1.0000 0.
0
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0.
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1.0000 0.
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0.
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0.
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0.
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1.0000
0.
0.
0.
0.
0.
0.
0.
0.
0.1675 0.
0.3137 0.
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0.0784 0.
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0.1388 -0.
0.
0.
0.0660 -0.
0.
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0.0765 -0.
0.1324 -0.
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.
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0.1388 -0.
0
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0. -0
0.1675
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0.
0.1388
0.2666 0.
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0.
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0.
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0.0784 -0.
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0.0002
0.
0.1324 -0.
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0.1675 -0.
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0.
0.1388 -0.
0.
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0.
0.
0.0004
00010
0.
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0.
0.1675 -0.
0.1388
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0.1388
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0
0.0660
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0.0002 -0.
0.
1.000
0.
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0.
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0.0784 -0.
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0.
0.
0.
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0.0004
0.
0.
-0.
1.0000
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0.
1.0000
0.
0.
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0.
17
18
12
20
0.
0.0
0.0004 0.
-0
. -0
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0.
0.1388 -0. 6 -00.0.134
0.2
-0.
0.0078 0.
-0.0189 0.0189 0.0078 0.
0.
-0.0784 0.
C.
0.3137 -0.0453 0.
0.1675 0.
0.0101
0.0101 -0.
-0.
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0.
0.
0.0660 -0.
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0.1388 -0.
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0.
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-0.0274
0.0375 -0.0189
-0.
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0.0660 0.0189 -0.
0.1388 0.
-0.
-0.
-0.
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21
22
23
0.
-0.2666 -0.
C.
0.1675 0.
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0.1388 0.
24
-0.
0.
0.
0.1388
0.2666 0.
0.
26
0. 1675
0.3137
0.
0.
-0.2666 -0.3658
0.
O.
27
28
29
0
31
32
33
-0.
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0.13
.31
17
18
5
-0.0765 -0.
00453
.
6
7
-0.0
0.1324
0.
0.
0.08
-0.0784
48 -0
0.8
-0.
- .
-0.3658
0
0.
00
8
9
10
11
12
13
14
15
0 .
-0.0189
-0.
0.
-0.0660 0.
0.0010 0.
0.0078
-0.
0.
0.
-0.0189
-. 0o0040-0.
0.0004 0.0189
-0.
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0.
0.
C.
0.
-.
160
-0.0274 -0.0375
17
18
23
20
21
22
0.
0.0189
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0.
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0.
24
-0.0274
28
0.
1.0000
0.
0.
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0.0189
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0.0004
0.0315
-0.
0.
O.
0.0274 .001
0.
0.0078 0.0189
0.
-0.0189 -0.0274
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0.0101
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0.
0.0189 0.0375
0.0078 -0.0189
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O.
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31
32
33
O.
0.0101
0.2666 -0.
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0.
4
5
6
0.
0.
0.1529 -0.
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0.1388
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7
8
0.
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0.
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9
0.
0.
0.
0.0189
0.0189
0.
16
17
18
0.
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0.
0.
-0.u274 -0.0375 -0.
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0.
0.0101
0.0189 -0.0189 -0.
-0.0274 0.0375 0.
0.0375 -0.0274 0.
0.
0.0101
0.0189 -0.
0.0189
19
20
-0.0274
,
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0.
0.0101 -0.
25
26
27
0.0375 -0.
0.0010 -0.
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0.
21
22
23
24
21
0.2666
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0
0.
0.0
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.
0.
0.
0004
O.
0.
0.
0.0101
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0.0189 -0.
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0.0375
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0.0101 -0.
-0.0274
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0.
28
0.
0.0004
0.
29
30
31
32
33
0.
0.
1.0000
0.
0.
0
0.
0.
1.0000
0.
0.0004
0.
0.
0.
1.0000
O.
0.
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0.
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0.
018
-.
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0.
0.
0.
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0
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0. 08
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0.
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0.0004
0.
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0.
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0.
0.
0.
0.
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0.
0.0078
0.0189
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0.0078
0.0189
0.
0.0189
0.
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.
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0.
0
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29
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0.1388 -0.
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0.071
0.
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0.010
0.0189
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0.
0.0375
0.
0.
0.0101
0.0375
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0.
0.
-0.0274 0.
0.0189 0.0002 -0.0010
0.0375 0.0010 -0.0040
0.
O.
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0.0101
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0.0004
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0.0375 -0.
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0.
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0.
0.0905
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1.
0.0078
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0.
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0.
0.
0.
0.
0.
0.
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0.
0.0002
0.
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1.C000
-0.0274 -0.0189 -0.0375 0.
-0.0189 0.0078 -0.0189 0.
-0.0375 0.0189 -0.0274 -0.
-0.
0.1675
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1
0
0.
0.
0.
1.0000 0.
0.
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0.
30
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0.
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0.
0.
0.0660-0.
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0.
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0.
0.0078
0.0189 0.
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0.010[ -0.
0.0078
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-.
0375.
0.
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0.
00189
0.1388 0.
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0.
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0.
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28
00905 -0.1529 -
0.0375
0.
0.01 0.0078
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0.
0
0.010 -0.
27
10000
0.0101
0.
0.0189-0.0274
0.0375
-. 018
0.1675 -0.2666 -0.
-0.0
0.3137 -0.365
0.
-0.004 0.0189 -0.0375 0.
-0.0189 0.0078 0.0189 0.
0.0375 -0.0189 -0.0274 -0.
0.
-0.3658
0-0.765
0.0274 0.
1.0000 0.0189
.
0.
0.0189
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0.
26
0.2666
0.
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0.0189 0.0189
0.
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0.
0.
00004
0.
-0.0010 1.0000 0. 8
0.0078
0.0375 -0.
0.00
15-0
-0.
25
0 .
-
0.
-0.0375 -0.0214 0.0189 0.
0.0189 -0.0274-0.0375 -0.
0.1
0.0189 -0.0375 -0.0274
0. 0.1388.
0
-0.
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0.0101
0.
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0.0101
0.
0.2666
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0.
0.
0.
-0.0274 -0.0375 -0.0189
0.0189 -0.0189 -0.
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0.0189 0.0375 -0.0274 -0.
0.
0.0101 -0.
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24
0.
0.
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1.0000
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6-0.58
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23
0.0
0.0189
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0.1388
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0.
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0.
0.
-0.0660
0.
0765 -0.0453 0.
0
0.0
-0.
0.066 0 .
0.0189 -0.0189
-0.
-0.
-0.0274 0.0375
0.0375 -0.0274
-0.0189 -0.0189
0.
-0.
-0.0375
0.
0.
22
0.1388.
0.0189 -0.0375 -0.
2
3
11
12
13
14
15
0.
0.1388
0.
-0.
20
-0.
-0.
0.
0.
0.
32
10
-0. 6.
-0.
-0.
0.0101
-0.
-0.
-0.
0101
O.
0.
-0.
0.0189
0.0375
1
0.
0.
0189
1.0002 O.
29
30
31
33
0.
-
0
0..
888-0.
0.0189 -0.0189 0.0002 0.
23
25
26
27
1.0000
0.0189
-0.
0.0660 0.
-0.
-0.
0.0905-0.
-.
0.
0.1388
3
0.
0.1529 -0.
-0.
0.0660
19
-105
0.
0.2666 -0.
-0.
0.
-0.
-0.1324 -0.
0.
-0.1529 -0.
0.1675 -0.3137
O.
0.
0.
0.0905
-0.
0.1388-0.
0.1388
0.
-0.
0.
0.2666 -0.3658 0.
0.
C.1388 -0.
-0.
16
5
2
-0.
0.
0.
-0.3658 -0.0765 0.
25
0.0375 -0.0274-0.0189 0.
-0.0189-0.
0.0078 0.
-0.0189 -0.0189 0.0078 0.
-0.
0.0101
-0.
-0.
0.0101 0.
0.1324 -0.
0.
-0.0784 -0.
-0.
0.
-0.0660 -0.
-0.3658 0.0765 -0.
-0.3137 -0.0453 0.
0.
0.
0.
O
1.0000
.
0.
0.0004
0.
1.0000
O.
O.
-152-
TABLE VI
ReC1 6 2
Eienvectors:
MO's Across and AO's Down
T
EIGENVECTCRS
Fe Et{6 -1
1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
10
12
12
1s
14
15
O.0O0 -0.0000 -0.C000 -1.4407 C.Occc OJccCO -0.0000 -Owooo0 -oJooo0-020000 oOOO0 -GJCCo0 02000 620000-010000
0b0093 0.0186 -1.4740 0.0000 0.OCCO
c00000
-0.0000 -0.0CO -020000 0.0000 -OJOOO0-CJCO0 CJ0366 0J0]85 -0J0248
-1.0424 1.0423 O;COE6-0;0000 O.OCCC-o.oCOO -OCCOO -0.0000 000O0 -00000
020000 CJCOC C
020321 0J0380 -030500
-10422 -1.0423 -0.0198 -0.0000 -0.0CO0 0.0000 -0.0000 -0.0000 O0000 -00.0000 -OJOO O CJCCCO 02080?-0J0228 0J0431
-OCCOO
0.0000
-0.COCO -0.0000
0.0000 -0.0000 -O.COCO 0.0000
-0.0000
0.0COO
0
-0.0000
0.0000
-01CCO
-0.Coco
0.0000
-C.0000
0.9533
0.2462
0.Cco 0.CO0
0.2462
-0.9533
O.OCCC
0.0000
-0JCCO0 -O.Ocoo -02o00o
-020000 -OJooO
0.9788 00ocoo020000 -0.0000
Oc0co
-0.COO0
0;0000
0,9788
-0J00
-0.0000
020000
.0000
0JCGCO
OJCO
0J0000 oC0o
OJ0000
OJOOO
CJCCCO
620000
0
OJOOO
020000 0J0000 -0J0000
C2CCCO C20C00
C0000
0J0060
00C0
.0 00.oooo-o.0Oco -o0 o0000
G.oCCo -OC000 -0o.0oo 0.0000 029785 020000 ?0 0000 C00CCO-C2c000 020000
030000
-010000
010000
10 0.3612 -0.3612 -0.0023 0.2549 0.0507 0.1824 -C.GCO0-0.0000 0.0000 -0.0000 0.0000 CJCOC062C065OJOl -010153
11 -0.0010 -0.0021 0.1634 0.0000 C.CCC -0.0000 -0.1994 -0.0000 -020000 0000 -025155
-CJ022 -021419
-'023354
0J1004
12 -0.41340.4133 0C026 -0.3847 -0.1171 -0.4215 O.CO0 0.0000 -OJOOO0020000-0.0000 -C2CCCO
-C1628 0J925 014054
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.1155
0.1155
C.0022 0.0000
-0.3612
-0.0010
-0.4134
0.1155
0.3611
-0.0010
0.1156
-0.4133
-0.3611
-0.0010
0.1156
-0.4133
-0.0032
0.0C37
0.1156
0.1155
010032
0.0037
0.1156
0.1155
0.3612
-0.0021
0.4133
0.1135
0.3612
-0.0021
-0.1155
-0.4133
-0.3612
-0.0021
-0.1155
-0.4133
-0.0064
0.0074
-0.1155
0.1155
0.0064
0.0074
-0.1155
0.1155
0.C023
0.1634
0.C026
CC022
0.C068
0.1634
-0.CC07
-0C078
-0.0068
0.1634
-0;0007
-00078
0;5107
-0.5845
-0.C007
0.0022
-C.5107
-0.5845
-0C007
C022
16
17
18
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
-0.0000
-0.0000
O.OCO0
-0.0coo
0.0000
0.0000
0.0C00
-0.0000
-0.0C0
-00ooo0
0.1900
-o.0o0
-0.2564
0.0000
0.1oo
-0.0000
-0.2564
0.0000
-0. 1900
-0.3914
o.ocoo
-o.ocoo
-0.1o00
-0.3914
O.0CO0
-0;00000
O.OCO0
0.3914
0.2564
-0.0000
0.0000
0.3914
-0.0000
-o.ocoo
-0.0000
-o.cooo
-0.0000
-0.0000
O.COO0
-0.C000
-0.0000
o.C0oo
0.4212
0.0000
-0.0903
-0.0000
0.4212
0.0000
-0.0903
o.0ooo
-0.4212
0.2637
0.0000
-0.0000
-0.4212
0.2637
0.0000
000000
0.0000
-0.2637
0.0903
0.C00
0.0000
-0.2637
0.000
-0.COCO
.CCCO
.coco
C.0000
C;cooo
-O.CCCO
-0.COCO
.COCO
-cCco
0.2039
-. 0COCO
0.4256
o.COCO
0.2C39
-0.C0CO
.4256
-o.cco
-0.2039
-0.1799
-0.COO
0oco
-0.2039
-0.1799
-C.COCO
-O.CCO
0.CCO0
0.1799
-0.4256
0.0000
O.CCCO
0.1799
33
0.2564
0.0903
t
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
31
O.OCO
-0.0210
0.0555
-0.0297
0.0C0
-0.0C0
-0.0CO0
00CO0
O.OO0
0.5699
-0.0069
0.0127
-O.OC97
-0.5699
-0.0069
0.0127
-0.0097
-0.3048
-0.0069
0.0182
-0.0C168
0.3048
-0.0069
0.0I82
-0.0068
-0.2157
-0.0048
0.0182
-0.0097
0.2157
-0.0048
0.0182
-0.0097
32
-O.OCO0
-0.0587
-0.0061
0.0302
O.CCO0
0.0000
-0.0000
0.0000
-0.0000
-0.0625
-0.0193
-0.0014
0.0099
0.0625
-0.0193
-0.0014
0.0099
0.3101
-0.0193
-0.0020
0.0069
-0.3101
-0.0193
-0.0020
0.0069
-0.6035
-0.0134
-0.0020
O.CO99
0.6035
-0.0134
-0.0020
0.0099
-C4256
33
-C.1560
C.CC
0.CCO
.0CCO
-CCOCO
-C.COCO
.CCO0
-0.CCO0
-C.CCO
-0;3682
0.0000
C.0148
0.0000
-0,3682
.OC0
-0.0148
O.COCO
-0.3602
.COCO
0CO0
0.0148
-0;3682
O.COCO
0.COO0
-C.0148
-0.3662
0.0148
.CCCO
C.CCCO
-0.3682
-0.0148
O.00CO
0CO00
0.2549
-0;0000
0.3847
00000
0.2549
0.0000
0.0000
-0.3847
0.254q
C.0000
0.0000
0.3847
0.2549
-0,3847
0.0000
0.0000
C.2549
0.3847
0.0000
0.0000
19
-0.0000
-0.0000
-0.0000
0o0000
0.3128
0.0000
0.3039
-0.0000
0.0000
-0.0143
-0.0000
-0.1131
0.0000
-0.0143
-0.0000
0.1131
0.0000
0.0562
-C.0000
-0.0000
0.4444
0.0562
-0.0000
-0.0000
-0.4444
-0.0419
-0.3313
-0.0000
0.0000
-0.0419
023313
-0.0000
0.0000
0.OCCC-0,0000
0.0000-0.0000 -0.1994 -020000 -OJ0235 C25195 -023252 00914 -021744
C.0507
0.CCC
C.1171
C.CCC
0.1326
C.00CC
-0.0CCC
-C.3065
0.1326
0.OCCC
-0.0CC0
C.3065
-0.1833
0.4235
-0.OC0
0.0CCC
-0.1833
-0.4235
-0.0000
C.CrCC
021824
O.C000
0.4215
-O.0CO0
-0;1351
0.0000
-0;0000
0.3121
-0;1351
0.C000
020000
-0.3121
-020473
0.1094
00C00
-O.COO0
-C0473
-0.1094
-0.0000
-0.C000
0.0000
0.1994
0.0000
-0.0000
-0.0CO0
O.OCO0
0.0000
O.CO0
0.;0000
-0.0CO0
-0.COO0
-0.0000
-020000
O.CCO0
-0.1994
0.0000
O.CO0
0.0000
0.1994
-O.OCO0
0.0000
0.0000
-0.000
O.0CO0
-OOCO0
-0.1994
-O.OCO0
0.0000
-0.0000
O.1994
0.0000
0.0000
-0.0000
0.0000
-O.OC00
-0.1994
0.0000
0.0
0.0000
0.1994
-0o0000
o20000
020000
-020000
-0;0000
0
000
0.1994
020000
0;0000
-020000
0.0000
025200
-01994
00000
0.0000
0.0000
-020000
020000
-020000
-025200
021994
-020000
-0O0000
000000
-0;0000
020000
0.0000
-O.00
-020000
-020000
0.0000
-025200
020000
-020000
0~0000
-020000
00 0
0;0000
-020000
025200
-00000
025195
-OCOOOO
00
020255
-020000
OJO000
0J0231
0.0000
0;0000
-020000
-020288
00000
-OJOOO0
OJOOO0
025195
-020000
0J00GO
0J0000
-0J5195
OJOOO0
-02C000
CJ023!
-C2C1C0
-C2615%
CC0
010CC
-CJ6185
-C0CCCO
-C0CCCO
-OJCCCO
0J195
-CJCCO
-CCCCO
CC00
C20235
-CJCCO
CCCCC
CCCO
-CC23
-C2CCCO
-C0015
-021419
-021628
-C23261
0J164
-6214T9
-6J1259
-024087
-C0164
-021419
-021299
-624087
2O0074
-021854
-01299
-C23262
-C0074
-CJ1854
-0Jl29
-023261
021926
00914
-OJ0046
-0J3344
021537
01145
020046
-023344
021537
021145
OJO169
-024216
021557
00914
-020149
-024216
021581
00914
014054
-021744
00088
0.1004
003235
-012186
-010088
0;1004
013235
-022186
-010050
OA'1259
003235
-0;1744
010050
011259
023235
-0.1744
20
21
22
23
24
25
26
27
38
29
30
0.0000
-0.0194
0.0768
0.0247
-0.0000
O.CCO
0.0000
-0.0000
0.0
-0.0830
-0.0750
-0.4263
0.0956
0.0830
-0.0750
-0.4263
o.0956
-0.0267
-0.0750
0.2970
-0.1373
0.0267
-0.0750
0.2970
-0.1373
0.0209
0.1076
0.2970
0.0956
-0.0209
0.1076
0.2970
-0.0000
0.0129
0.0280
-0.0771
000
O.CO0
0.0000
O.OCO0
-0.0000
-0.0302
0.0483
-0.1554
-0.2982
0.0302
0.0489
-0.1554
-0.2982
0.0833
0.0489
0.1083
0.4280
-0.0833
0.0489
0.1083
0.4280
-0.0135
-0.0696
0.1083
-0.2982
0.0135
-0.0696
0.1083
020000
-0.0000
-020000
020000
020000
-020000
-020000
022608
0.0000
0.0000
-02000
0o0000
oJoo o
-0.0000
oJoooo
oo000
-o000
-0.0000
0.4460
0J00o
-o20000
0.0000
-0.4460
-0o2000
-020000
0.0000
0.0000
-0JOOO0
044460
-0JOO0
0.0000
020000
-O200
-020000
020000
OJOCO0
020000
-020000
0200C0
;0000
020000
0J0324
020000
OJ0000
-0.2588
0o0000
0o0553
020000
-0.4426
-020000
-0J0553
ojo000
0.4426
-ojooo0
o20000
-024426
-o00oo0
OJOOOO
-OJOOOO
0J4426
-020000
-0J0000
-OJOOO0
020553
020000
02000O
-020000
-020553
-C2133
CCCC
02cc
02CCC
CCOCO
-CJCCCC
-OCCCCO
-CJCCC
-CCOCO
C196
-0CCCC
023248
CCCCO
C96
-0c06o
-CJ3248
C2C00
CJ3198
C000
CCCC
c3248
C1196
-0C0
O2000
-0J3248
CJ196
023248
0JCC
020000
J02196
-0J3245
CJC000
02o6e
-CCCCO
-C0c0
CCCO
-02018
-CC000
C1053
-0C000
CCO
5633
-cCC6o
620246
C06O
02$6!3
-0C000
-0246
CCC O
-C2923
-CCo0
-CC00O
-620128
-C2922
-02000
-C0000
020128
-C271
-020119
-COCO
C2C0CO
-C3711
0J0119
-62060
020000
OJO0O
0200C
020000
021065
6006
0205T
-0J0000
020C
-0Jo122
020000
-0J0005
020CO
020122
0occ0
o0005
0o000
-024818
ooc0
020066
-o0211
-024818
6J006
60006
020211
0J4940
020216
6J0000
60000
024989
-020216
0J0000
-020000
-040225
-0.0358
-010511
0;0000
0/0000
010000
-040000
-020000
-03681
-010074
-0;0083
-010167
023681
-010074
-020082
-0.0167
-025246
-O6o074
-oio117
-0.0116
o5246
-010074
-0;0117
-0.0116
-022314
-010051
-010117
-010167
012314
-010051
-00117
-0.2982
-024460
-0J0000
-0167
o.occc
oCOO0
-0.cccc
020797
.CCC
0.0143
-0.0cc0
0.0181
0.3039
0.0000
0.CCCC -020000
-0.3125
-00COO
-C.0cc0
0.000
-o.0CCC
0.0000
0.0567
-0.0154
-0.0CCC
0.3083
0.4478
-0.0793
-c.occc
0.0701
C.0567
0.0154
-c.0ccc
0.3083
-0.4478
-0.0793
-o.occc
00701
-0.0159
-o0196
-0.0CCC
0.3083
.CCCC
0.0552
-0.1260
-0.1007
-C.0159
0.0196
-0.0CCC
o3083
C.0ccc
0.0552
0.1260
-021007
-0.0407
-020861
-0.3218
-0.4425
C.OCCC
0.0552
-0.0COC
0.0701
-c.0407
00861
0.3219
-0.4425
O.CCCC
0.0552
-O.CCC
0C0701
0.0956
020000
-022588
-020000
-020000
-020324
-020000
-024426
-o0000
-o20553
o20000
4426
-020000
o20553
-o20000
-o20000
-o20553
-o20000
o20000
0200O
o20553
-020000
0;0000
0;000
-024426
-020000
-020000
00000
024426
020000
-020060
CCO
000
OJ001
010163
.023354 021004
T
-154-
TABLE VII
OsCl 8 2
Eigenvectors:
M's
Across and AO's Down
EIGENVECTORS
OsQ1
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-0.0000
1.4452
-0.0000
-0.CCO0
-0.CO00
-0. 0000
0.0000
O.CC00
0. 0000
0. 0000
-0.1570
-O.CCO0
0.0000
-0. 0000
-0.1570
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
i7
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0. 0000
0.C002
-0,0000
0.0000
-0.cooo
-0.0000
-00000
0.0000
-0.COO0
0.oco0
0.5047
0.0000
0.O0
-00000
0.5047
0.COO0
0COO0
-0.0000
-0.5054
-0.0000
-0.0000
0OOCO
-0.5054
-0.0000
-0.0000
-0.CCO0
-0.0008
0.0000
-. 0.00
0.0000
-0. 0008
0.0000
-0.COO0
0.0027
0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0. 0000
-0.0000
-0.0000
0.5003
0.0000
-0.0000
-0.0000
0.5003
-0.0004
0.0000
0.0004
-0.0117
0.0004
0.0000
0.0004
-0.0117
0.0000
-0.0000
-0.0005
-0.5095
-0. 0000
0.0000
-0.0005
-0.5095
-0.0000
-0.000
0.0000
-0.0000
-0.0000
0.0000
-0.0004
0.0000
-00108
-0.0004
0.0004
0.0000
-0.0108
-0. 0004
0.0000
-0. 0000
0.5007
0.0000
-0.0000
-0.0000
0.5007
0.0000
0.0000
-0.0000
-0.5092
0.0005
0.0000
-0. 0000
-0.5092
0.0005
31.
-0.0000
32
-0.0000
33
0.1729
-0.0CO0
0.C000
-0.0825
-0.ccoo
-0.0000
-0.CCO0
0.0000
-0.COO0
0.0000
-0.CC0
0.COO0
-0.0209
-0.0000
-0.CCO0
0.0CO0
-0.0209
-0.6763
-0.CCO0
0.0000
-0.0168
0.6763
-0.0000
0.cooo
-0.0168
-0.OCO
-0.COO0
0.00o
-0.0210
0.0000
-0.0000
0.0000
-0.0210
-0. 08 23 -0.0000
-0.0000
0.0000
0.0000
-0.0000
0.0000
0.0007
-0.0000
0.0000
0. 0000 -0.0000
0.0000
0.0000
-0.0000
0 0000
-0.0000
0.362 3
-0. 02 08 -0. 0000
-0.0000
-0.0158
0.0000
-0. 0000
0. 0000
0.3623
-0. 02 08 -0.0000
-0. 0000
0.0158
0.0000
-0. 0000
0.0000
0.3628
-0.0208
-0.0000
-0 0000
0.0000
0.0000
-0. 0158
-0.0000
0.3628
-0. 02 08 -0.0000
-0.0000
0.0000
0.0000
0. 0158
-0.6764
0.3692
-0. 0167 -0. 0157
-0. 0000
-0. 0000
0.0000
-0.0000
0. 6764
0.3692
-0. 0167
0 0157
-0.0000
0.0000
0. 0000 -0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000
-0.0000
-1.4451
-0.0000
-0.0000
-0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.1570
0.0000
0.0000
0.0000
0. 0000
0.0000
-0.0000
0.0000
-0.0000
-0.4947
-0.0000
0.5887
-0.0000
0.4947
-0.0000
-1. 4090
-0.0000
-0.0000
-0.0000
-0 .0001
-0.0000
0.0000
-0.0000
-0.0000
0.2453
0.0000
-0.38 38
0.0000
0.2453
0.0000
-0.C00
0,0000
0.0000
-0.1570
0.C000
-0.0000
-0.0000
-0.1570
0.Co00
-0.0000
-0.4947
0. 5885
0,0000
0.0000
0. 4947
0.5885
0.0000
0.0000
0.0000
0.1570
0.4947
0.0000
-0.0000
-0.5886
-0.494
7
0.0000
-0.0000
-0.5886
0.0000
-0.0000
-0.0000
0.1570
- 0. 0000
- 0.0000
-0.0000
0.1570
0.5887
-0.0000
-0.0000
-0.0000
-0.1570
0.0000
0.0000
-0.0000
-0.1570
0.0000
-0.0000
0.0000
-0.1570
-0.0000
0.0000
0.0000
-0.1570
-0.0000
0.3838
0.0000
0.2453
0.0000
0.0000
-0.3 838
0.2453
0.0000
0.0000
0.3838
0.2453
-0.3837
0.0000
0.0000
0.2453
0.38 37
0.0000
0.0000
0.3726
0.0000
-0.1245
0.0000
0.0000
0.3589
-0.1245
0 .0000
0 .0000
-0.3589
-0.0047
0 .0136
0.0000
-0.0000
-0.0047
-0 .0136
0.0000
-0.0000
-0.1994
-0.0000
-0.0774
-0.0000
-0.0000
0.2230
-0.0774
-0.0000
0.0000
-0.2230
0.1466
-0.4216
0.0000
-0.0000
0.1466
0.4216
0.0000
-0.0000
-0,0000
0.1750
0.0000
0.0000
-0.1749
-0.0000
-0o0000
-0.0000
0.1749
-0.0000
-0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
0.0000
-0.0000
16
17
18
19
20
21
-0. 0000
-0.0000
-0. 0002
0.0000
-0.0000
-0.0000
0 0156
0.0000
-0.482
3
0.0000
0.0000
0.0376
0.0000
0.4019
-0.0000
0 .0376
0.0000
-0.4019
-0.0000
-0.0361
0.0000
-0.0000
-0.3868
-0.0361
0.0000
-0.0000
0.3869
-0.0013
-0 .0 145
-0.0000
-0.0000
-0.0013
0.0 145
-0.0000
-0 0000
-0. 0018
-0.0000
-0.0000 0.0000
0.0000 1.4451
00000 0.0000
0.00000.0025
8
9
0. 0000
-0,0001
-0. 0000
-0.
0000
-0. 0000
-0.0000
-0.0000
0.0299
-0.0000
-0.9249
0.0000
0.0000
0.1293
-0.0000
-0.3726
-0.0000
0.1293
-0. 0000
-0.0000
-0.92 54
-0.0000
-0.0299
-0.0000
0.0000
-0.0691
-0.0000
0.1994
-0.0000
-0.0691
-0.0000
0o.0000
0.0000
0.0000
0.0000
-0.0000
0.9752
0.0000
-0.0000
0.0000
-0.1750
-0.0000
0.0000
0 .0000
0.0 000
0.97 54
-0.0 000
-0 .0 000
-0 .0 000
-0 .0 000
-0.1754
0 .0000
0.0000
0.0000
0.1754
-0.0000
0.0000
0.0000
0.9754
0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
-0. 0000
10
11
12
13
14
15
-0. 0000
0.0000
-0.0000
-0. 0000
-0.0000
-0O.u
-.
0. 0000
0.0000
0.0000
0.0000
0.0030
0.0000
-0.0000
0o.0000
0.0000
-0.0000
0.0000
-0.0000
-0.0001
0.0000
-0.0000
0.0000
0.0000
-0.0000
-0 .0158
0.0000
0.4618
0.0004
0 .0158
0.0000
0.0000
0000
-0.0000 0.0000 -0.0000 -0.0000
-0.0000
0.0000 -0.0000 -0.0000 -0.1020
-0.0000-0.0000 -0.0000 -0.0 000 0.0000 -0.0000 0.0000 -0.0000 -0.1034
-0.0001 0.0000
-0.0000
-0.0000
-0. 0000 -0 1088
0.0000
0. 4814
-0.0000
0. 0156
0 0000
-0.0000
0.0 208
-0.0000
0. 2172
0.0000
0.0208
-0.0000
-0.2 172
0.0000
0.023 2
-0. 0000
-0.0000
0. 2427
0.0232
-0.0000
-0.0000
-0.7427
-0.0415
-0.4538
-0.0000
0.0000
-0.0415
0.4538
-0.0000
0.0000
0.0001
-0.0000
-0.0000
0.0000
-0.0000
0.0000
0.1008
-0.0000
0.4619
0.0001
-0.1008
0.0000
0.4619
0.0001
-0.0000
-0.0000
-0.3061
-0 0002
0.0000
-0.0000
-0.3061
-0.0002
0.0000
0. 0000
-0.3131
0.0001
-0.0000
0.0000
-0.3131
0.0001
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
-0.0002
-0.0000
0.0000
0.0000
-0.5202
0.0000
0.0000
0.0000
0.0000
-0.0000
-0 .0000
-0.0000
-0.0000
-0 .0000
-0.0 000
0.0 000
-0.1 737
0.0000
0 .0000
0 .0000
0.1737
-0.0 000
-0.1753
-0.0000
-0.0000
-0.0000
0.1753
0.0000
-0.0000
-0.0000
0.0000
-0.0000
-0.1738
0.0000
0.0000
0.0000
0.1738
0.0000
0.5202
0.0000
0.0000
0.5198
-0.0000
-0.0000
-0.0000
-0.5198
-0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
-0.0000
22
23
24
25
0.0000
0.0000
0.0001
0.1088
-0.0000
0.0000
-0.0000
0.0000
-0.0000
-0.0000
0.0000
-0.0002
0.3055
0.0000
0.0000
0.0000
0.1097
-0.0000
-0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
0.0000
0.3050
0.0000
-0.0000
-0.0000
0.3051
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0.2506
0.0000
-0.0000
0.0000
-0.4528
-0 0000
0.0000
0.0000
0.0000
-0.0000
-0.0000
0.0000
0.2498
0.0000
0.0000
-0.0000
0.0000
0.4498
0.0000
-0.0000
-0. 0000
-0.4497
0.3055
-0.1008
0.0000
0.0001
-0.4623
0.1008
0.0000
0.0001
-04623
-0.0000
-0.0000
0.0001
0.3131
0.0000
-0.0000
0.0001
0.3131
-0.0000
0.0000
0.3056
-0.0000
0.0000
-00000
0.3056
-0.OO0
0.0000
-0.1004
-0.4671
-0.0000
-0.0000
0.1004
-0.4671
0.0000
-0.0000
0.4528
0.0000
0.0000
-0.4533
0.0000
-0 0000
-0.0000
0.4533
0.0000
0.0000
0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0.0000
-0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
-0. 0000
0.0000
-0.0000
0.0000
-0.0000
-0.0000
0.4566
0.0000
0.0000
-0.0000
-0.4566
-0.0000
-0.0000 0.0000
-0 .0000
0.0000
-0.0002 0.0000 0.0000 0.0000
0.0000
0.0000
-0.0032
0.0000
0.0000
-0.0000
0.0000
-0.5227
-0.0000
-0.0000
-0.0000
0.52 27
0.1033 -0.0000
0.0000 0.0000
0.0000
0.0000
-0.0000
0.0000
-0.0000 -0.0000
-0.0000 -0.0000
-0.0000 0.0000
0.0000
0.0005
-0.3985
0.0000
0.0000
0.3933
-0.0000
0.0000
-0.0000
0.3933
0.0005
-0.3985
0.0159
0.0000
0.0004
-0.4614
-0.0159
0.0000
0.0004
-0.4614
-0.0000
0.0000
0.0004
-0.3805
0.0000
0.0000
0.0004
-0.3805
-0.0000
0.0000
-0.0000
0.3920
-0.0000
0.0000
0.0000
0.3920
-0.0000
0.0000
-0.0168
0.4568
-0.0000
0.0000
0.0168
0.4568
-0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
0.5173
-0.0000
0.0000
0.0000
-0.5173
0.0000
0.5225
0.0000
-0.0000
-0.0000
-0.5225
0.0000
-0.0000
0.0000
-0.0000
-0.0000
-0.5175
-0.0000
-0.0000
0.0000
0.5175
0.4618
0.0004
-0.0000
0.0000
0.3976
0.0005
0.0000
0.0000
0.3976
0.0005
-0.0000
0.0000
0.3809
0.0004
0.0000
0.0000
0.3809
0.0004
26
27
28
29
30
-0.0001
-0.0015
0.0000
0.0000
-0.0000
0.0000
-0 .0825
0.0000 -0.0000
-0.0000 0.0000
0 0000
-0.2377
-0.0000 0.0000
-0.0000 0. 0000
-0.0000
0. 0000
-0. 0000 -0.0025
-0.0000
0.0000
0. 0002
0.2497
-0 0000
0.0000 -0. 0000
0.0000
0.1284
-0.0000
0.0000
0.0000
0. 3157
0.0000
0.0000
-0 0000
0.1284
0.0000
0. 0000
0.0000 -0. 3157
-0.0000
0 0000
0.0000
0. 1284
0.4500
0.0000
0.0000
0. 0000
0.0000
0. 3161
-0.0000
0.1284
-0.4500
0 0000
-0.0000
0 0000
0.0000
-0.3161
0.0000
0.1283
0.0000
0. 3209
-0 0000
0.0000
0.4564
0. 0000
-0 0000
0. 1283
0.0000
-0.3209
0.0000
0 0000
-0. 4564
0 0000
-0.0000
-0.0000
0.0000
0.0000
0. 0033
0.0000
-0.1004
0.0000
0.0000
-0.5027
-0.0000
-0.0209
0.0000
-0. 5027
-0.0000
0.0209
0.0000
0. 4836
-0.0000
-0.0000
0.0202
0.4836
-0.0000
0.0000
-0.0202
0.0183
0.0008
-0.0000
0.0000
0.0183
-0.0008
-0.0000
0.0000
0.0000
-0.0000
0. 1003 0.0000
-0.0000 0.0000
0.0033 -0 .0000
-0 0000
-0.
0000
0 0000 -0.0000
-0.2715 -0.6763
0.0000 0.0000
-0.0110 -0 .0168
-0.0000 -0.0000
-0.2715 0. 6763
0.0000 0 .0000
0.0110 -0 0168
-0.0000 -0.0000
-0.3036 -0.0000
0 .0000
0.0000
0.0000 -0. 0209
-0.0123 -0 0000
-0.3036 0.0000
0.0000 0 0000
0.0000 -0. 0209
0.0123 -0 0000
0.5667 0 0000
0 0240 0.0000
0.0000 -0 .0210
-0.0000 -0 .0000
0.5667 -0. 0000
-0.0240 0.0000
0.0000 -0.0210
-0.0000 -0.0000
-156-
TABLE VIII
IrC16 2
Eigenvectors:
i
MO's across and AO's down
EIGENVECTORS
I
D 210
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
I
2
3
4
5
6
7
8
9
10
1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1
2
3
4
5
6
7
0.0000
-0.0000
0. 0000 -0.0000
0.0000
1.4688
-1.4688
0.0000
-0.0000 -0. 0000
-0.0000
0.0000
-0.0000
0.0000
0. 0000
0. 0000
-0. 0OOO -0.0000
-0.0000 -0.5219
-0.0000
0. 0000
0.6007
0.0000
0.1683 -0. 0000
0. 0000
0.5219
-0. 000
0.0000
0.0000
0.6007
0. 1683 -0.0000
0.5219 -0.0000
-0. 000
0.0000
-0. 3000 -0.1683
-0.6006
0.0000
-0. 5219
0.0000
-0.0000
0.0000
-0.0000
-0.1683
-0.6006
0.0000
-0.0000
0.0000
0.0000
-0.0000
-o.0000
-0.1683
0. 1683 -0.0000
0.0000
-0.0000
0.0000 -0.0000
-o0.0000
-0.1683
0. 1683 -0.0000
-0. OOO0 -1.4312
1.4688
-0.0000
0 0000 -0.0000
0.0000
-0.0000
0.0000
0.0002
-0.0000
-0.0000
0. 0000
0.0000
-O. COOO0 -0.0000
0.0000
-0.0000
-0.0000
0. 2 590
-0.1683
0.0000
0. o0000 -0. 3932
-0.0000
0.0000
0.0000
0.2590
-0.1683
0.0000
0.0000
0.3932
-0.00 00
0.0000
-0.0000
0.2590
-0.1683
0.0000
-0. 0000
0.0000
O.00CO -0. 3932
0.00CO
0.2 590
-0.1683
0.0000
-0. 0000
0. 0000
0.0000
0.3932
-0.52 20
0. 2590
0.6009
-0. 3932
-0.0000
0.0000
-0.0000
0.0000
0. 5220
0. 2 590
0.6009
0. 3932
-0.0000
0.0000
-0.0000
0.0000
16
17
18
0.0000
-0.0000
0.0000
-0.0041
0.0000
-0.0000
0.0000
-0.0000
-0.0000
-0.0000
o0.0000
0 .000
0.5128
0.0000
0.0000
-. 000G0
0.5128
0.0006
-0.0000
-0.0000
0.0169
-0.0006
-0.0000
-0. 0000
0.0169
-0.0000
.000G0
0.0000
-0.4969
-0. 0000
0.0000
0.0000
-0.4969
-0.0000
-0.0000
-O .0045
-0.0000
0.0000
0.0000
-0.0000
-0.0000
0o.O0o0
0.0006
0.0000
0.0186
0.0000
-0.0006
0.0000
0 .0186
0.0000
0. 0000
-0 .0000
0.51 34
0.0000
-0 .0000
-o.0000
0.5134
0.0000
-0.0000
0.0000
-0.4961
-0.0000
-0.0000
0.0000
-0.4961
-0.0000
-0.0000
0.0032
-0. oo0004 -0.0000
-0. 00CO 0.0000
-0.0000
0.0000
0.0000
0.5142
-0.0000
-0.0000
-0.0000
-0.0210
0.0000
0.0000
-0.0000
0.0000
0. 0000
0.0322
-0. 5043 -0.0000
0.0000
0 .2292
0.0000
0.0000
0. C0000 0.0322
-0.5043
-0 .0000
0. 0000 -0.2292
0. 0000
0. 0000
0. 0000
0.0278
0.5057
-0.0000
0.0000
0.0000
o.0000
0.1984
-0. C0000 0.0278
0.5057
-0.0000
0.0000
0.0000
-0.1984
0.0000
-0. 0648
0.0001
0.0017
-0.4385
-0.0000
0.0000
-0 .0000
0.0000
-0. 0001 -0.0648
0.0017
0.4385
-0. 0000
0O 0000
0.0000
-0.0000
31
32
-0.0000
-0.0000
0.0000
-0.0978
0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.0001
-0.0000
0.0000
-0.0198
-0.0001
-0.0000
0.0000
-0.019 8
-0.6699
-0.0000
0.0000
-0.0181
0.6699
33
-O. 1917
-0.0000
0. 0000
0.0000
0.0012
-0.0000
0.0001
-0.0000
-0 .0000
-0. 36Z1
O0.0000
0.0158
0.0000
-0. 3621
-0. 0000
-0. 0158
0.0000
-0.3631
0.0000
0.0000
0.0158
-0.3631
-0.0000
0.0000
-0.0181
-0.0000
-0.0000
0.0000
-0.0195
0.0000
-0.0000
0.0000
-0.0195
0.0000
0. 0000
-0.0158
-0. 3528
0.0158
0. 0000
O. 0000
-0.3528
-0.0158
0.0000
0.0000
-0.0000
-0.0000
-0.0978
-0.0000
-0.0000
0.0000
0.0000G
8
9
10
11
12
-0.3000
-o0.0obo
-0.6698
-0.0000
-0.0181
13
-0.0000
14
0.6698
15
-0.0000
16
-0.0181
18
19
20
-0.0001
-0.0000
-0.0198
21
-0.0000
22
0.0001
17
-0.0000
23
24
-0.0000
-0 .0198
25
-0.0000
26
27
28
29
30
-0.0000
-0.0000
-0. 0195
-0.0000
0.0000
32
-0.0195
31
-0.0000
33
-o. 0000
19
11
12
13
14
15
-0.0002
-0.0000
-0.0000
0. 0000
-0.0000
0.0000
0.0000
0. 0000
0.9148
0.0383
-0.0000
-0.0000
-0.0383
0.9156
-0.0000
-0.0000
-0.0000
0. 0000
0. 0865 -0. 1363
0.0000
-0. 0000
-0.2401
0. 3786
0o. ooo00C 0.0000
0.0865
-0.1363
0. 000C -0. 0000
-0.3786
0.2402
0.0000
0.0000
0.0748
0.1430
0.0000
-0. 0000
0.0000
-0.0000
-0.2077
-0. 3973
0.0748
0.1430
0. 0000 -0. 0000
0. 0000 -0.0000
0.3973
0.2077
-0.1612
-0.0067
0.4490
0.0188
0.0000
-0.0000
0.0000
0. 0000
-0.0067
-0.1612
-0.4490
-0.0188
0 0000 -0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
-0. 9553
0.0000
-0.0001
-0.0000
0. 0000
0.2118
-0. 0000
0.0000
-0.0000
-0.2118
-0.0000
-0.0000
-0.0000
0.0000
0. 0000
-0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.0000
0.2156
0.0000
0.0000
0.0000
-0.2156
-0.0000
-0.0000
-0.0000
-0.0000
0.0000
0.0000
-0.0001
0.0000
0.9553
-0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
-0.0000
0.0000
-0.2115
0.0000
-0.0000
0.0000
0.2115
-0.0000
-0.0000
-0.0000
0.0000
0.0000
-0.2157
0.0000
0.0000
-0.0000
0.2157
0.0000
0.0000
-0.0000
0.0000 -0.0000
-0.0000
-0.0000 -0.0000 -0.0000
0.0000
-0.0000ooo-0.0000
0.0000 -0.0000 -0.0000
0.0063 -0.0000
-0.0000
0.0000 -0.0000
-0.0000
0.0069
0.0000
0.0000
0.0000
0.9559 -0.0000
0.0000
0.0000 -0.0000
0.0000
0.0000 -0.5170
0.0000
0.0000ooo 0.0000
0.0000 -0.0000
-0.2131
0.0000
-0.0000
0.0000
0.5170
-0.0000
-0.0000
.o000
0.0000aooo 0.0000
0.2131 -0.0000 -0.0000
0.0000
-0.0000
0.0000
-0.0000 -0.5167
-0.0000
-0.2127
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000 -0.0000 -0.0000
0.0000
0.0000
0.5167
0.2127
0.0000 -0.0000
0.0000
0.0000
-0.0000
-0.0000
0.0000 -0.0000
0.0000
-0.0000
0.0000
0.0000
0.5230
-0.0000
-0.0000
0.0000
0.5232
0.0000 -0.0000
0.0000
-0.0000
-0.0000
0.0000
-01.0000
-0.5229
0.0000
0.0000
-0.0000
-0.5233
0.0000
0.0000
0.0000
-0.0000 -0.1046
0.0000oo 0.0000
0.0000
0.0000
-0.0000
-0.0000 -0.0000
0.0000
0.0000
0.0000
0.0000
-0.000o
-0.0000
-0.0000
-0.0000
-0.0006
0.0000
0.0000
0.3942
-0.0000
-0.0000 -0.0000
-0.5203 -0.0000
-0.0000
-0.0000
0.3942
0.0000
-0.0000C
-0.0000
-0.0000
0.5203
0.0000
0.0000
0.3915
0.0000
-0.0000
0.5197
-0.0000
-0.0000
-0.0000 -0.0000
0.3915
-0.0000
-0.5197
-0.0000
-0.0000
0.0000 -0.0130
-0.0000
-0.0000
-0. oo00CO
-0.0000
-0.0000
0.0000
-0.0000
-0.00CO
-0.0000
-0.0000
-0.0000
20
21
22
23
24
27
30
0.0004
-0.0000
O.0 000
0.0000
0.0210
0.0000
0.5129
-0. 0000
0.0000
-0.0533
-0.0000
-0.3688
0.0000
-0.0533
-0 0000
0.3688
0.0000
0.0555
-0.0000
0.0000
0.3856
0.0555
-0.0000
0.0000
-0.3857
-0.0028
- 0.0183
0.000
0.0000
-0.0028
0.0183
0.0000
0.0000
-0.0000
-0.0000
0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.0000
-0.0000
-0.0000
-0.3032
-0.0000
-0.0000
0.0000
-0.3032
-0.0000
-0.0000
0.0000
-0.1252
0.0000
0.0000
-0.0000
0.0000
-0.0000
-0.0000
0.1108
-0.0000
0.4675
0.0000
-0.1108
-0.0000
0.4675
0.0000
-0.0000
0.0000
-0.0000
0. 0000
0.0000
0.0000
-0.0000
-0.3043
0.0000
0.0000
0.1114
-0.3033
-0.0001
0.0000
-0.0000
-0.3033
-0.0001
0.0000
0.0000
-0.0000
-0.1114
0.4604
0.0000
-0.0000
-0.2922
0.0000
-0.0000
0.0000
-0.2922
0.0000
-0.1239 -0.0000
-0.3043 -0.0000
0.4604 0.0000
25
0.0000
-0.0000
0.Ooo000-0.0000
-0.00
-0.0000
-0. 000
-0.0000
-0.0000
0.0000
0.0000
0.0000
0. 3228
0. 0000
-0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0. 3226
-0.0000
0.0000
-0.0000
-0.0000
0.0000
0. 00oo00
0.0000
-0.0000
0.4414
0.0000
-0.0001
0.0000
0.302 1
-0.0000
0.0000
0.0000
-0.0000
0.0000
-0.4414
-0.0000
-0.0000
-0.0001
-0.0000
0.3021
-0.0000 -0.0000
-0.0000
-0.1107
0.0000
-0.0000
-0.4419
0.0000
-0.0000
0. 0000 -0.0000
-0.4682
0.0000
-0.0000
0.1107
-0. 0000 -0.0000
-0.0000
-0.0000
0.4419
-0.0000
0. 0000
0.0001
0.0000
-0.4682
0.0000
-0.OOO
0.0000
0.0000
0.0000
0.0000
-0.000oo0
0.4324
0.0000
0.0000
0.0000
-0.4320
-0.0000
0.0000 -0.0000
0.0000
-0 .0000
0.0000
-0.0000
0.0000
0.4320
0.2921
-0.0000oo
0.1253
0.0000
-o0o0o
0.2921
-0.4324
26
-0.0000 -0.0000
-0.1023 0.0001
-0.0001 -0.1021
-0.0000
-0.0000 -0.0000
0.0000 -0.0000
0.0000
-0.0000 -0.0000
-0.0146 0.0000
0.0000 0.0000
0.4495 -0.0002
0.0002 0.3840
0.0146 -0.0000
0.0000 0.0000
0.4495 -0.0002
0.0002 0.3840
-0.0000 -0.0148
0.0000 0.0000
0.3822 -0.0002
0.0002 0.4488
0.0000 0.0148
0.0000 0.0000
-0.0000 0.3822 -0.0002
0.0002 0.4488
-0.0000 -0.0000
0.4568 0.0000 0.0000
0.4125 -0.0002
-0.0000 0.0002 0.4117
0.0130 O.0000 0.0000
0.4568 0.0000 0.0000
0.4125 -0.0002
0.0002 0.4117
28
29
-0.2452 0.00-24 0.0003 0.0000
-0.0000ooo
0.0000 0.0000 -0.0981
0. 0000 -0.0000 0.0000 0.0000
-0.0000 0. 0000 0.0000 -0.0000 0.0000
-0 0000 0.0051
0.1224 0.0051 0.0000
0 0000 0.0000
0.0000 0.0000 -0.0000
0.0004
-0.0051 0.1222 0. 0000
0 0000
0.0000
-0.0000
-0.000
-0.0000
-0.0000
0.0000 -0.0000 -0.0000
-0. 3210 -0.0000
-0.0000
0.1364 -0.2908 0.4784 0.0000
0.0000
0.0000
-0.0000 0.0000 -0.0199
-0.0000
0.3168 -0.0123 0.0189 0.0000
-0.4368
-0.0000
0.0000
0.0000
0.0000
0.1364
-0.2988 0.4784 -0.0000
0.0000
-0.0199
0.0000
-0.0000
0.0000
0.0000
-0.0000
-0. 3168 0.0123 -0.0189 0.0000
0.4368 0.0000
0.0000 -0.0000 0. 0000
0.0000 0.1365 -0.2584 -0.5007 0. 0000
0.0000 0.0000 0.0000 0.0000 -0.0199
-0.4378 0.0000 -0.0000 0.0000 0.0000
0.0000
0.3177 -0.0107 -0.0199 0.0000
-0.0000 0.1365 -0.2584 -0.5007 -0.0000
-0.0000 0.0000
O.00CO 0.0000 -0.0199
0.4378 0.0000 -0.0000 0.0000 0.0000
0.0000 -0.3177
0.0107 0.0199 0.0000
0.0000 0. 1361 0.5692 0.0239 -0.6697
0.0000
0.3087 0.0221 0.0009 -0.0182
0.0000
0.0000 -0.0000 0.0000 0.0000
-0.0000
0.0000 -0.0000 0.0000
0.0000
0.5692 0.0239 0.6697
0.0000 0.1361
-0.3087
-0.0000
-0.0221 -0.0009 -0.0182
-0.0000
0.0000 -0.0000 0.0000 0.0000
-0.0000
0.0000
0.0000 -0.0000 0.0000
-0.0000
_o-0. 0000
0 0000
-158-
TABLE IX
ptc
Eigenvectors:
6
z2
MO's Across and AO's Down
-T
EIGENVECTORS
Pt Ct.62
10
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000
0.0186
0.0006
-1.4137
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0002
-0.3020
0.0003
0.1525
0.0002
-0.0020
0.0003
0.1525
0.4827
-0.0020
-0.0001
-0.5979
-0.4827
-0.0020
-0.0001
-0.5979
-0.0063
0.0078
-0.0001
0.1525
0.0063
0.3078
-0.0001
0.1525
-0.0000
-0.02 28
1. 4137
0.0003
-0.0000
-0.0000
-0. 0000
0. 0000
0.0000
-0. 48 27
0. 00 25
0. 5978
-0.0000
0. 4827
0. 0025
0. 5978
-0.0000
-0. 0001
0. 00 25
-0.1524
0.0001
0.0001
0.0025
-0. 524
0. 0001
0.0078
-0.0096
-0.1524
-0.0000
-0.0078
-0. 009 6
-0. 15 24
-0.0000
0. 0000
-1.4135
-0.0228
-0. 0186
-0. 0000
0.0000
0.0000
-0. 0000
-0. 0000
0.0078
0.1524
-0.0096
0.0020
-0. 0078
0.1524
-0. 0096
0. 0020
0. 0063
0.1524
0. 0025
-0. 0079
-0. 0063
0.1524
0. 0025
-0. 0079
0.4826
-0.5978
0. 0025
0.0020
-0. 4826
-0.5978
0. 0025
0.0020
-1.3741
-0.0000
-0 0000
-0. 0000
-0. 0000
-0. 0000
0. 0000
-0.0000
-0.0000
0. 2 374
0. 0000
-0.3858
0. 0000
0. 2 374
0.0000
0.3 858
0. 0000
0. 2 374
0. 0000
0. 0000
-0.3858
0. 2374
0. 0000
0. 0000
0. 3858
0. 2374
-0.3858
0. 0000
0.0000
0. 2 374
0.3858
0. 0000
0. 0000
0.0000
-0.0000 0. 0000 -0.0000-0. 0000 -0.0000
-0.0000 0 0000 0.0000
0.0000
0. 0000 -0. 0000
0.0000 -0. OCOO 0.0000
0.6305 -0. 6312 -0.0000
0. 0000 -0.0000
-0.0000 -0.0000
0.9311
0. 0010
0.0009
-0.6312 -0. 6305 -0. 0000
0.0000
-0.0000
-0. 0000
0.0009
0. 0000
0.0092
-0.9311
-0.0000
0.0000
-0. 0010
0. 9311
0.0092
0.0000 -0.0000
0.1563
0. 0418
0.0000
0.0000 -0. 0000 -0. 2422
-0,0003 -0.0002
-0.4491 -0.1201 -0. 0000
0. 0000 -0.0000
-0.0000 -0. 0000
0. 000 3 -0. 2422 -0.0024
0.1563
0. 0418 -0. 0000
0. 0000 -0.0000
0. 0000 -0. 0000
0.2422
0.0003
0.0002
0.1201 -0. 0000
0.4491
0. 0000 -0.0000
-0. 0000
0. 0000 -0. 0003
0. 2422
0.0024
0. 0000
-0.0420 -0.1562
-0.0000
0.0000
0.0000
-0.0000 -0. 0002 -0.0024
0.2422
0. 0000 -0.0000
0.0003 -0. 2422 -0.0024
0.1206
0.4490
0. 0000
0.0000
-0.0000
0. 0000
0. 0000 -0.0000
-0.042C
-0. 1562
0.0000 -0. 0000
0.0002
0,0024 -0.2422
0. 0000 -0.0000 -0. 0003
0. 2422
0.0024
-0.1206 -0.4490
0. 0000
-0.0000
0.0000
-0. 1143
0. 1145
0.0000 -0. 0000
0. 3285 -0. 3289
0. 0000
0.0000
0. 0000 -0.0000
-0. 2422 -0. 0003 -0.0002
-0.0000
-0. 0000 -0.0002 -0 0024
0.2422
-0.1143
-0.0000
0. 0000
0.1145
0.0000
-0. 3285
0. 32 89 -0.0000 -0. 0000
0.0000
0. 0000 -0.0000
0. 2422
0. 0003
0.0002
0. 0000
0. 0000
0. 0002
0. 0024 -0.2422
18
19
20
21
-0.0000
-0.1389
0.0560
0.0095
0.00
0.0000
0.0000
0.0000
-0.0000
-0.0450
-0.2645
-0.1752
0.0181
0.0450
-0.2645
-0.1752
0.0181
-0.0076
-0.2645
0.1067
-0.0297
0.0076
-0.2645
0.1067
-0.0297
0.1116
0.4342
0.1067
0.0181
-0.1116
0.4342
0.1067
0.0181
0.0000
0.0010
-0.0226
0.1484
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0182
0.0020
0.0707
0.2825
-0.0182
0.0020
0,0707
0.2825
-0.1192
0.0020
-_.0431
-0.4637
0.1192
0.0020
-0.0431
-0.4638
-0.0008
-0.0032
-0.0431
0.2825
0.0008
-0.0032
-0.0431
0.2825
16
17
1
2
3
4
5
6
7
8
9
0
I1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0.000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
-0.0000
0.0000
0. 0000
0. 0000
-0.0492
0.0000
0.0390
-0.0000
-0.0492
0.0000
0.0390
-0.0000
0.0492
0.5011
0.0000
-0.0000
0.0492
0.5011
0.0000
0.0000
0.0000
-0.5011
-0.0390
0.0000
0.0000
-0.5011
-0.0390
-0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000
-0.0000
0.0000
-0.0000
-0.0000
-0.0000
0.0000
0.0000
0.0000
-0.4659
0.0000
-0.1923
-0.0000
-0.4659
0.0000
-0.1923
-0.0000
0.4659
-0.0308
-0.0000
0.0000
0.4659
-0.0308
-0.0000
0.0000
0.0000
0.0308
0.1923
-0.0000
0.0000
0.0308
0.1923
-0.0000
0.0000 -0.0568
-0.0000 -0.1374
0.0000
-0.0205
-0.0000 -0.0000
-0.0000
-0.0000
-0.0000
0.0000
0.0000
0.0000
0.0001
0.0000
0.0000
0.1104
0.1885 -0.1082
0.0000
0.4294
-0.4653
-0.0391
-3.1104
-0.0000
0.1885 -0.1082
0.0000
0.4294
-0.0391
-0.4653
-0.0000
0.0165
-0.1885 -0.1082
0.0547 -0.2616
-0.0000
0.0642
0.0000 -0.0165
-0.1885 -0.1082
0.0547 -0.2616
-0.0000
0.0642
-0.0000
0.0457
-0.0000
0.1777
-0.0547
-0.2616
0.4653
-0.0391
0.0000
-0.0457
-0.0000
0.1776
-0.0547 -0.2616
0.4653 -0.0391
31
-0.000
-0.0661
-0.0184
-0.0848
0.0000
0.0000
0.0000
0.0000
-0.0000
-0.1127
-0.0122
-0.0030
-0.0156
0. 1127
-0.0122
-0.0030
-0.0156
-0.5188
-0.0122
-0.0034
32
0. 0000
-0. 0856
0.03 11
0.0600
0.0000
-0.0000
0.0000
-0.0000
0.0000
0.190
-0.0158
0.0051
0.0110
-0.1901
-0.0158
0.0051
0.0110
0.3672
-0.0158
0.00 57
33
-0.2028
0.0000
0. 00Co
0. 0000
-0. 0000
-0. 0000
0. 000
-0. 0000
-0. 0000
-0. 3580
0. 0000
0. 0180
0. 0000
-0. 3580
0 0000
-0. 0180
0. 0000
-0.3580
0.0000
0.0000
-0.0138
0.5188
-0.0122
-0.0034
-0.0138
-0.4045
-0.0108
-0.0034
-0.0156
0.4045
-0.0108
-0.0034
-0.0156
0. 0098
-0. 3672
-0.0158
0.0057
0.0098
-0.52 39
-0.0140
0.00 57
0.0110
0.5240
-0.0140
0.0057
0.0110
0.0180
-0.3580
0. 0000
0. C00
-0.0180
-0.3580
0. 0180
0. 0000
0. 0000
-0.3580
-0. 0180
0. 0000
0.0000
-0.0000
0.0000
0. 0000
-0. 0000
-0. 0000
-0.0000
I1
12
13
-0.0000
-0. 0000
-0.0108
0. 0000
23
24
0.0000
0. 0000 -0.0000 0.0000
-0. 0000 -0.0000
-0. 0000
0.0000 -0.0000
0.5116
0.2005
0.0000
-0.0000
-0. 0000 -0.0015
0.2005
0.0000
-0.5116
-0. 0000
0.3867
0.0000
0.0030
-0. 0000 -0.0000
0.0113
0.0745
-0.U000
0.0000
-0.0016
-0.0000
0.0625
0.4130 -0.0000
-0 0000
0.0000
0.0032
0.0745 -0.0000
0.0113
0.0000
-0. 0000
0.0016
-0.0624 -0. 4130
0.0000
-0. 0000
0.0000 -0.0032
0.0589
-0.0470
0.0000
0.4217
0. 0000 -0.0000
-0.0000
-0. 0000
0.0032
0.3264 -0.2606
0.0000
-0.0000
0.05 89 -0.0470
0.0000 -0. 0000
-0.4217
-0.0000
-0.0032
-0.0000
-0. 3264
0.2606
0.0000
-0.0702
-0.0275
-0.0000
-0.3889 -0.1524
-0.0000
-0. 0000 -0. 0000
-0.0016
-0. 0000
0. 0000
0.4217
0.0000
-0. 0702 -0 .0275
0.3889
0.1524 -0.0000
-0. 0000
-0.0000
0.0016
-0.0000
0.0000
-0.4217
-0.0000
0. 0000
15
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0074
-0.0000
-0.5199
-0.0000
0.0074
-0.0000
0.5199
0.0000
-0.0001
0.5199
-0.0000
-0.0000
0.0001
-0.5199
-0.0000
-0.0000
0.0000
0.0000
-0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.5199
0.0000
-0.0074
0.0000
-0.5199
0.0000
0.0074
0.0000
-0.0030
0.0074
-0.0000
-0.0000
0.0030
-0.0074
-0.0000
-0.C000
-0.0000
0.0000
-0.0000
0.0000
-0.0000
-0.0000
-0.0000
0.0030
0.0000
-0.0002
0.0000
-0.0030
0.0000
0.0002
-0.0000
0.5200
0.0002
0.0000
0.0000
-0.5200
-0.0002
0.0000
0.0074
0.0001
0.0000
0.0000
-0.0074
-0.0001
-0.5199
0.0030
-0.0000
-0.0000
0.5199
-0.0030
-0.0030
-0.5200
0.0000
0.0000
0.0030
0.5200
0.0000
0. 0000
-0.0087
0.1114
-0. 0103 -0.0116
0. 1114
0. 0076
0. 0000
0. 0000
0.0000 0. 0000 -0.0000
0. 0000
0. 0000
0.0000
-0. 0000
-0. 0000 0.0000
-0. 0000
-0.0124
-0. 0012 -0. 0013
0.03 90 0. 0315 -0.4026
0.4277
0. 0397
0.0445
0.0402
-0.4028
-0.0276
0.0124
0.00 12
0.0013
0.0390
-0.4026
0.4277
0.0445
-0 4028 -0.0276
0.0402
-0.0012
0.0009
0.0390
-0.4026
0.4018
0.0373 0.0418
-0.0294
0.0428
-0.0009
0.0012
0.03 90
-0.4026
0.4018
0.0373 0.0418
-0. 4287 -0.0294
0.0428
-0.0010 0.0124
-0.00[2
0.0415
0. 0336 -0.4285
0.4018
0. 0373
0.0418
0.0402
-044028 -0.0276
-0.0124
0.0012
-0.4285
0.0415
0.4018
0.0418
0.0402
-0. 4028 -0.0276
25
26
27
28
29
-0.0000
0.0000
-0.0000
-0.0000
0.0000
0.3863
-0.0000
0.0014
0.0170
0.0000
0.4213
0.0000
0.0185
-0.0000
-0.4213
0.0000
-0.0185
0.0000
0.0015
0.0185
0.0000
-0.0000
-0.0015
-0.0185
0.0000
-0.0000
-0.0000
0.4213
0.0015
-0.0000
0.0000
-0.4213
-0.0015
-0.0000
-0.0000
-0.0000
0.0000
-0.0000
0.0170
-0.0000
0.0030
-0.3863
0.0000
0.0185
0.0000
-0.4213
-0.0000
-0.0185
0.0000
0.4213
-0.0000
0.0033
-0.4213
-0.0000
0.0000
-0.0033
0.4213
-0.0000
0.0000
0.0000
0.0185
0.0033
0.0000
-0.0000
-0.0185
-0.0033
-0.2713
0.0000
0.0000
0.0000
0.0000
-0.0000
-0.0000
-0.0000
-0.0000
0.1436
0.0000
0.3067
0.0000
0.1436
0.0000
-0.3067
0.0000
0.1436
00C00
0.0000
0.3067
0.1436
0.0000
0.0000
-0.3067
0.1436
0.3067
0.0000
0.0000
0.1438
-0.3067
0.0000
0.0000
-0.0000
0.0000
-0.0000
0.0000
0.0744
0.0000
-0.1126
-0.0000
-0.0000
-0.5629
0.0000
-0.0000
-0.0000
0.0000
0.0000
-0.1126
-0.0000
-0. 0744
-0.0000
-0.0000
-0.0339
-0.0000
0.0000
-0.5629
0.0000
0.0210
0.0000
0.2521
0.0000
-0.0000
0.0094
0.2521
0.0000
-0.0000
-0.0094
0.3108
0.0116
-0.0000
O.00O0
0.3108
-0.0116
-0.0000
0.0000
0.0000
-0w0339
-0.0000
0.0013
-0.0000
0.5044
-0.0000
0.0000
0.0188
0.5044
-0.0000
0.0000
-0.0188
-0.4705
-0.0175
0.0000
0.0000
-0.4705
0.0175
0.0000
-0.0000
-0.0000 0.0000 -0.0000
-0.0000 0.0000 0.0000 -0.0000
0.0000 0.0000 -0.0000 0.0000
22
14
0.0000
-0.1112
-0.0111
-0.0000
0.0000
-0.0000
0.0315
0.0397
0.0124
0.0315
-0.4287
-0.0124
0.0315
0.0010
0.0336
0.0373
-0.0210 -0.0013
30
0.0000
0.0140
0.1029
-0.0333
0.0000
-0.0000
-0.0000
0.0000
0.0000
0. 6298
0.0026
0. 0168
-0. 0061
-0.6298
0.0026
0.0168
-0.0061
-0.2037
0.0026
0.0189
-0.0054
0.2037
0.0026
0.0189
-0.0054
0.0858
0.0023
0.0189
-0.0061
-0.0858
0.0023
0.0189
-0.0061
-16o0-
TABLE X
MOEnergies and Occupations
o0
1II
0
0
I
0
0
I
N
N
N
?0a,M N
LA
1
4r
LA
0I
1
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.0
LA
I
LA
II
LA
II
0
I
-.
n
LA~
4'
0i
--d
U
0
I
I
H!-
0
0
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N
N
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N
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4
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I
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HI
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;
If
,o
H-
co
I
LA
0.
0
"'
I
It
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I-a'1
a,
LA
0d
I
N
N
N
N
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4
N
Ia,
0
PIt
r
a'
H4
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N
N
N
N
N
N
N
N
LA
0
0
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o
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Po
0
-.
L
LA
.
.0a-2
a,
laN
v
0
0
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LA
0'
.0
0
-
LA
L
.
N
I
I
II
II
II
II
N
LA
-
4
N
N
N
N
N
LA
4
H.0
N
N
0
0
04
4t
N
N
N
N
0m
N
0'
0
0
0
N
N
N
N
I
.- .- a, N
LU
0
0
I
I
IL
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I
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o
N
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4
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o
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a
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0
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H.-
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it
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It
it
N.
LA
4.
LA
-
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0
,
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N
N
II
I
4
0
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.0
0
0
.0
0
0
I
I
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III
I
0U
0
-
N
N
N
N
N
N
N
N
N
'0
0
4
-
.0
0
4
H-
-4
H-
0
0'
a'
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LA
N
0
.
0
0
.
0
H-
0I
n
N
N
N
N
a'
4
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..0
I-
0
i
N
N
N
L
N
In
N
N
N
N
Wj
0
a'
l
I
oI-I
u
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a,
N
I
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0
N
II
u
uJ
I
iJ
N
N
N
N
0
.0
a'
H-
.0
N'l
4
4t
0
LA
a'
LA
N
.0
N
.0
-4
0
N
"
N
N
II
I
II
'4
N1
LA
N
N
N
N
0
'0
.0
0
IN
N
.
a0
N
N
N
N
a'
N
0
4
LA
'0
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m
D.
6
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A
LA
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t1-Y
4
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4
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00
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H-
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LA
.
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I
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5,
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0
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0
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0
0
0
o'
H.-
a'
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0~
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w
o0
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o
o0
o0
4
'0~
LAI0
N.
LA
0
H0
4
oCa
LA
MI
0-
10
N
N
0'
I
N
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HH-
L
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I
#4
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I
of
;-00'O-4
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.
L
A
I
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N
N
N
N
N.
0
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.
.
o
0
LA
LA
I
I
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II
o
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0
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N
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I
#
LA
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P-
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~=1=
;; 4L
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7
0
140
HI
I
LA
0,
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0
N
N
N
0
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a'4
0
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I
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i
N
N
wJ3
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N
N
.
N
N
N
N
VI
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N
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44
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N
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4,
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.
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11
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iz
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H0'
0
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4
4
4
4
4
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N
,
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w
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N
N
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0'0
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I
LA
LA
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N
4
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4
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II
II
II
11
I
Ili
N
I
4;
N
N
I0
0
11
1
1
N
I
0
W
I
I
I
II
II
II
L
LI
LA
0
0;
N
"I
aJ
00
k-./
cm)
N
44
I
I
H,
gm
N
NN
44
0
N
4
N
N
44
I
0
I
0
I
N
a0
0'
0
m
o0
o0
L
40
4
40
t.L
P-
0' 0
a' 0'
.
44
44
44L'
N
N
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4
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4
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H 0
0 0
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0,
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0
0,
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H-
..# 04 .-
0 0'
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#40
40
#
44
I~~~~~~~~~~~~~~.
,I
44 44
.44
0
44 r
-
P
0
4
0
40
4
0
N
N
N
0
I
ND
0
W
D
.
0
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4
0
0
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a,
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le
0
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944
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-44
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I,
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.44
N
fV
0'
0
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#0
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N
4
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4
N
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in4
t
N
40
a
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4?
in"
W
In
00 4
I*
0
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,1
.44
N
.44
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N
4
0
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*.
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1-
40
(44
40
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44
lI
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44
44
7
N
4
w
N
0
4'4
Ag 0
40
Ne
40
H
944
4
0
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to
0'
40
N
1
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444 4
N
.44
N
0.
N
40
A
H
0%
0
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N
N
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4
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40
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-~~~~~~~~~~~~~~~~~~
H0
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P-..
4
Wo
..
T
-162-
TABLE XI
ReCl 2
Mulliken Overlap Populations:
AO's Down and Across; ReCl1e2
Bond Order Matrix
MUlLIKEN
POPULAT IONS
CVERtAP
OR
3! EUBCTRRNS
10
1l
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
062793
0
-0
-0.
-0
O'
0O
0
0.
0.0228
0.
010778
0.
0.0228
0.
0.0807
-0.
-0.
0.
0.
0.
0.
0.
-0.
-0.C046
-0.
-0.
0.
-0.
-01
0s0607
-C;
-0,
0
-0.
0.
-0.
0.0527
0.
C.12C4
-0.
0;0527
-0.
-0.
-0.
0.0807
-0.
04
-0.
-0.
-0.
0.
-0.
-C.
-0.0046
0.
-0.
0.
-0.
-0.
0.81084
-0.
-0.
-0.
-0.
0.0048
-0.
C.C356
-0.
0.0048
0.
OJ
0O
04
-0.
2,1882
O
O
0
0Z
0.0062
O;
04
O;
0.
O;
-0.
-0.
-0.
04
0.8184
O
0.
0.0144
0.
0.1067
0.
0.0144
0.
0.
O.
-0.
-0o
0a
0.
2.1882
-0.
0.
-0.
0;
-0.
-0.
O
O
-04
-O
-0o.
O;
O
-04
241882
-o
O
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0JO062
O
040228
-04
040527
04
040048
04
040144
04
-04
347736
-04
O
-04
-040000
O
-0J0046
O
-O
-0.
040062
O
-04
O
-O
349715
O
-04
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C40778
-C4
CJ1204
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C0356
C
CJ1C67
@4
-04
04
O
8404C0
Ca
-0J001
04
-04
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-0C046
-0.
C.
041
-4
@0062
-0
-@
04
34?97.5
-@4
040228
04
0J0521
04
0J0048
01
0J0144
-'04
O
'040000
-'O
-0JO0l
-04
347736
-04
-040046
-01
01
-Oa
040083
OJ
O
O
-04
030000
-03
O
-OJ
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0.
0.0778
-0.
0.0228
0,
0.
0.0778
0,0228
0.
-0.
0.0778
0.0228
0.0778
0.
0.
0.0228
0.0778
0.
0.
-0.0046
-0.
0.
-0.
-0.0046
-0.
-0.
0.
-0.0046
0.
0.
0.052?
0.1204
-0.
-0.
0.0527
0.1204
0.
0.
-0.
C12C4
-04
-0.
0
-0,C046
0.
0.
-0.
-0.C046
-0;
-0.
-0.
-0.C046
-C;
0.
-0.
-C.CC46
O
0.
-0.
-0.0046
C.0527
-0.
-0.
041204
0.0527
-0.
-0.
0.1204
-0.
0.
0.
-0.0046
C.
-0;
-0.
-0.0046
-0.
0.0356
.
0.0048
-0.
-0.
O
0.0356
C.0048
-0.
-0.
0.0356
0.0192
0.1423
-0.
0.
0.0192
0.1423
-C.
-0.
0;0062
O
-04
O
-04
O
0.
-04
-0,
O
0.
04
0.0062
-04
-0.
04
0.0062
-04
04
0.1067
-04
0.0144
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0.
0.1067
0.0144
-0.
-0.
0.1067
0.
0.
0.
0.
0.
O;
-0.
-04
O
-0.
-0.
0.
0.0062
0.
0.
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0.0062
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0.
0.
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0.0062
0.
O;
-0.
040062
04
O
0J0062
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0J0062
04
-04
O
0J0062
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O
O
O
O
-04
O
O
-04
-04
-040001
-04
-040003
-04
-040016
-0400100
-040003
-04
-040086
-040010
-040003
-0400O1
-OJO016
-04
-040003
-040010
-040016
-04
Oj00
-O
O
-O
-OJ0003
-O
-04
-04
-OJO003
OJ
O
-OJOO16
-040038
-00077
O
-0J0016
-OJO038
-OJ0077
O
-@4
-C4@@20
-@4
-C0010
C
-CJCO8
-CJ0002
-040010
-@4
-@J0038
-@J0002
-@40010
-CJC02
-CC038
-@4
-040010
-@CC02
-00O38
04
04
-04
040@0
-J4OO6
-04
-J0o17
-@J0038
-4-0016
-@4
-0JC01?
-04C038
-04
-04
-0J
-0400
0J
-0J
0J
-0J0003
-04
_04
04
-4040003
04
-OJO0
404O010
-040003
04
-'400&6
-0JOO4
-040003
-OJO10
-OJOO16
-40J
40JO003
-40JO00
-0JOOi
404
349715
-O
-04
O
-030003
0.
04
-OJ
-010003
04
-03
-040016
-010038
-0.0077
04
-040016
-010038
-OJO071
-04
22
1
2
3
4
5
7
6
.
8
9
16
17
18
19
20
21
23
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
0.0778
-0.
0.1204
-0.
0.0356
0.
0.iC67
-0.
0.
-0.0101
-0.
-0.
0.
-0.
-0.0046
0.
-0.
-0.
-0.
0.0062
-0.
0.
0.0228
-0.
-0.
C.0527
040048
O.
0.0144
0.
-0.
-0.0003
-0.
0.
-0.0046
O;
-0.
-04
-0.
-0.
0.0062
0.
-0.
-040003
0.
-0.
-0.0046
-0.
-0.
0.
0.
0.
0.0062
-0.0016
-0.
040778
-0.
0.
0,1204
00356
0:
0.1067
0.
0.
-0.0010
-04
0.0228
0.
0.
040527
0.0048
0.
0.0144
-0.
-0.
-0.0003
-- 0.
0.
-0.0046
-0.
-0.
-0.
-0.
-0.
0.0062
0.
-0.
-0.0003
-04
O
-040046
-O
-04
-04
-04
-04
040062
-040016
O
040778
041
-04
041204
040388
04
041067
04
-04
-040010
04
040228
0J0527
-O
-O
003OO2
O
O
04
O
-OJ0003
-040016
0J0718
0J204
-@4
@4
01423
04
C
-04
04
-OCO10
-C40038
04
-04
-C@4046
04
-04
C0062
04
-CJ
04
-0OO16
-040037
OJ
-0i
-OJ
_-0J0046
04
404
04
0JO02
04
-'04
04
040228
030527
04
O
030192
-01
04
OJ
-04
-010003
-030016
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0.
-0.
-0.
3.0400
0.
-O.OC10
0.
-0.0C38
-0.0002
-0.0010
-0.
-0k0038
-0.0002
-0.0010
-0CC02
-0.0C38
-0.
-0.0010
-0.0C02
-0.0038
0.
0.0000
0.
-0.
0.
3.9715
-0.0016
0.
-0.0077
-0.0038
-0.0016
-0.
-0.0077
-0.0038
0.
-0.
-0.
-0.0003
-0.
0.
0.
-0.0003
-0.C016
-0.0003
0.
-0.C010
-0.C016
3.7737
-0.
0.
0.
-0.C000
-0.
0.
-0COOl
-0.003
-0.C010
C.
-040016
-0.C003
-C.0010
0.
-0;0016
-0.
0.
-0.0003
0.
0.
-0.
3.9715
0.
0.
-0.
0;0000
-C.
0
-0.0016
-040038
C.
-0.0077
-0.0016
-0.0038
-0.
-0.0077
-0.0077
-O.CO16
0.
-0.0038
-0.0077
0.
0.
3.9715
-0.
-0.
0.
C.0000
-0.
-0.
0.
-0.0003
0.
0.
04
-0.0003
-0.
-0.0038
-0,0010
0.
-0.0C02
-C.0038
0.
0.
-0.
340400
-0.0001
O
-0.
-040020
-0.0010
-0.002
-0.
-040038
-0.0010
-0.0002
0.
-040038
-0.0016
-C.0003
-0.
-0.0010
-0.0016
-0.0000
-0.
-0.
-0.COO1
3.7737
-0.
-0.
-0.
-0.0003
-0.0010
0.
-0.0016
-0.0003
-0.0010
0.
-0.0016
-0.
0.
-0.0003
-0.
-0.
-0.
0.0000
0.
O.
-0.
3.9715
0.
-0.
-0.0016
-0.0038
-0.
-0.0071
-0.0016
-0.0038
-0,
-0.0071
-0077
-040016
O
-040038
-O400TT
04
-0.
040000
-04
-04
O4
849715
-04
-04
-04
-040003
O
-0.
-04
-040003
0.
-040038
-040010
-04
-040002
-040038
-040001
04
-04
-040020
-04
-04
-04
340400
-O40010
-040002
-0
-0;0038
-040010
-040002
0
-0;0038
-O
-040003
-040016
-040010
O
-OOO03
-OJOO16
-04
-0JOOO
-040003
-040016
-04
-040010
847737
O
-0
O
-OJO000
-040001
0.
-04
-@4
-040010
-@JC038
-C002
-C
-C40IO
-C0038
O
-0CC02
-0CO1
-CC038
-,.
-CJCC02
C
8ic4CO
C
C
-00jC01
-CCC20
C
-@4
-@4
-0J006
-C00T
-040088
-@4
O
14
-@C003
-C
04
-C
-040003
-C
-@4
@4
349715
-@4
@.
@
C.
00CCO
-04
4040008
-0J
0J
-'O
0J003
-0J0086
~0400vy
OJ
-'04008
'0OO16
40JO01
04
-0JOO88
04
O
-04
349718
-OJ
01
-00003
-030016
-0.0010
-03
-040003
-030016
03
-030010
-030003
-030016
-Oj
-O10010
-010000
-O10001
01
-01
347737
-01
O;
-01
31
32
33
0.0778
0.1204
-0.
-0.
0.1823
0.
0.
0.
0.
-0.0010
-040038
-0.0002
-01
-0.0010
-01.C038
-0.0002
04
-O.OCIO
-0.0038
0.
-0.0002
-O.CCIO
-0.CC38
-0.
-0.0002
-0.0001
-0.0020
0.
0.
-0.
3.0400
0.
0.
0.
0.
-0.0046
-0.
-0.
0.0062
-0.
-0.
0.
-0.0016
-0.0077
-0.0038
0.
-0.0016
-0.C077
-0.0038
0.
0.
-0.
-0.C003
0.
0.
-0.
-0.C003
0.
0.
0.
0.0000
-0.
0.
0.
3.9715
-0.
0.
0,
0,
-0.046
-0.
-0,
-0C
0.0062
-0.
-0o.
0.
0,
-0;C003
-0.
-0.
C;
-C0003
-0.0016
-040077
-0.
-0.0038
-0.0016
-0.0077
0.
-0.C038
-0.
-C.
-0.
0.OCCO
-0.
0,
-0.
3.9715
12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0.0020 -0.
-0.Coo
0.
-0.003e -0.0002 -0.0010 -0.
RErUCED
1
2
3
4
5
6
7
1
8k7226
0.4383
0.4383
0.4383
0.4383
0.4383
04383
-oo038 -040002 -040010 -40002 -040088 -'04
OVERLAP POPULATION
2
0.4383
14.7566
-0.0022
-0.0212
-0.0212
-0.0212
-0.0212
3
0.4383
-0.C022
147566
-0.0212
-040212
-0.0212
-010212
4
0.4383
-C.0212
-0.02t2
1447566
-040022
-010212
-0;0212
MATRI
AtOM BY ATOM
5
0.4383
-C.0212
-0.0212
-0.0022
14;7516
-0.0212
-040212
6
0J4383
-0J0212
-040212
-@40212
-040212
1447566
-040022
7
04383
-0.0212
-040212
-0.0212
-040212
-0.0022
1'47516
-04
JC0
-OJO010
-164-
TABLE XII
OsCl8 2 '
Mulliken Overlap Populations:
AO's Down and Across;
OsCl62 ' Bond Order Matrix
MULLIKEN OVERLAP POPULATIONS
1
2
-0.
-0.
-0.
-0.
0.1173 -0.
-0.
0.
-0.
-0.
0.
0.
-0.
0.
0.
0.
-0.0028
-0.
0.
0
-0.0028
-0.
-0.
-0.
-0.0028
-0.
-0.
-0.
0.
-0.
0.
0.
0.9681
-0.
-0.
0.
0. 0842
0.0225
0.
-0.
0. 0842
0.0225
0.0842
0.
-0.
0 0225
0.0842
-0.
-0.
-0.
-0.
16
1
2
0.3457
-0.
-0.
0.1168
3
-0.
-0.
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-0.
-0.
O.
0.
0.
0.
0.0225
0.
0.0842
-0.
0.0225
0.
0.0842
0.
0.0225
0.
0.
21
22
23
24
25
26
27
28
29
30
31
32
33
~-5.*
6
8
9
10
11
0. 0225
0.
0.0601
-0.
0.0030
0.
0.0091
0.
O.
3.7751
-0.
0.
-0.
0.0000
0.
-0.0001
0.
-0.0004
0.
-0.0018
0.
0.0842
-0.0028 -0.
0.
0.1416
-0.
-0.
0.
0.0312
0. 0069
0.
0.
0.0936
-O:
0.
-0.
-0.
0.
-0.
0.
3.9749 -0.
-0.
2.9450
-0.
-0.
-0.
-0.0001
0.0000 -0.
-0.
-0. 00 19
O.
0.
-0.
-0.0014
-0.0003
0.
0.
-0.0041
-0.
0.
0.
-0.
-0.
-0.0003
-0.
-0.
-0. 0018
-0,0041
-0.0041
-0.0018
0.
-0.0075
-0.0041
-0.
-0.
-0.
26
0. 0225
0. 0600
-0.
-0.
0. 0122
0.
-0.
0.
0.
-0.0004
-0.0018
-0.0014
-0.
-0.0004
-0. 0018
-0. 0014
0.
-0.0004
-0. 0018
0.
-0,0014
-0. 0004
-0.0018
0.
-0.0014
3.7753
0.
-0.
0.
0.0069
0.
0.13312
-0.
-0.
0.(3030 -0.
0.
0.0069
0.
0.1 0312
0.
0.
0.
0.(0030
-0.
-0.
-0.
0.
-0.0028
-0.
0.
-0. 0028
-0.
-0.
0.0600
-0.
0.1413
-0.
-0.
-0.0028
0.
0.
0. 0600 -0.
0.1413
0.
-0. 00 28
0.
-0.
-0.
0.1415
0.0601
0.
0.
0.1415
-0.
0.
0.
-0.0028
0.
0
-0.
-0.0028
0 .0312
0.
0,0030
O.
-0.
0.
O.
0.0 312 0.
0 .0122
0.
O:
0.1245
0.
-0.
-0.
0.
0.0 122
0.1245
0.
-0.
0.0067
0.
-0.
0.0935
0.0091
-0.
-0.
0.0935
-0.
0.
-0.
0.
-0.
0.
-0.
-0.
-0.
-0.
-0.0138
-0.
-0.
0.
-0.
0.
-0.0138
0.
-0.
-0.
-0.0138
0.0068
-0.
O.
0.
-0.
0.
-0.
0.
-0.
0.
-0. 0014
-0.0004
-0.
-0.0018
-0. 0014
-0.0004
-0.0014
-0.0018
0.
-0.,0004
-0 0014
-0.0018
0.
17
19
20
21
22
23
24
25
0.
-0.
-0.0028
-0.
-0.
0.
0.
0.
0.0068
-0.0018
0.
-0.0041
-0.0075
-0.0018
0.
-0.0041
-0.0075
0.
0.0842
-0.
-0.
0.1415
0.0312
0.
0.0935
-0.
0.
-0.0014
-0.
-0.0005
-0.0041
-0.0014
0.
-0.0005
-0.0041
0.
0.0225
0.
-0.
0.0601
0. 0030
0.
0.0091
-0.
-0.
-0.0004
0.
-0.0028
-0.
O.
-0.
O.
-0.
-0.0 138
-0.
-0.
-0.0003
- 01.
-0.
-0.
-0.
-0.0014
-0.0018
o.0000
-0.
-0.
-o0.
0001
3.7751
0.
-0.
-0.
-000003
-0.
0.
-0.
-0.0 000
-0.
-0.
-0.
4.0 365
0.
-0.
-0.0 018
-0.0041
0.
-0.0 052
-0 .0 018
-0.0041
-0.
-0.0 052
O.
0.0601
0.
0.1416
0.
0.0601
0.
0.1416
-0.
-0.
-0.0028
-0.
18
-0.
-0.
0.
-0.
-0.0028
0.
0.
0.
0.
0.0068
0.
0.
0.
0.0000
0.
-0.
-0.
3.9752
-0.0018
-0.
-0.0075
-0.0041
-0.0018
0.
-0.0075
-0.0041
0.
0.
-0.
-0. 0003
-0.
0.
0.
-0. 0003
0.0225
0.
-0.
-0. 0028
-0.
0.
0.0601
0.
0.0030
-0.
0.
-0.
0.0091 -0.
-0.
-0.0138
-0.
0.
-0. 0004
0.
-0.
-0.000 3
-0.00
14
0.
-0.0018
-0.
-0.0004
-0.
0.
-0.000
3
-0.00
14
0.
-0. 0018 -0.
3. 7751 -0.
-0.
4.0365
0.
0.
0.
0.
0. 0000
-0.
-0.
-0.
-0.
0.:
-0. 0004 -0.0018
-0.0014
-0.0041
0.
0.
-0. 0018 -0.00
52
-0. 0004 -0. 0018
-0.0014
-0.0041
0.
-0.
-0. 00 18 -0.00O52
1
2
3
4
5
6
31
00842
0.1413
0.
O.
0. 1245
0.
32
-0.
0.
-0.0028
-0.
-0.
0. 0067
33
-0.
-0.
-o
-0. 0028
0.
-0.
-0.
-O
-0.
-0.
-0
-0.
-0.
-0.0138
0.
0.:
0.
-0.
-0.0003
-0.
0.
-0.
-0.,0003
-0 0018
-0.00
52
0.
-0.0041
-0. 0018
-0.0052
-0.
-0.0041
-0.
0.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.
ELECTRONS
-0.
-0.
-0.0028
-0.
0.
-0.
-0.0028
0.0601
0.
-0.
O.
0.1172
0.
0.
-0.
-0.
0. 0842
-0.
0.1416
-0.
0.0312
0.
0.0936
0.
o.
-0.C001
-0.
-0.0019
0.
-0.
-0.
2.9450
-0.
-0.0014
0.
-0.0041
-0.0005
-0.0014
-0.
-0. 0041
-0 0005
-0.0014
-0.0005
-0.0041
0.
-0.0014
-0.0005
-0.0041
-0.
0.
-0.
9 O.
-0.0014
-0.0041
-0.0005
-0.
-0.0014
-0.0041
-0.oo5
0.
-0.0014
-0.0041
-0.
-0.C005
-0.0014
-0.0041
0.
-0.C005
-0. 0001
-0.0019
0.
-0.
-0.
2.9483
-0.
0,
7
0.
52
0.
-0.
O.
-0.
0.
-0.
-o.
0.
-o.
0.
0. 9717
0.
0.
4.0552
O.
0.
0.0091
0.
0.
-0.
0.0936
0.
-0.
-0.
0.0091
0.
0.
-0.
0.0936
0.
0.
0.
0.0091 -0.
-0.
-0.0138
0.
0.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
7
8
6
FOR
-o
0018
0075
0041
-0. 0018
-0 0075
-0. 0041
0.
0.
-0.: 0003
0.
0.
-0.O:
-0.0003
0.
0.
0.
0.0000
0.
0.
-0.
3.9761
0.
-0.0001
-0.
-0.0000
-0.
0.
0.
4.0365
-0.
O.
0.
0.
-0.
-0.
2.1524
-0.
0.
O.
0.
0.,3030
-0.
3.9753
-0.
-0.
-0.
0.0000
0.
0.
-0.
-0.0003
0.
· 0.
-0.
-0.0003
0.
-0.
2.9452
-0.0001
-0.
-0.
-0.0019
-0.0014
-0.0005
-0.
-0.0041
-0.0014
-0.0005
0.
-0.0041
-0. 0004
-0.0014
-0.
-0. 0018
-0. 0004
-0.0014
-0.0004
-0. 0018
0.
0.
0.
-0.
-0.
0.
0.
0.
2.1532
0.
-0.
0.
0.0068
0.
-0.
0.
0.0068
-0.
0.
0.0068
0.
-0.
-0.
0.0842
O.
-0.
-0.0028 -0.
0.
0.1415
O.
0. 0312
-0.
0.
-0.
0.0935
-0.
-0.
0.0068 -0.
-0. 0018
-0.0014
-0.
-0.
-0.0041 -0.0005
-0. 0075
-0.0041
-0.0018 -0.0014
-0.
0.
-0.0041
-0.0005
-0. 0075 -0. 0041
-0.
-0.0001
-0.
0.
0. COO0
O.
-0.
-0.0019
-0.
-0.
0.
-0.
3.9753
0.
0.
2. 9452
O.
-0. 0014
0.
-0. 0005
-0. 0003
0.
-0.
-0. 0041
-0.
-0. 0014
0.
-0.0005
-0. 0003
0.
-0.
-0. 0041
REDUCED OVERLAP POPULATION
1
1
2
3
4
5
6
7
10.9977
0.4535
0.4535
0.4328
0.4328
0.4321
0.4321
2
0. 4 535
14. 6 702
-0.0020
-0.02
31
-0.0231
-0. 0231
-0. 0231
3
0.4535
-0.0020
14.6702
-0.02 31
-0.02 31
-0.02 31
-0.023
1
12
-0.0075
-0.
-0. 0018
-0.0041
-0.0075
0.
0.
0.000
-0.0001
0.
-O
13
5
0. 4328
-0.0231
-0.0231
-0.0020
14.7321
-0.0208
-0.0208
15
0.0225 0.
0.
-0.0028
0.0601
0.0030
-0.
0.0091
-0.0004
-0.0018
0.
0.
0.
0.0069
0.
-0.
-0.
O.
0.0000
-0.
O.
0.
3.9749
-0.
-0.
0.
-0.0003
0.
-0.0003
-0.0014
-0.0004
-0.
-0.0018
-0.0014
-0.0004
-0.0014
-0.0018
-0.
-0.0004
-0.0014
-0.0018
-0.
0.
-0.
-0.0003
-0.
.
-0.0018
-0.0041
-0.0075
-0.
-0.0018
-0.0041
-0.0075
0.
27
28
29
30
0. 0842
0.1413
-0.
0.
0.1245
0.
O.
-0.
O.
-0. 0014
-0.0041
-0.0005
-0.
-0. 00 14
-0.0041
0.
-0.
-0.
0.
0.0225
0.0600
-0.
O.
0.0122
0.
-0.
0.
-0.
-0.0004
-0.0018
-0.0014
0.
-0.0004
-0.0018
-0. 0014
-0.
-0.0004
-0.0018
0.
-0.0014
-0 .0004
-0.0018
-0.
-0.0014
0.0000
-0.0001
0.
-0.
3.7753
-0.
-0.0005
-0.0014
-0.
-0.0041
-0.0005
-0.0014
-0.0005
-0.0041
0.
-0.0014
-0. 0005
-0.0041
-0.
-O.OO05
0.
-0.0014
-0.0041
-0.
-0.0005
-0.0014
-0. 0041
0.
-0.0005
0.
2.9483
0.
-0.
-0.0001
-0.0019
0.
0.
-0.0o028-0.
-0.
-0.
-0.
-0.
0.0068
-0.
-0.
-0.
3. 9752
-0.
0.
0.
0.0000
-0.0018
-0.
-0.0075
-0.0003
0.
-0.
0.
-0.0028
6
0.4321
-0.0231
-0.0231
-0.0208
-0.0208
14.7361
-0.0020
0.
0.
0.0000
-0.
-0.0001
-0.
3.7751
0.
-0.
0.
-0.
0.
0.
-0.
-0.0028
-0.
0.0067
-0.
0.
-0.
-0.0018
-0.0075
-0.0041
-0.
-0.0018
-0.0075
-0.0041
-0.
0.
0.
-0.0003
-0.
0.
0.
-0.0003
0.
-0.
0.
3.9761
0.
0.
0.
0.0000
-0.
0.
0.
-0.0138
0.
O.
-0.
O.
-0.0003
-0.
-o.
0.
-0.0003
-0.0018
-0.0052
0.
-0.0041
-0.0018
-0.0052
-0.
-0.0041
0.
-0.
0.
4.0365
-0.
-0.
-0.
-0.0000
MATRIX ATOM BY ATOM
4
0.4328
-0.0231
-0.0231
14.7 32 1
-0.0020
-0.0208
-0.0208
14
7
0. 4321
-0. 02 31
-0.0231
-0.0208
-0.0208
-0.0020
14.7362
0.
-0.
-166-
TABLE XIII
IrC162-
Mulliken Overlap Populations:
AO's Down and Across; IrCle 2 - Bond Order Matrix
OVERLAP POPULATIONS
MULLIKEN
FOR
53
ELECTRONS
-" C.L
1
1
2
3
4
5
6
7
8
10
11
12
13
14
15
16
17
8
19
20
21
22
23
25
26
27
28
29
30
31
2
-0.
0.
0.
-0.
0.
-0.
0.
0.
0.0253
0.
0.0871
0.
0.0253
0.
0.0871
-0.
0.0253
0.
-0.
0.
0.
-0.0009
0.
0.
0.
-0.0009
0.
-0.
-0.
-0.0009
0.0871
0.0253
0.
-0.
0.
0.0871
0.0253
0.0870
0.
-0.
0.0253
0.0870
-0.
0.
-0.0009
0.
0.
-0.
27
28
29
30
31
32
33
0.
0.
-0.
0.
0.
-0.
0
0
0.0101
-0.
0.1022
0.
0.0101
-0.
0.1022
-0.
0.0101
0.
4063
0
0.
0.
0.
0.
-0.
0.
-0.
0.
-0.
-0.0168
0.
0.
2.2421
0.
-0.
0
-
0.0101 -0.
-0.
0
0
-0.0009
0.
0.
0.
0.0034
0.
.
0.
-0.
-0.
4.0360
-0.
-0
0.
-0.0000
-0.0019
-0.
-0.
-0.018
0.
0.0000
0.
-0.0001
-0.
3.7316
-0.
0.1022 0.
0.
0.
0.
-0.0168
0.
-0.
0.
-0.0168
0.
0.
0.
3.7316
0.
0.
0.
0.0000
-0.
-0.0001
-0.
-0.0004
0.
0.
3.9462
0.
-0.
0.
0.0000
-0.
-0.
0.
-0.0003
0
0.0
0.
0.
2.8437
-0.
-0.0001
-0
-0.0021
0.
-0.0013
-0.
-0.0044
-0.0019
-0.
-0.0051
-0.0044
.
-0.
0.
-0.0003
-0.
-0.
0.
-0.0003
17
18
19
20
21
22
23
24
25
26
27
-0.
-0.
0.0253
-0.0.
-0.
0.
-0.0009
0.
0.
o.
-0.0009
0.0871
-0.
-0.
0.0253
o.
0.
0.
-0.0009
-0.
-0.
0.
-0.0009
0.0871
0.
-0.
-0.
-0.0009
0.
-0
-0.
0.
-0.0168
-0.
-0.
0.
-0.0000
0.
-0.
-0.
4.0360
-0.0019
0.
-0.0051
-0.0044
-0.0019
0.
-0.0051
-0.0044
-0.
0.
-0.
-0.0003
0.
0.
-0.
-0.0003
0.0709
0.0034
0
0.0101
-0.
0.
-0.0004
0.
-0.0013
-0.0019
-0.0004
0.
-0.0013
-0.0019
3.7316
0.
-0.
0.
0.0000
-0.
0.
0.
O.
-0
0.
0.
-0.0168
-0.0019
0.
-0.0044
-0.0051
-0.0019
-0.
-0.0044
-0.0051
-0.
0.
4.0360
0.
0.
0.
-0.0000
0.
O.
0.
-0.0003
-0.
0.
0.
-0.0003
0.
0.1505
0.0340
0
0.1022
-0.
-0.
-0.0013
-0.
0.0006
-0.0044
-0.0013
-0.
0.0006
-0.0044
0.
0.
0.
2.8442
-0.0001
0.
-0.
-0.0021
-0.0013
0.0006
0.
-0.0044
-0.0013
0.0006
-0.
-0.0044
0.0709
0.0034
0
0.0101
-0.
0.
-0.0004
-0.
-0.0013
-0.0019
-0.0004
-0
-0.0013
-0.0019
0.0000
-0.
0.
-0.0001
3.7316
-0.
0.
-0.
-0.0004
-0.0013
-0.
-0.0019
-0.0004
-0.0013
-0.
-0.0019
-0.
0.
0
0.
-0.0168
0.
-0.
-0.0003
0.
-0.
-0.
-0 .0003
-0.
0.
-0.
-0.0000
0.
0.
-0.
4.0359
0.
0.
-0.0019
-0.0044
-0.
-0.0051
-0.0019
-0.0044
O.
-0.0051
0.
-0.
0
0.
-0.
-0.0168
-0.0019
o.
-0.0044
-0.0051
-0.0019
-0.
-0.0044
-0k0051
-0.
0.
-0.0000
-0.
0.
0.
4.0360
-0.
0.
-0.
-0.0003
-0.
0.
-0.
-0.0003
0.
0.1505
0.0340
0.
0.1022
-0.
.
-0.0013
0.
0.0006
-0.0044
-0.0013
0.
0.0006
-0.0044
-0.0001
0.
0.
-0.0021
-0.
0.
-0.
2.8442
-0.0013
0.0006
0.
-(.0044
-0.0013
0.0006
-0.
-0.0044
-0.
0.0134
-0.
-0.
0.
0.
-0.0004
-0.0019
-0.0013
0.
-0.0004
-0.0019
-0.0013
-0.
-0.0004
-0.0019
0.
-0.0013
-0.0004
-0.0019
0.
-0.0013
3.7314
0.
0.
-0.
0.0000
-0.0001
-0.
0.
0.
0.0000
0.
0.
0.
3.9429
-0.
-0.
-0.0001
-0.0004
-0.0013
-0.
-0.0019
-0.0004
-0.0013
O.
-1.0019
33
-0.
0.
0.
. -0.0009
0.
0.
-0.
-0.0168
-0.
0.
-0.
-0.
-0.0003
-0.
-0.
-0.
-0.0003
-0.0019
-0.0051
0. 04
-0.0044
-0.0019
-0.0051
0.
-0.0C44
0.
0.
0.
-0.0000
0.
0.
-0.
4.0359
0.
-0.0168
0.
0.
-0.0003
-0.
-0.
-0.
-0.0003
-0.
0.
0.
4.0359
0.
0.
-0.
-0. 0000
O.
0.
-0.0019
-0.0044
-0.
-0.0051
-0.0019
-0.0044
0.
-0.0051
0.
-0.
-0.
0.
-0.0168 -0.0019
REDUCED OVERLAP POPULATION
1
2
3
4
5
6
1
13.4268
0.4751
0.4751
0.4480
0.4480
0.4762
0.4762
2
0.4751
14.5574
-0.0023
-0.0205
-0.0205
-0.0239
-0.0239
3
0.4751
-0.0023
14.5574
-0.0205
-0.0205
-0.0239
-0.0239
4
0.4480
-0.0205
-0.0205
14.6477
-0.0023
-0.0205
-0.0205
0.
00253
MATRIX
5
0.4480
-0.0205
-0.0205
-0.0023
14.6477
-0.0205
-0.0205
0.
0.1366
-0.
0.
-0.
0.
-0.0013
-0.0044
0.0006
-0.
-0.0013
-0.0044
0.0006
0.
-0.0013
-0.0044
0.
0.0006
-0.0013
-0.0044
-0.
0.0006
0.
2.8388
0.
0.
-o.0001
-0.0021
O.
0.
0.
-0.
-0.
0.
-0.0004
-0.
0.0000
-0.
-0.
-0.
3.9462
-0.
-0.
0.
-0.0003
-0.0013
-0.0004
-0.
-0.0019
-0.0013
-0.0004
-0.0013
-06.0019
-0.
-0.0004
-0.0013
-0.0019
-0.
-0.
-0.
-0.0003
-0.
O.
-0.0019
-0.0044
-0.0085
0.
-0.0019
-0.0044
-0.0085
-0.
28
29
30
0.
-0.
-0.0009
-0.
o.
0.
0.0253
0.0710
-0.
-0.
0.
0.0106
0.
-0.
0.
-0.0019
-0.0085
-0.0044
0.
-0.0019
-0.0085
-0.0044
-0.
-0.
-0.
-0.0003
0.
-0.
-0.
-0.0003
0.
O.
0.
3.9429
-0.
0.
0.
0.0000
0
-0.0009
-0.
-0.
0.
-0.0168
0.
-0.
0.
0.
-0.0003
-0.
0.
0.
-0.0003
-0.0019
-0.0051
-0.
-0.0044
-0.0019
-0.0051
-0.
-0.0044
-0.
0.
-0.
4.0359
0.
0.
O.
-0.0000
-0.
0.0134
-0.
-0.
0.
0.
-0.0004
-0.0019
-0.0013
-0.
-0.0004
-0.0019
-0.0013
0.
-0.0004
-0.0019
0.
-0.0013
-0.0004
-0.0019
0.
-0.0013
0.0000
-0.0001
'0.
0.
3.7314
-0.
0.
0.
ATOM BY ATOM
6
0.4762
-0.0239
-0.0239
-0.0205
-0.0205
14.5490
-0.0023
0.
0.
0.0102
0.0101 -0.
0.
-0.0044 -0.0051 -00019
0.0870
0.0710 0.1509
-0.
15
0.0253 0.
-0.0009
0.
0.0709 0.
-0.
0.0340
0.
0.0006
-0.0013
0.
-0.0044
0.0006
-0.0013
0.0006
-0.0044
0.
-0.0013
0.0006
-0.0044
-0.
0.
0.
0.0102
0.
0.
0.
0.0102
0.
-0.
0.
0.
-0.
0.
0.0102
0.
0.
0.
-0.
-0.
-0.0003
0.
0.
-0.0019
-0.0044
-0.0085
0.
-0.0019
-0.0044
-0.0085
-0.
-0.0009
0.0034
0.
0.0340
0.
0.0034
0.
0.0340
0.
0.0034
0.
-0.
0.0034
0.
14
13
0.0871
0.
0.1505
-0.0013
-0.0004
-0.
-a.0019
-0.0013
-0.0004
-0.0013
-0.0019
-0.
-0.0004
-0.0013
-0.0019
0.
0.
0.0710
0.1509
-0.
0.
0.0710
0.1509
0.0709
0.
0.1505
0.
0.0709
1.1137 0.
12
11
0.0253 0.
-0.0009
0.
0.0709 0.
-0.
a.
0.
-0.0168
0.
0.
0.
0.
0.
E.
0.
-0.
-0.
32
0.
0.
-0.0009
O
0.
0.0106
0.
0.
-0.
-0.0019
-0.0085
-0.0044
0.
-0.0019
-0.0085
-0.0044
-0.0.
-0.0013
0.
-0.0044
0.
0.
-0.0003
0.0006
-0.
-0.0013
-0.
-0.0044
0.
-0.
-0.0003
0.0006
-0.
-0.0001
-0.
0.
0.
-0.
0.
0.
1.1195
0.
10
-0.
-0.
-0.0168
-0.
-0.
0.
-0.
-0.
-0.0168
0.
0.
0.
-0.0168
31
0.0870
0.1509
-0.
-0.
0.1366
-0.
0.
0.
0.
-0.0013
-0.0044
0.0C06
-0.
-0.0013
-0.0044
0.0006
-0.0021
0.
0.
-0.
2.8388
0.
0.
0.
-0.
0.1022
0.0101
0.
0.
0.1022
-0.
0.
0.
0.
-0.
0.
0.
-0.
o.
-0.
0.0340
0.
0.1022
-0.
0.
-0.0001
-0.
-0.0021
0.
-0.
-0.
2.8437
-0.
-0.3013
-0.
-0.0044
0.0006
-0.0013
-0.
-0.U044
0.0006
-0.0013
0.0006
-0.0044
0.
-0.0013
0.0006
-0.0044
-0.
0.
9
0.
-0.
0.
0.0340
0.
0.0034
-0.
0.
-0.
-0
.
0.0340
0.
0.0134
-0.
0.1366
-0.
0.
0.0106
-0.
-0.
0.0134
-0.
0.1366
-0.
0.
0.0106
o.
o.
0.
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.
0.
8
0.
-0.
-0.
0.1505
0.0709
-0.
0.
0.1505
-0.
0.
-0.
-0.0009
-0.
-0.
0.
-0.0009
0
0.0871
o.
0.1505
-0.
7
0.
-0.
0.
-0.
0.
-0.
-0.0009
-0.
-0.
-0.
-0.0009
0.
-0.
-0.
-0.0009
o.
0.
-0.
16
0.
0.1428
0.
0.
6
0.
0.
0.
0.1505
-0.
-0.
0.
33
1
2
3
-0.
0.
0.
5
-0.
-0.
-0.
-0.0009
0.
0.
0.
-0.
-0.0009
0.0709
-0.
32
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4
3
0.3875 0.
-0.
-0.
0.1436 0. 0.
-0.
-0.
0.1429 -0.
7
0.4762
-0.0239
-0.0239
-0.0205
-0.0205
-0.0023
14.5490
-0.
I
-168-
TABLE XIV
ptc .2Mulliken Overlap Populations:
AO's Down and Across; PtCCl62-Bond Order Matrix
MULLKEN
OVERLAP POPULATIONS
FR
54
9
0.4590
-0.
-0.
-0.
-0.
-0.
-0.
0.
-0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.0 226
0.
-0.0003
0.
0. 0926 -0.
0.
0.
0.0226
0.
-0. 000 3
0.
0. 0926
0.
-0.
-0.
0.0 226 -0.
0.
-0.000
3
-0.
0.
0. 0926 -0.
0. 0226
0.
0.
-0.000
3
-0.
-0.
0. 0926
0.
0. 0226
0. 0704
0.0926
0.1711
-0.
0.
0.
0.
0.0 226
0.0704
0.0926
0. 17 11
-0.
-0.
0.
0.
-0.
0.1881 -0.
4
5
6
7
a
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
16
1
0.0926
17
-0.
-0.
0.1881
-0.
0.
-0.
0.
0.
0.
3.0704
-0.
0.1711
-0.
0.0704
-0.
0.1711
0.
-0.
-0.
-0.0003
0.
0.
0.
-0.0003
0.
-0.
-0.
-0.0003
-0.
0.
0.
-0.0003
0.
-0.
-0.
0.1881
-0.
0.
0.
0.
0.
-0.
-0.
-0.
-0.0003
0.
-0.
0.
-0.0003
0.0704
0
-0.
0.1711
0.0704
-0.
-0.
0.1711
-0.
0.
0.
-0.0003
0.
-0.
-0.
-0.0003
18
19
0.0226
0.
0. 1711
0.
0.0347
-0.
0.1040
-0.
-0.
-0.0001
-0.
-0.0022
0.
-0.
-0.
2.7046
-0.
-0.0012
0.
-0.0046
0.0010
-0.0012
-0.
-0.0046
0.0010
-0.0012
0.0010
-0.0046
0.
-0.0012
0.0010
-0.0046
-0.
-0.
-0.0051
-0.0046
0.
-0.
-0.
-0.0003
0.
-0.
0.
-0.0003
-0.0003
-0.
-0.
-0.
-0.
0.
-0.0165
0.
0.
-0.0003
0.
0.
-0.
-0.0003
0.
-0.
-0.
4.0343
-0.
0.
0.000O-0.
-0. 0000
0.
-0.
-0.
-0.0001 -0.
-0.0004 -0.0020
-0.0012
-0. 0046
-0.
-0.
-0.0020
-0.0051
-0.0004
-0. 0020
-0.0012
- 0.0046
-0.
-0.
-0.0020
-0. 0051
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
31
0.0926
0.1711
0.
-0.
0. 1387
-0.
0.
-0.
0.
-0.0012
-0.0046
0.0010
-0.
-0.0012
-0.0046
0.0010
-0.
-0.0012
-0.0046
0.
0.0010
-0.0012
-0.0046
-0.
0.0010
32
-0.
-0.
-0.0003
-0.
0.
-0.0165
0.
-0.
-0.
-0. 0020
-0.0051
-0.0046
0.
-0.0020
-0.0051
-0.0046
0.
-0.
-0.
-0.0003
-0.
0.
0.
-0.0003
0.
33
0.
0.
0.
-0.0003
0.
0.
0.
-0.0165
-0.
-0.
0.
-0.
-0.0003
-0.
-0.
-0.
-0.0003
-0.0020
-0.0051
-0.
-0.0046
-0.0020
-0.0051
-0.
-0.0046
26
27
28
29
30
31
32
33
-0.0001
-0.0022
0.
-0.
-0.
2.7046
0.
-0.
-0.
-0.
-0.0020
-0.
-0.
0.0704
0.0031
-0.
0.0094
-0.
0.
-0.0004
-0.
-0.0012
-0.0020
-0.0004
-0.
-0.0012
-0.0020
3.7306
-0.
-0.
0.
0.
-0.
0.
-0.
-0.
-0.0000 -0.
-0.
-0. 0000
-0.
0.
4.0343
-0.
4. 0 343
0.
0.
-0.
1.2808
0.
0.
0.
0.
0.0031
-0.
0.0347
-0.
0.0031
0.
0.0347
-0.
0.0031
-0.
0.
0.0347
0.0031
-0.
-0.
0.0347
0.0126
0.1387
0.
-0.
0.0126
0.1387
0.
0.
20
.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
-0.
0.
-0.0003
-0.
0.
0.
0.
-0.0165
0.
-0.
0.
-0.0000
0.
0.
-0.
4.0343
-0.0020
-0.
-0.0051
-0.0046
-0.
-0.
0.
-0.0003
-0.
0.
0.
-0.
-0.
-0 .0165
-0.002C
0.
-0.0046
-0.0051
-0.0020
0.
-0.0046
-0.0051
-0.
-0.
4.034 3
0.
-0.
-0.
-0.0000
-0.
0.
0.
-0.0003
0.
-0.
0.
-0. 0003
-0.
0.
0.
-0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
-0.
4.0659 -0.
-0.
-0.
-0.
-0.
-0.0165
0.
-0.
-0.
-0.0165
-0.
0.
-0.
-0.
0.
-0.
0.
0.
-0.
0.
0.
-0.0165
-0.
-0.
-0.
-0.0165
0.
1.2808
0.
0.
0.0094
0.
0.1040
0.
0.0094
0.
0.1040
0.
0.0094
0.
-0.
0.1040
0.0094
-0.
0
0.1040
0.
0.
0.
0.
0.
0.
0.
0.
0.
4.0659
-0.
0.
-0.
0.
0.
-0.
-0.
-0.
0.
-0.
-0.0165
-0.
-0.
-0.
-0.0165
-0.
-0.
-0.
-0.
0.
-0.0165
-0.
-0.
-0.
-0.0165
21
22
23
0.0926
0.0226
-0.
0.
0.
0.
0. 1711 0. 0704
0.0347
-0.
0.1040
-0.
-0.
-0. 0012
-0.
-0.0046
-0. 0012
0.
0.0010
-0. 0046
0.
0.
0.
2.7046
-0.0001
-0.
0.
-0. 0022
-0.0012
0.0010
0.
-0.0046
-0. 0012
0.0010
-0.
-0.0046
.
0.
0.
0.
0.
0.
-0.
0.
-0.
4.0659
0.
0.
0.
-0.0165
0.
0.
-0.
-0.0165
0.
0.
-0.0165
-0.
0.
-0.
-0.0165
0.
0.
0.
-0.
0.
0.0031
0.
0.0094
-0.
0.
-0.0004
-0.
-0.0012
-0. 0020
-0.0004
-0.
-0.0012
-0. 0020
0. 0000
-0.
-0.:oo
-0.
-0.
-0. 0001
3. 7306 -0.
-0.
4. 0344
-0.
-0.
-0.
-0.
-0.0020
-0.0004
-0. 0012 -0.0046
0.
0.
-0.00 51
-0.0020
-0. 0020
-0.0004
-0. 0012 -0.0046
0.
0.
-0.0051
-0. 0020
1
15.7826
0.4745
0.4745
0.4745
0.4745
0.4745
0.4745
2
0.4745
14.5039
-0.0024
-0.0203
-0.0203
-0.0203
-0.0203
11
12
0.0226
0.
0.0704
-0.
0.0031
-0.
0.0094
0.
o.
3.7306
-0.
0.
0.
0.0000
-0.
-0.0001
0.
-0.0004
0.
-0.0020
-0.0012
-0.0004
-0.
-0.0020
-0.0012
-0.0004
-0.0012
0.
-0.0003
-0.
-0.
-0.
-0.0165
0.
-0.
0.
-0.
4.0343
-0.
0.
0.
-0.0000
-0.
-0.
0.0926
-0.
0.1711
-0.
0.0347
0.
0.1040
0.
0.
0.
-0.
2.7046
0.
-0.0001
-0.
-0.0022
0.
-0.0012
0.
-0.0046
0.0010
-0.0012
-0.
-0.0046
0.0010
-0.00rz
0.0010
-0. 0046
0.
-0.0012
0.0010
-0.0046
-0.
-0-.0020
O.
-0.
-0.
-0.0004
-0.0012
-0.0020
-0.
24
25
-0.
-0.0003
-0.
-0.
0.
-0.
-0.
-0.0165
-0. 0020
-0.
-0.0046
-0.005[
-0.0020
-0.
-0.0046
-0.05r
-0.
-0.
-O.0000
0.
-0.
-0.
4.0343
-0.
0.
-0.
-0.0003
0.
-0.
-0.
-0.0003
-0.
3
0,4745
-0.0024
14.5039
-0.0203
-0.0203
-0.0203
-0.0203
-0.
26
0.
0.
0.1711
0.0347
-0.
0. [040
-0.
O.
-0.0012
0.
0.0010
-0.0046
-0.0012
-0%
0.0010
-0.0046
-0.0001
-0.
-0.
-0.0022
-0.
-0.
-0.
2.7046
-0.00
12
0.0010
-0.
-0.0046
-0.0012
0.0010
0.
-0.0046
13
27
0.0226
0.0704
-0.
-0.
-0.0012
0.
0.1387
0.
0.
-0.
0.
-0.0012
-0. 0046
0. 0010
0.
-0.0012
-0. 0046
0.0010
-0.
-0.
-0.0012
-0.0020
0.
-0.00 12
3. 7306
0.
0.
0.
0.0000
-0.0001
-0.
-0.
5
0.4745
-0.0203
-0.0203
-0.0024
14.5039
-0.0203
-0.0203
28
29
0.
-0.0003
0.
0.
-0.0165
O.
0.
-0.
-0.0020
-0. 0051
-0. 0046
-0.
-0.0020
-0.0051
-0.0046
-0.
-0.
-0.
-0.0003
0.
0.
0.
-0.0003
-0.
O.
0.
4. 0343
-0.
-0.
0.
-0.0000
-0.
-0.0012
0004
-0.0003
-0.
-0.
0.
0.
-0.0165
0.
O.
0.
4.0343
-0.
-0.
0.
-0. 0000
-0.0020
0.
-0.0051
-0. 0046
-0.0020
0.
-0.0051
-0.0046
-0.
0.
-0.
-0.0003
-0.
-0.
0.
-0.0003
0.
-0.
0.1711
-0.
-0.0046
0.
0.0010
-0.0046
-0.
0.0010
0.
2.7046
0.
-0.
-0. 0001
-0.0022
0.
-0.
BY ATOM
6
0.4745
-0.0203
-0.0203
-0.0203
-0.0203
14.5039
-0.0024
14
01.0226
0.
0.0704
0.
060031
-0.
0.0094
-0.
0.
0.0000
0.
-0.0001
-0.
3.7306
0.
-0.
0.
-0.0004
-0.
-0.0020
-0.0012
-0.0004
-0.
-0.0020
-0.0012
-0.0004
-0.0012
-0.0020
-0.
-0.0004
-0.0012
-0.0020
-0.
-0.
-0. 0004
-0.0020
0.
-0.0012
0.
0.0926
0.
0.0126
0.
0.
-0.
0.
-0.0004
-0. 0020
-0.0012
-0.
-0 .004
-0.0020
MATRIX ATOM
4
0.4745
-0.0203
-0.0203
14.5039
-0.0024
-0.0203
-0.0203
0003
-0.
-0.
-0. 0003
-0.
0.
-0.0020
-0.0046
-0.0051
0.
-0.0020
-0.0046
-0.0051
0.
0.0926
REDUCED OVERLAP POPULATION
1
2
3
4
5
6
7
10
-0.
0.
-0.
-0.0003
0.
-0.
-0.
-0.
-0.
-0.0165
-0.
-0.
-0.0003
-0.
0.
-0.
-0.000
3
-0.
-0.
0.
ELECTRONS
7
0.4745
-0.0203
-0.0203
-0.0203
-0.0203
-0.0024
14.5039
06
0.
-0.
-0.0003
-0.
-0.
0.
-0.0165
0.
-0.
15
0.
-0.0003
-0.
-0.
0.
-0.0165
0.
-0.
0.
-0.
-0.0000
-0.
-0.
0.
4.0343
-0.
0.
-0.
-0.0003
0.
0.
-0.
-0.0003
-0.
-0.
-0.0020
-0.0046
-0.0051
-0.
-0.0020
-0.0046
-0.0051
-0.
30
0.0226
0.0704
0.
0.
0.0126
-0.
0.
-0.
0.
-0.0004
0.
-0.0020
0.
-0.0012
-0.
-0.0004
-0.0020
-0.0012
0.
-0.0004
-0.0003
-0.
-0.
0.
-0.0003
-0.0020
-0. 0051 -0.0020
0.
-0.
-0.0046
-0.0020
-0.0012
-0.0004
-0.0046
0.
-0.
-0.
4.0343
0.
-0.
-0.
-0.0000
-0.0012
0.0000
-0.0001
-0.
O.
3.7306
-0.
-0.
0.
-0.0051 -0.0020
0.
-0.
-170-
TABIE
ReC 6e2
XV
MO Carge
Matrix:
MO's Across and AO's Down
l
CHARGE ATRIX FOR WR-S W(tR TU EEOTRWR
IN liCR
Re. C
1
2
5
6
7
3
4
Cj0CO
1.5587 -OOCOC OJ.00 0.0000
8
9
0.0000
0.J0000 OJOo0
10
11
12
1
14
i
I
000O0 0.0000
2
O:oCO
000003
1179.54 O;
3
4
0.8980
0.8976
0.8977
0.8978
0,0000
0 0 .0000
0.0
C0 -OdOO0 OJOoOO 0.0
O&oooo 0&0000 0000
040000 001Jc 04012 00315
0.C003 0,0000 -0.OCC -OJOOO0 040000 '0.0000 -0;0000 0.0000 0.10000CCCOo 040320 0JO025 010092
5
6
7
8
9
10
O.OCOo O.COO
o0oooo OJOOO
040000
0.00
000 CJcOCO e0.000o0o
OdOOO0 040000
-O.OCO0-0.0000 0.OOCO0.0000 1.2643 0J0843 0.0000 0.0000 0J0000 0.10000 0Jooe
0.OCO 0.0000
0.0000
0
O.COOO O0rOO0 OO0O
.0000O
O.OCO0 0.0000
OJGOO0 1.7871
040000
0JO00 040000
0400
0JC00 0C00
O.OCCO 0.0000
0.0000 1.7871
0.OCCO OJ400
0.0016 0J0205
0.0000 0.0C00 1.791
J00000 0.0000 0.0000
OJOOO0 00000
020030
00000 010000
OJOOo oJ00Co 0C0000 Q4O9O8 0oo0
COOO010000 0.0843 1.2643 OC00 0.0000 0.0000 040000010000
0J0000 0;.CG
O.COco 0.0000
0.0000 0.0000 C.CCCO 0.0000
0.0158 0.0158 0.COO
0.0180
0*0000
00CJCCC
04 0G
0341
OJO000 0JCC0
CC
0J0000 0J1000
0JCO0
0J000 -0*0000
000000
M
0 .J1C00 0000
1oooo0 oj0000 c0000 0Jo00
0.10000 0.0000
12
13
@J000
ojoo0
0.0000 0.0000 0;CCO2 010000 0;00C0 04000 0J0532 0;0000 OJ000 OJOO0 0J4990 010010 CON400 0J2081 010154
0.0351 0.0350 O.COCO 0,0556 0.0140 O.118110.0000 0.0000 0
0.10000
J0000 0.00 O JCCO 0J0520 0JOY28 0O3323
0.0C01 0.0001 C.C0 00000 0.00CC O.00
0.0000
00CO0 0J0532 OO000 OJO010 CJ4990 041943 0J0183 0*0556
17
11
14
15
16
0.0158 0.0158 0.0000 0.0180 0.0016 0J0205 0,0000 -0.0000 0O000 0.JO00 .1000 0JC0O0 0.001 0.000 0*0000
0.0000 0.0000 0.0002 -0.0000 O.00CC 0;0000 0.0532 0OC0
0.0000 040000 @J4990 0JC0IC CJ0400 @42041 0O10e
0.0351 0.0330 0.C000 0.0556 0.0140 O.18110.0000 0.0000 OO00 04000 OJ00000JC000 040520 0J0728 083223
0M0001 0.0001
01COC0 0;0000
18
0.0158 0.0158
0.C000 0,0180
19
20
0.0000
0.0001
0.0000
0.0001
0C002 010000 o~OOCC 0.0000 OCO0
0.C000 0.0000 -O.occo o.eoo00.0000
22
23
0.0158
0.0000
0.0158
0.0000
0.0000
0.0180 0.0109 0.0113 -040000 0;0000
0;002
010000 C00CC OJOO0 OJOCO0 010532
0.0000 0.100000.1008 0.1000 00
OJ10 045000 0J0000 CJ4CO C0000
0.0000 0.0000
0CO
0.0001
0.0001 0.0001
C;0701 010556 0.1828 00122
00COO0 0.0000 0.00CC 0OOO
0.COCO0000 0;0O
C0. 0 0;0000
040000
000
o0000 o0oo0
OJOOO0 045000
0.0000 0.000
OOCO1 0.0001
0.00010 0.0001
0.0701 010556 011828 0~0122 0.0000 0.0000 -JO0000 040000 OJO0O0 CJCCC 0J0674 0J3486 040322
OCOCO 0.0000 0.0CC0 0ooo0
0J0532 0.0000 04000 0JOOO0 044990 040010 0J0308 @0432 031912
0.0000 0.0000 0.00 040000 0.0000 0.0532 040000 045000 040000 0CCC
(J943
0J0182 020556
21
24
25
26
27
28
29
30
31
32
33
2
3
4
5
0.0o0
0.OCCO 0J0532 0J0000
OJO1O 044990 0JI941
0.0000 0
040182 0.J055
040000
JOO
0 0000
@J0000
0.0532
0.0000
000
04O00
0J0O0 05000
0J0532 00000
04o0
00002
0J000 0C000 0J0400 0J2061
0J010 044990 0J0308 0J0432
030194
0J1913
0.0350 0.0350 C;COCO0.0556 0.0957 0.0993 0.0000 O.0CO0 O0100 040000 0.OO0 CJ0000 043277 0J0257 0JO931
040000 040002
OM0IT 000184
0;0001 0.0001 0.C000 0.0000 -0.0000
-0.10000,0000 0.0000 0405820.0000 OJO1O CJ490 0J0308 0J0432 011912
0.03.50 0.0350 0;C000 0;0556 0.0957 040993 O.OCO0 0.000
040000 040000 040000 CJCCO 0J3277 0O0251 0*0931
0.0000 0.0000 0.0316 0.0180 0.0207 0400140.0000 0.0000 0O0000040000 J0000 0J0000 JC001 0J0006 J0100
0
0.0532
0.0000
.0000
0.000o
0;0532
40000
0J0000 0
40CC
674 oj3480 040311
0J4990
0JCCI0 040308 0J0432 Ot191
0J0000 CJCCO OJ1943 040156 010556
0.0000 0.0000 0.0316 0.0180 0.0207 0J0014 -0.0000 0O00000.0000 0400000400000400000J0001 0J0006 OJO02
16
1
.O00CC0jCC0O0 0.0000
0.0109 0.0113
17
1e
20
19
21
22
23
24
-0.0000 0.0000 0.0CO00;0000 0.00000400000.0000 0.0000 0400
0.0000 0.0000 -O.C000 0.0000
O.0CO0 0.0000 O.CCCO 0.0000
O.CO0 0.0000 O.COCO 0.0000
0.0000 0.0000 OCOCO 0`298I
C.OCC
0.OCCC
0.00C0
0.2814
6
0.0000
000000 0000C
OJCOO
7
8
0.0000
0.0000
9
0.0o00
0.0000
0
0.0000
0.0000
0.00
0C0
00
040842
0J0027
0.0044
O.C00
25
26
2?
28
29
30
040000 040000 042622 0J0000 @40000 030000
0.0050
0.0782
0.0081
0.0000
0*0021 0.0000 00000
O
4OOO
0 0JCCCO
4CC00 04
0.0104 0.0000 040000 OJOOO0 O;CCCO JCOO0 0J0086
0.0788 040000 0C0000 040000 CJCCCC 040000 0J0000
0000 040000 040000 .100000.
CJ0C
040100 840582
030080
0J0202
040411
040000
0
0.000
0
O000
040OO0 042096
0JO033 -CJ0CO
0Jc0O
0M0000
O.00CO 0.2814 0.2981 0.0000 0.0000 0.0000 040000 040000 0.100
040000
0J0582
014
0JO000
0.COCO 0.0000 0.00CC 0.0000 0.0000 O.OCO0 0J2129 040000 oJo000 0JCCCO 0J000 0J0000 0*0000
C.00co 010000 C.00CC OJO000 00000 0.0000 OJO000 040033 OJ2090 CC40C 040000 4O0000 0J000
10 -OOCO0-0.0000 -O.C0CO 0.0002 0.0027 0.0002 0.0059 0.10008 o.000040000 000
CJ0145 0J6423
11
0.0708 0.3477 0.0815 O10000OOCOC0.2142 0.0127 0.0053 040000 044399 0J0069 -040000 04000
12 0.0000 0.0000 0o00co 0.0282 0.4423 0.0143 0.4139 0.0550 OJO000 040000 oJooo0 0J2712 0J001
13 0.1239 0.0160 0J3551 0;0000 010000 0.0111 0.0206 0.2004 OJOO0 040009 0J4399 CJO00 0JC000
14 -0.OCO -0.0000 -O.CCCO0.0002 0.0027 0.0002 0.0059 0.0008 00000 0.10000 ojo000 0J0145 0J6413
15
0.0708 0.3477 0.0815 010000 00CCC 0;2142 0.0127 0.0053 0400000443990J0069 CCC00 0J000
16
0.000 0.0000 O.COCO0.0282 0.4423 0.0143 0.4139 0.0550 040000040000 OJO000 0J2752 0J01
17
0.1289 010160 013551 000000 0.0000 0.0011 0.0206 0.2004 040000 040069 @44399 oCCC 040000
18 0.0000 -0.0000 -0.0000 0.0027 0.0002 0,0003 0,0006 0.0059 040000 000000 0400000J0143 C1726
19
0.0708 0.3477 0.0815 0;0000 0.0000 0.2142 0.0127 0.0053 0;4488 040000 040000040000 040
20
0.3003 0.1363 0.0634 0.0000 0.0000 0.0069 0.1989 0.0264 OJOOO0040069 0J4399 0JO00 0J0000
0J0003 0.2804
0J0000 020003
0J0000 -0O000&
0J000 040015
000813 0*2804
@J0080 030003
@JO000
-J0001
040000 OJO05
0J469 0*5695
@4000 0.0003
04J000 O*00?
21
22
23
O.0C00o.0OO0
C.00C0 014356 0.0350
0.0000 -O.0CO0 -O0CO0 0.0027 0.0002
0.0708 0.3477 070815 010000 0.0CC
0,0231 0.0429
0JO003 0,0006
0.2142 0.0127
0.4177
0.0059
0.0053
0.0000 -040000
0.10000 040000
0J4468 0400o0
040000 CJ2782 0C403 040008 -0O0002
OJO000 040141 0J1736 0J469! 015095
0J10000 -CJCC0 000 0 @J0060 040003
25
26
0.0000 0.0000
0.0000 -0.0000
040231
040063
0.0429
0004
0.4172
0.0002
040000 040000
0.0000 03000
040000 042782 @40003 040006 -OJ000
OJOOO
0
10JO145
041486 044932 011108
010000 C.0000 0.0111
0.0206
0;2005
0;446
0
0J0004
0.0002 040000
24
27
28
29
30
31
32
33
0.3003 0.1363 0.0634 0.0000 0.0000 0.0069 0.1989 0.0264 0.0000 040069 044399 0J0000 040000 0J40 030007
C.CCCO 014356 0.0350
O.CO0 0.0015 0.0014
0.0000 0.0000 O.CCCO0.2421 0.2285 0.4458 0.0284 0.0110040000 040000 04000O0J2752 JO003 04J0008-030000
0.3003 0.1363 0.0634 0.0000 0.0000 0.0069 0.1989 0.0264 040000 044399 0J0069 040000 04C0 0.0006 0*0007
0.12389 0.0160 0.3551
-OOO0
0.0000
00
0.3003
0.1289
31
0.1363
0.0160
32
0,0634
0.3551
3
4
5
0104B5 0.0006 000CO
0.0139 0.0144 O.CCCO
O;0C00 0.0000 0CCCO
0.0069 0.0544 0.CCO
O.OC0
0.0000
OCO0
O.COO0
O.GCO0 0.0000
OCO0
O0OCCO
0.0000
10 0.6722 0.0081
010002 0.0019
12 -0.0002 -0.0000
13
0.0005 0.0005
14
0.6722 0.0081
15
0.0002 0.0019
16 -0.0002 -0.0000
0,3009
0.00M0
0.026
0.COCO
0.3009
O.00CO
0*0026
9
010000 0.C000
11
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000 OOCCC 0.0069
010000 C.OCCC 0.0111
33
010000 O.COCO 031791
6
7
8
0J0000
0C00
040000 040000
0CJ0141
041486 OJ4911 0*1108
0J000
0J0015
O.OCO 0.0000 0.C000 0.2421 0.2285 044458 0.0264 0.0110 0.0000 040000 OJOOO00J27820J0003 0J0008 -0*0000
1
2
M0015
0.0014 0.C063
040000 oJoooo
0.0005
0.1923
060002
0.0017
-0C0001
0.0005
0.1990
0.0019
0.C000
-0.0001
CCCO
O.COCO
043009
0.0000
OCOCO
0.0026
0.1923 0.1990 0,3009
0.0002
0.0017
0.0019 O.00CO
0.0000 0.C000
-0.0001 -0.0001
0.0962 0.7537
-OOCO0 -0.0003
0.0017 0.0000
0.0005 0.0005
0.0962 0.7537
0.0026
0.3009
0.0026
OC00
C.COCO
0.3009
-010000-0.0003 0.0026
0.0017 0.0000 0o.C000
0M0005
0.0005
O.COCO
0.1989 0.0264
0J0206 0.2005
0JOO0
044468
044399 0JO06 CJOC00 048000 0J0000 0*0001
040000 0JOO00 C00000 040000 J0000 040015
-172-
TABIE XVI
OsC1e
2 -
MO Charge Matrix:
MO's Across and AO's Down
CHARGE
1
1
2
0.0000 0.0000
3
4
5
0.0000 1.5069 0.0000
MATRIX
FOR
MO-S
-
9
6
7
0.0000
0.0000 0.0000
8
WITH
TWO
ELECTRONS
10
IN EACH
11
12
13
14
15
0.00000 0.o000 -0.0000 -0.0000 0.0000 -0.0000 0.0000
2
3
4
5
6
7
8
9
i0
11
12
1.7458
0.0000
0.COO0
-0.0000
-0CCO0
0.0000
0.0000
0.0000
0.CCO0
0.0014
0.COOO
0.0000
0.0000
1.7453
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.7453
0.0000
0.0000
0.0000
-0.0000
0.0000
-0.0000
0.0380
0.0000
0.0867
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0190
0.0000
0.0632
0.0000
0.0000
0.0000
0.0014
0.0000
1.3074
0.0000
0.0000
0.0119
0.0000
0.1673
0.0000
0.0000
-0.0000
1.3094
0.0000
0.0014
0.0000
0.0000
0.0034
0.0000
0.0479
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
1.8194
-0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
1.8204
0.0000
0.0000
0.0000
0.0000
0.0454
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
1.8205
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5058
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0473
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0006
0.0000
0.4203
0.0000
0.0000
0.0472
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0454
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2841
0.0000
13
14
!5
26
17
28
19
20
21
22
23
24
35
26
0.0000
0.COO0
0.0014
0.0000
0.0000
0.CCO0
0.0014
0.0000
0.OCO0
0.OCO0
0.0014
0.COOO
0.CO0
0.0379
0.0865
0.0000
0.OC0
0.0379
0.0865
0.0000
0.OCCO
0.0014
0.0000
0.0000
0.0000
0.0014
0.0380
0.0000
0.0000
0.0866
0.0380
0.0000
0.0000
0.0366
0.0000
0.0000
0.0000
0.0014
0.0000
0.0000
0.0000
0.0014
0.0000
0.0380
0.0000
0.0867
0.0000
0.0000
0.0000
0.0014
0.0000
0.0000
0.0000
0.0014
0.0000
0.0000
0.0000
0.0014
0.0000
0.0000
0.0000
0.0014
0.0000
-0.0000
0.0190
-0.0000
0.0632
0.0000
0.0190
0.0000
0.0000
0.0632
0.0190
-0.0000
-0.0000
0.0632
0.0190
0.0632
0.0000
0.0000
0.0190
0.0632
0.0000
0.0000
0.0000
0.0119
0.0000
0.1573
-0.0000
0.0110
0.0000
0.0000
0.1552
0.0110
0.0000
0.0000
0.1552
0.0000
0.0002
0.0000
0.0000
0.0000
0.0002
0.0000
0.0000
0.0000
0.0034
-0.0000
0.0479
0.0000
0.0043
-0.0000
0.0000
0.0599
0.0043
0.0000
-0.0000
0.0599
0.0153
0.2138
-0.0000
0.0000
0.0153
0.2138
-0.0000
0.0000
0.0452
0.0000
0.0000
0.0000
0.0452
0.0000
0.0000
0.0451
0.0000
0.0000
0.0000
0.0451
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.000
0.0454
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0444
0.0000
0.0000
0.0000
0.0444
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0453
0.0000
0.0000
0.0000
0.0453
0.0000
0.0000
0.0000
0.0000
0.0000
0.0444
0.0000
0.0000
0.0000
0.0444
0.5004
0.0000
0.0000
0.0000
0.5004
0.0000
0.0000
0.4996
0.0000
0.0000
0.0000
0.4996
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5058
0.0000
0.0000
0.0600
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4942
0.0000
0.0000
0.0000
0.4942
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5054
0.0000
0.0000
0.0000
0.5054
0.0000
0.0000
0.0000
0.0000
0.0000
0.4946
0.0000
0.0000
0.0000
0.4946
0.0000
000006
0.0000
0.4203
0.0000
0.0000
0.0000
0.2900
0.0000
0.0000
0.0000
0.2900
0.0000
0.0000
0.0000
0.2654
0.0000
0.0000
0.0000
0.2654
0.0000
0.2914
0.0000
0.0000
0.0000
0.2914
0.0006
0.0000
0.0000
0.4196
0.0006
0.0000
0.0000
0.4196
0.0000
0.0000
0.0000
0.2648
0.0000
0.0000
0.0000
0.2649
0.0000
0.0000
0.2841
0.0000
0.0000
0.0000
0.2821
0.0000
0.0000
0.0000
0.2821
0.0000
0.0000
0.0007
0.4105
0.0000
0.0000
0.0007
0.4105
0.0000
0.0000
19
20
21
37
28
29
30
31
32
33
16
17
18
1
2
3
4
5
6
7
8
9
I0
11
12
23
14
15
16
17
18
!9
20
21
22
23
24
25
26
27
38
29
30
31
32
33
0.C0
OCCO0
0.COC
0.0000
0.COO0
0.CCO0
0.CCO0
0.0000
0.OCO0
0.CC00
0.4993
0.0000
0.OCO0
-0.OCO0
0.4994
0.0000
0.0C00
0.CCO0
0.5006
0.0000
0.CCO0
-0.OCO0
0.5006
0.0000
0.CC00
-0.C00
0.C000
0.CCO0
0.0000
-0.0000
0.0000
0.C000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.4916
-0.0000
0.0000
0.0000
0.4916
-0.0000
0.0000
0.0000
0.0003
-0.0000
0.0000
0.0000
0.0003
0.0000
0.0000
0.0000
0.5081
0.0000
0.0000
00000
0.5081
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0002
00000
-0.0000
0.0000
0.0002
0.0000
-0.0000
0.0000
0.4922
0.0000
-0.0000
0.0000
0.4922
0.0000
0.0000
0.0000
0.5075
0.0000
-0.0000
0.0000
0.5075
0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
i4
65
16
17
18
19
20
21
22
23
24
25
26
27
28
29
'30
31
32
33
31
0.COO0
0.OCO0
0.0000
0.0857
0.0000
-0.COO0
0.0000
0.CCO0
0.CCO0
0.0000
0.0000
-0.COO0
0.0024
0.0000
0.0000
-0.0000
0.0024
0.9528
0.0000
0.0000
-0.0005
0.9528
0.0000
0.0000
-0.0005
0.0000
-0.0000
0.CCO0
0.0024
0.0000
-0.0000
0.0000
0.0024
32
0.0000
0.0855
9.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0024
-0.0000
0.0000
0.0000
0.0024
-0.0000
0.0000
0.0000
0.0024
0.0000
-0.0000
0.0000
0.0024
0.0000
-0.0000
0.9529
-0.0005
0.0000
0.0000
0.9529
-0.0005
0.0000
0.0000
33
0.1995
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2933
0.0000
0.0029
0.0000
0.2933
0.0000
0.0029
0.0000
0.2941
0.0000
0.0000
0.0029
0.2941
0.0000
0.0000
0.0029
0.3041
0.0029
-0.0000
0.0000
0.3041
0.0029
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0007
0.0000
0.6439
0.0000
0.0000
0.0012
0.0000
0.3504
0.0000
0.0012
0.0000
0.3504
0.0000
0.0011
0.0000
0.0000
0.3245
0.0011
0.0000
0.0000
0.3245
0.0000
0.0005
0.0000
0.0000
0.0000
0.0005
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.6420
0.0000
0.0007
0.0000
0.0000
0.0004
0.0000
0.1025
0.0000
0.0004
0.0000
0.1025
0.0000
0.0005
0.0000
0.0000
0.1280
0.0005
0.0000
0.0000
0.1280
0.0015
0.4458
0.0000
0.0000
0.0015
0.4458
0.0000
0.0000
0.0000
0.0000
0.1216
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0086
0.0000
0.4933
0.0000
0.0086
0.0000
0.4933
0.0000
0.0000
0.0000
0.2140
0.0000
0.0000
0.0000
0.2140
0.0000
0.0000
0.0000
0.2233
0.0000
0.0000
0.0000
0.2233
0.0000
22
0.0000
0.0000
0.0000
0.1217
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2133
0.0000
0.0000
0.0000
0.2133
0.0096
0.0000
0.0000
0.4940
0.0086
0.0000
0.0000
0.4940
0.0000
0.0000
0.0000
0.2232
0.0000
0.0000
0.0000
0.2232
23
0.0000
0.1232
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2128
0.0000
0.0000
0.0000
0.2128
0.0000
0.0000
0.0000
0.2135
0.OCO0
0.0000
0.0000
0.2135
0.0000
0.0000
0.0085
0.5036
0.0000
0.0000
0.0085
0.5036
0.0000
0.0000
24
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1806
0.0000
0.0000
0.0000
0.4544
0.0000
0.0000
0.0000
0.4544
0.0000
0.0000
0.4553
0.0000
0.0000
0.0000
0.4553
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
25
0.0000
0.0000
0.0000
0.0000
0.0000
0.1796
0.0000
0.0000
0.0000
0.0000
0.4488
0.0000
0.0000
0.0000
0.4488
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4614
0.0000
0.0000
0.0000
0.4614
0.0000
26
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1795
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4493
0.0000
0.0000
0.0000
0.4493
0.0000
0.0000
0.0000
0.0000
0.0000
0.4610
0.0000
0.0000
0.0000
0.4610
27
0.2936
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0172
0.0000
0.2644
0.0000
0.0172
0.0000
0.2644
0.0000
0.0172
0.0000
0.0000
0.2650
0.0172
0.0000
0.0000
0.2650
0.0172
0.2722
0.0000
0.0000
0.0172
0.2722
0.0000
0.0000
28
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0465
0.0000
-0.0000
0.5059
0.0000
0.0010
0.0000
0.5059
0.0000
0.0010
0.0000
0.4681
0.0000
-0.0000
0.0010
0.4681
0.0000
0.0000
0.0010
0.0007
0.0000
-0.0000
0.0000
0.0007
0.0000
-0.0000
0.0000
29
0.0000
0.0000
0.0000
0.0000
0.0465
0.0000
0.0000
0.0000
0.0000
0.1477
0.0000
0.0003
0.0000
0.1477
0.0000
0.0003
0.0000
0.1847
0.0000
0.0000
0.0004
0.1847
0.0000
0.0000
0.0004
0.6423
0.0014
0.0000
0.0000
0.6423
0.0014
0.0000
0.0000
30
0.0000
0.0000
0.0857
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.9528
0.0000
-0.0005
0.0000
0.9528
0.0000
-0.0005
0.0000
0.0000
0.0000
0.0024
-0.0000
0.0000
0.0000
0.0024
-0.0000
0.0000
-0.0000
0.0024
0.0000
0.0000
-0.0000
0.0024
0.0000
-174-
TABLE XVII
IrC16 2- MO Carge Matrix:
MO's Across and AO ' s Down
CHARGE MAtRiX
FOR
TC7
I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
0.0000
0. 000
0.0000
1. 7090
-0.0000
0.0000
-0.0000
0.0000
0. 000
0. 000
O. 0S00
0. 00oo
0.0026
0.0000
0.0000
O.0OOO
0.0026
0. L461
0.0000
0.0000
0.0942
0.0461
0.0000
0.0000
0.0942
0.0000
0. 0000
0. J000
0.0026
0. 000
0.0000
0.J000
33
0.0026
7
0.0000
O. COOO 1.4692
1.7081
0.0000
0.0000
0.0000
0.0000
I .7089
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
O.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0. COOO 0.0000
0.0000
0.0000
0.0000
O.
0.0000
0.0217
0.0461
0.0026
0.0000
0.0000
0.0943
0.0000
0.0667
0.0000
0.0000
0.0000
O.0OO0
0.0217
0.0461
0 0000
0.0026
0.0000
0.0943
0.0000
0.0667
0.0000
0.0000
0.0000
0. 0000
0.00CO
0.0217
0.ooo
000 0 0.0026
0.0000
0.002o
0.0000
0.0000
0.0000
0.0667
0.0000
0.0000
0.0217
0.0000
0.0026
0.0000
0.0000
0. 00 26
0.0000
-0.0000
0.0000
0.0667
o.00oo0o
0.0462
0.0217
0.0000
0.0945
0.0668
0. 0000
o. 0026
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0462
0.0217
0.0000
0.0945
0.0668
0.0000
-0.0000
0.0026
0.0000
0.0000
16
17
18
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000
0.0000
0.0000
0.3001
0.0000
0.0000
-0.0000
0.0000
0.0000
-0.0000
0.3000
0.0000
0.5142
-0.0000
0.0000
0.0000
0.
142
-0.0000
0.0000
0.0000
0.0006
-0.0000
0.9000
0.0000
0.0006
0.0000
0.0000
0.0000
0.4852
-0.0000
0.0000
0.0000
0.4852
0.0000
0.0000
0.0001
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0007
0.0000
-0.0000
0.0000
0.0007
0.0000
0.0000
0.0000
0.5154
0.0000
-0.0000
0.0000
0.5154
0.0000G
0.0000
0.0000
0.4838
0.0000
-0.0000
0.0000
0.4838
0.0000
0.0000
0.0000
0.0000C
0.0000
0.0000
0.0000
0.0000O
0.0000
0.0000
-0.0000
0.4987
0.0000
0.0000
0.0000
0.4987
O.0000
0. 0000
-0.0000
0.5013
0.0000
0.0000
-0.0000
0.5013
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
31
0.3000
0.O000
0.1062
0.0000
0.0000
0.0000
0.0000
0.0000
0.3000
0.9430
0.3000
-0.0007
0.0000
0.9430
32
0.0000
0.0000
0.0000
0.1062
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0023
0.0000
33
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.0000 0.0000
0 .2308
0.0000
O. COOO
0.0000
0. 0000
O.0000
0.0000
0.0000
0.0000
0. 2 960
0.0000
0.0031
0. 0000
0.2960
O0.0000
0.0031
0.0000
0.2975
16
17
18
-0.0007
0.0000
0.0000
-0.0000
0.0023
0.9430
19
20
21
22
23
24
0.0000
0.0023
-0.0000
0.3000
0.0000
0.0023
0.0000
0.0000
-0.0007
0.9430
0.0000
0.0000
-0.0000
0.0000
0.0031
0.2975
-0.0000
0.0000
26
27
28
0.0000
-0.0000
0.0023
0.0000
-0.0000
0.0000
0.2819
0.0031
0.0000
0.0000
0.2819
25
29
30
31
32
33
-0.0000 -0.0007
0.0031
0.0000 0.0023 0.0000
0.0000
-0.0000 -0.0000 0.0031
0.0023 0.0000 0.0000
0.0000 0.0023 0.0000
0.0000
19
0.0000
0.0000
0.0000
0.0000
0.7177
0.0000
0.0012
0.0000
0.0000
0.0010
0.0000
0.1169
0.0000
0.0010
0.0000
0.1169
0.0000
0.008
0.0000
0.0000
0.0875
0.0008
0.0000
0.0000
0.0875
0.0041
0.4302
0.0000
0.0000
0.0041
0.4302
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
-0.0000
-0.0000
0.0000
0.0000
0.0021
0.0000
1.2134
0.0000
1.7163
0.000
OOCO
1.2164
0.0000
0.0021
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0135
0.0000
0.0054
0.0000
0.0695
0.0000
0.1723
0.0000
0.0693
0.0000
0.0000
0.0000
0.0135
0.0000
0.0054
0.0695
0-0000
0.0000C
0.1723
0.0000
0.0693
0.0000
0.0000
0.0000
0.0149
-0.0000
0.0041
0.0000
0.0000
0.0000
0.0000
0.0000
0.000
0.1896
0.0000
0.0518
0.0149 -0.0000
0.0041
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.1896
0.0000
0.0518
0.0000
0.0000
0.0189
0.2429
0.0004
0.0000
0.0000
0.0723
0.0000
0.0000
0.0000
0.0000
0.0000o 0.0000
0.0189
0.2429
0.0004
0.0000
0.0000
0.0723
0.0000
0.0000
20
0.0000
21
0. 0000
0. 0000
0.0000
0. 1402
0.0000
0.0000
0.0000
0. 0000
0.0012
0. 0000
0.0000
0. 0000
0.7149
0. 0000
0.0000
0.0000
O.0000
0. 0000
0. 0000
0 .0028
0.2115
0.0000
0.30 36 0. 0000
0. 0000
0.C000
0.0028
0.0000
0.0000
0.2115
0. 30 36 0.0000
0.0000
0.0000
0.0030
0.0000
0.0000
0.2129
0.0000
0.0000
0. 0000
0.3318
0.0030
0.0000
0.0000
0.2129
0.0000
0.0000
0.3318
0. 0000
0. oon0000
0.0106
0.0007
0.4949
0.0000
O.0000
0.0000
0. 0000
0.0106
0.0000
0.0007
0.4949
0.0000
0. 0000
0.0000
0.0000
0.0000
22
0. 0000
0.0000
0.1425
0.0000
0. 0000
0.0000
0.0000
0. 0000
0. 0000
0.0104
0.0000
0. 5088
0.0000
0.0104
0.0000
0.5088
0 000
0.0000
0.0000
0.2118
0.0000
0.0000
0. 0000
0. 2118
0. 0000
0. 0000
0 000
0.1977
0. 0000
0.0000
0.0000
0.1977
0. 0000
r
MO-S
~
C
8
WITH
TWO
LECTRONS
IN EACH
-
9
11
10
12
13
14
0.0000
-0.0000
0.0000
0.0000
0.0000
o0.000oo0 0.0000
0.0452
0.0000
0.0000
0.0000
o.oooo
o.oooo0000 0.0000
0.0000
0. 0423
0.0000 -0.0000
0.0000
0.0000
0.
o000
0.0000
060000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0. o0000oO 0.0001
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0000
0o.0000
1.7165
0.0000
0.0000
0.0000
0.0000
1.7190
0.0000
0.0000
0.0000
0.0000
0.0005
-0.0000
0.0000
0.0000
0.0000
0.0000
0.2 848
0.0000
0.0000
0.0000
0.4933
0.0000
0.0000
0.3969
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0704
0.0000
0.0000
0.5007
0.0000
0.0000
0.0000
0.000
0.0000
0.0005
0.0000
0.0000
0.0000
0.0000
(.0000
0.4933 0.0000 0.0000 0. 2 848 0.0000
0o.oooo
0.0000oo
0.3969
0.0000
0.0000
0.0000
0.00CO
0.0000
0.0704
0.0000
0.0000
0.0000
0.5007
0.0000
0.0000
0.0000
0.0000
0.0000
0.C0000 0.0000
0.0000
0.0693
.
oo0000O.0000
0.2808
0.4926
0.0000
0.0000
0.0000
0.0701
0.2679
0.0000
0.0000
0.4993
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0. 000
0.0693
0.0000
0.0000
0.4927
0.0000
0. 0000
0.2808
0.0000
0.0701
0.0000
0.0000
0.4993
0.0000
0. 2679
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0005
0.0000
0.0000
0.0000
0.00o00 o.0000oo0.4113
0.0000
0.0000
0.0000
0.5066
0.0000
0.0000
0. 00C0
0.3135
0.0724
0.0000
0.0000
0.5073
0.0000
0.
o00000. O00
0.0000
-0.0000
0.0000
0.0000 -0.0000
0.0000
0.0005
0.0000
0.0000
0.0000
0.0000
0.0000
0.4113
0.0000
0.0000
0. 000O
0.5066
0.0000
0.0000
O.00CO
0.3136
0.0000 0.0000 0.0000oooo
0.0724
23
0.0000
0.0000O
0.0000
0.1427
0.0000
0 .0000
0.0000
0. 000
0.0000
O.000
0.0000
0.0000
0.2103
0.0000
0.0000
0. 0000
0.2103
0 .0104
0.0000
0.0000
0.5103
0.0104
0.0000
0. 000
0.5103
0.o0000
0.0000
0.0000
0. 1976
0.0000
0.0000
0.0000
0.1976
0.0000
24
0. 0000
0.0000
0.0000
0.0000
0.0000
0.2836
0.0000
0.0000
0.0000
0.o000o
0.4371
0.0000
0.0000
0.0000
0.4371
0.0000
0.0000
0 .0000
0 .0000
0.0000
0.0000
0.0000
0.0000
0.0000
25
0.5073
26
0.0000
0.0000
0.0000
.0000
0.0000
O.0000
0. 0000
.2834
0.0000
0. 0000
0. 0000
O.0000
0.0000
0. 0000
0.0000
0.0000
0.0000
0.0000
0. 4380
0. 0000
0. 0000
0.0000
0.4380
0.0000
27
28
0.0000
29
0.0000
0.0000
0.0000
0.0420
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2705
0.0000
0.0000
0.0000
0.2706
0.0005
0.0000
0.0000
0.3956
0.0005
0.0000
0.0000
0.3956
0.0000
0.0000
0.0000
0. 3123
0.0000
0.0000
0.0000
0.3123
30
0.0000 0.2999 0.0000 0.0000 0.0000
0.0000 -0.0000 0.0000 0.0000 0.1065
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0001 0.0654 0.0001 0.0000
0.0000 0.0000 O.00CO0.0000 0.0000
0.0000 0.0000 0.0001 0.0652
0.0000
0.0000 0.0000 -0.0000 0.0000 0.0000
0.2810 -0.0000 0.0000 0.0000 0.0000
0.0000 0.0199 0.1793 0.4604 0.0000
0.0000 0.0000 -0.0000 0.0000 0.0023
0.0000 0.2671 0.0003 0.0007 -0.0000
0.4289 0.0000 0.0000 0.0000 0.0000
0.0000
0.0199
0.1793
0.4604 0.0000
0.0000
0.0000C
0.0000
0.0000 0.0023
0.0000 0.2671 0.0003 0.0007 -0.0000
0.4289
0.0000
0.0000
0.0000 0.0000
0.0000 0.0199 0.1340 0.5042 0.0000
0.0000 0.0000 0.0000 0.0000 0.0023
0.4306 0.0000 0.0000 0.0000 0.0000
0.0000 0.2684 0.0003 0.0008 -0.0000
0.0000 0.0199 0.1340 0.5042 0.0000
0.0000 0.0000 0.0000 0.0000
0.0023
0.0000 0.4306
0.0000
0.0000 0.0000
0.2684
0.0000
0.0000 0.019B
0.0000 0.0000 0.0000 0.2549
0 .-4211 0.0000
0.0000 0.0000
0.0000 O. 4203 0.0000 0.0000
0.ooo00000.0000
0.0000 0.0198
0.0000 0.2549
0.0000 0.0000
0.4211 0.0000
0.0000 0.0000
0.0000
0.4203
0.0000 0.0000
0. 0000
0.0000
0.0000
0.0000
15
0.0000
0.0003
0.6524
0.0009
0.0000
0.0000
0.6524
0.0009
0.0000
0.0000
0.0000
0.0008
0.0012
0.0000
0.0000
0.0000
0.0012
0.0000
0.0000
0. 0000
0.0000
-0.0000
0.9427
-0.0007
0.0000
0.0000
0.9427
-0.0007
0.0000
0.0000
-176-
TABLE XVIII
PtCle 2 - MOCharge Matrix:
MOt s Across and AO's Down
CHARGE
ATRIX
FOR M
t
7
2
1
2
3
4
5
6
7
8
9
I0
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
0.0000
0.0003
0.0000
1.6646
-0.0000
0.0000
-0.0000
0.0000
0.J000
0O.3000
0.0000
0.0000
0.0031
0.0000
0.000
0.0000
0.0031
0.0483
0.0000
0.0000
0.1129
0.0483
0.0000
0.0000
0.1129
0.0000
0.0000
0.0000
0.0031
0.0000
0.0000
32
33
O.J000
0.0031
16
0.0000
0.0000
1.6642
0.0004
0.0004
1.6645
0.0000
0.00
3
0.0000
0.0000
-0 .0000
0.0000
0.0000
-0.0000
0.000 0 0.0000
0. 0000
0.0000
0.0483
0.0000
0.0000
0.0031
0.1129
0. 0000
0.0000
0.0000
0.0483
0.0000
0.0000
0.0031
0.1129
0.0000
0.0000
0.0000
0. 0000
0.0000
o.00 o00oo 0.0031
0.0031
0. 0000
0.C0000
0.00oCO
0.0000
0.0000
0.0031
0.0000
0. 00 00
0.0031
0.0000
0 0000
C. 0000
0.0483
0. 0000
0.1129
0.0000
0.0000
0 .9031
0.0000
0.0000
0.0483 3
0. 0C00
0.1129
0.0000
0.0031
0.0000
17
1.4250
0.0000
0. 0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0209
0.0000
0.0749
0.0000
0.0209
0.0000
0.0749
0.0000
0.0209
0.0000
0.0000
0.0749
0.0209
0.0000
0.0000
0.0749
0. 0209
0. 0 749
0.0000
0.0000
0.0209
0.0749
0.ooo0000 0.0000
0.0000
-0.0000
18
19
I
2
3
4
5
6
7
8
9
1U
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.0000
0. 000oo 0.0000
0.0000
0.0000
0.0000
0.0000
0.0248
0.0000
0.0000
O.00CO
0.1450
0.0032
0.0000
0.3oCOO
0.0000
0.0000
0.0000
0.0000
0.0000
0. J000
0.0000
0.0000
0. 0000
0.0000
0 .9000
0.0000
0.0000
0.000
0.0000
00 000 o 0.0000
0.0000
0oo
o.0000
0. oo0000o0.0000
-0.J000
0.0000
0.0000
0.0106
0. 047
0.4256
0.0696
0.0273
0.0000
0.0000
0.0000
0.4352
0.0030
0.0725
0.4245
0.0036
-0. JOO
0.0000
0.000
oOco
0
0.0106
0.0047
0.4256
0.0696
0.0273
0.u OOO
0. D000
0 0000
0.4352
0.3030
0.0725
0.4245
0.0036
0.00-0000
-0.0000
-. 0000
0.0002
0.0273
0.0047
0.4256
0.0696
0.4923
0.0019
0.0059
0.1598
0.0097
0.0000
0.0000
0. 000
0.3000
-0.0000
-0.0000
0. 0002
0.u047
0.4256
0.0696
0.0274
0.4923
0.0019
0.0059
0. 1598
0.0097
0.000
0.0000
0.0000
-O.J000
-0.0000
-0.0000
0. 0018
0.0000
0.0000
0.0000
0.0745
0.1598
0.4923
0.0019
0.0059
0.0030
0.0725
0.0036
0.4245
0.000
-0.000
-G.00CO
0.0018
0.0000
0.0000
0.0000
0.0745
0.4923
0.0019
0.0059
0.1598
0.0030
0.0725
0.4245
0.0036
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
31
0.0000
0.0422
0.0033
0.0693
0.0000
0.0000
0.0000
0.0000
0.000
0.0268
0.0009
-0.0000
0.0015
0.0268
0.0009
-0.0000
0.0015
32
0.0000
0.0707
0.0093
0.0347
0.0000
0.0000
0.0000
0.0000
0.0000
0.0762
0.0015
-0.0001
0.0007
0.0762
0.0015
-0.0001
0.0007
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.5671
0.0009
.COO1
-0.0005
0.5671
0.0009
0.0001
-0.0005
0.3448
-0.0 003
0.0001
0.0015
0.3448
-0.0003
0.0001
0.0015
0.2841
0.0015
0.0002
-0.0003
0.2841
0.0015
0.0002
-0.0003
0.5784
-0.0005
0.0002
0.0007
0.5784
-0.0005
0.0002
0.0007
33
0.2400
0.0000
O.CO0
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2897
0.0000
0.0037
0.0000
0.2897
0.0000
0.0037
0.0000
0. 2897
0.0000
0.0000
0. 0037
0.2897
0.0000
0. 0000
0.0037
0 .2 897
0.0037
0. 0000
0.0000
0 .2897
0.0037
0.0000
0. 0000
O.COO0
0.0000
0.0000
0.0000
0.5657
0.o0OC
0.5670
0.0000
0.0000
0.0186
0.0000
0.2512
0.0000
0.0186
0.0000
0.2512
0.0000
0.0013
0.0000
O.000C
0.0181
0.0013
0.0000
0.0000
0.0181
0.0099
0.1344
0.0000
0.0000
0.0099
0.1344
-0.0000
0.0000
0.0000
-0.0000
0.5670
0.0000
0.5657
0.0000
0.0000
0.0013
0.0000
0.0180
0.0000
0.0013
0.0000
0.0180
0.0000
0.0185
0.0000
0.0000
0.2511
0.0185
0.0000
0.0000
0.2511
0.0100
0.1348
0.0000
0.0000
0.0100
0.1348
0.0000
0.0000
-0.0000
0.0000
20
0.0000
0.1482
0.0241
0.0007
0. 0000
0.0000
0.0000
0. 0000
0.0000
0.0018
0.1634
O.0724
0.0008
0.0018
0.1634
0 0 724
0.0008
0.0001
0. 1634
0.0266
0.0021
0.0001
0.1634
0.0266
0.0021
0.0108
0.4449
0.0266
O.0008
0.0108
0.4449
0.0266
0.0008
21
0. 0000
0o.0000
0.0039
0.1691
0.0000
0. 0000
0. 3000
0.0000
0. 0000
0.0003
0.0000
0. 0118
0.1864
0.0003
0.0000
0. 0118
0.1864
0.0123
0. 0000
0.0043
0.5076
0.0124
0.0000
0. 0043
0.5076
0.0000
0.0000
0. 0043
0.1864
0.0000
0.0000
0.0043
0.1864
8
0.C0000 0.0000
-0.0000
0.0000
-0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
1.6148
0.G0000
0.0000
0.0000
0.0002
0.0000
1.6147
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
0.0000
0.0000
0.0963
0.0000o
0.0000
0.0963
0.0000
0.0000
0.0000
0.0963
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
0.0000
0.0000
-0.0000
0.0000
0.0000
0.0963
0.0000
22
0.0000
0.0000
0. 0000
0.0000
0.6866
0.0000
0.1055
0.0000
0.0000
0. 0001
0 000
0. 089
0. 9000
0. 0001
0.0000
0.0089
0.0000
0.0037
0. 0000
0.0000
0.2423
0.0037
0. 0000
0.0000
0. 2423
0.0052
0. 3438
0.0000
0. 0000
0.0052
0.3438
0.0000
0.0000
0.0000
0.0000
23
0.0000
0.0000
0.0000
0.0000
0.1055
0.0000
0.6866
0.0000
0.0000
0.0059
0.0000
0. 3878
0.0000
0.0059
0.0000
0.3878
0.0000
0.0023
0.0000
0. 0000
0.1544
0.0023
0. 0000
0. 0000
0.1544
0.0008
0 .0528
0 0000
0.0000
0 0008
0.0528
0.0000
0.0000
2-
WITH T
a-S
9
0.0000
0.0000
0.0000
-0.0000
-0.0000
0.0000
0.0000
1.6147
0.0002
0.0000
0.0000
0.0000
0.0000
-0.000
0.0000
-0.0000
0.0000
0.000
0.0963
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
0.0000
0.0000
0.0000
0.0963
0.0000
0.0000
00000
0.0963
24
0.0000
0.0000
0 .0000
0.0000
0. o000oo
0.0000
0.0000
0.3851
0. 0000
0.0000
0.0000
0.0000
0. 0000
0.0000
0. 0000
0.0000
0.0000
0.0000
0.4037
0.0000
0. 000
o.o000oo0
0.4037
0.0000
a. o000
0.0000
0. 0000
o .0000
0.4037
0.0000
a.0000
0.0000
0.4037
ELeCTRONS
10
11
0.0000
0. 0000
0.0000
0. 0000
0.0000
0.0000
0.0000
0. 0000
0 .0000
0. 0000
0.0001
0.0000
0.4999
0.0000
0.0001
0.0000
0.4999
0.0000
0. 0000
0.4999
0.0000
. 0000
0.0000
0.4999
0.0000
0. 0000
0.0000
0.0001
0.0000
0. 0000
0.0000
0.0000
0.0001
0.0000
25
0. 0000
0.0000
0 .0000
0.0000
(0.0000
0.3844
0.0000
0.0000
0.0007
0.0000
0.4029
0.0000
0.0008
0.0000
0.4029
0.0000
0.0008
0. 0000
0.0000
0.0008
0.0000
0. 0000
a. 0000
0.0008
0.0000
0.0000
0.0000
0.4029
0.0000
0. 0000
0.0000
0.4029
0.0000
IN EACH
12
-0.0000
13
0.0000
14
0.0000
0.0000ooo0.0004
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4999
0.0000
0.0001
0.0000
0.4999
0.0000
0.0001
0.0000
0.0000
0.0001
0.0000
0.0000
0.0000
0.0001
0.0000
0.0000
0.0000
0.4999
0.0000
0.0000
0.0000
O.000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000:
0.0000
0.0000
0.5000
0.0000
0.0000
0.0000
0.5000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5000
0.0000
0.0000
0.0464
0.0005
0.0000
0.0000
0.0000
0.0000
0.0000
0.0004
0.0028
0.3614
0.0030
0.0004
0.0028
0.3614
0.0030
0.0000
0.0028
0.2979
0.0036
0.0000
0.0028
0.2979
0.0036
0.0000
0.0034
0.2979
0.0030
0.0000
0.0034
0. 0000
0. 0003
0. 0004
0.04866
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0018
0.0031
0.2993
0.0000
0.0018
0.0031
0.2993
0.0004
0.0018
0.0026
0.3631
0.0004
0.0018
0.0026
0.3631
0.0000
0.0022
0.0026
0.2993
0.0000
0.0022
0.4999
0.0000
0.0000
05000
0.2979
0.0030
0.0026
0.2993
26
0.0000
0.0000
0 0000
0.0000
0.0000
0. 0007
0.0000
0.0000
0.3844
0.0000
0.0008
0.0000
0.4029
0.0000
0 .0008
0.0000
0.4029
0.0000
0.0000
0.4029
0.0000
0 .0000
0.0000
0.4029
0.0000
0.000
0.0000
0.0008
0.0000
0.0000
0.0000
0.0008
0.0000
27
28
0. 3350
0.0000
0.o00o00
0.0000
0'. 0000
0.0000
0.0000
0.0000
0O.0000
0.0228
0.0000
0.0000
O. COOO 0.0524
0.0000
-0.0000
0.0000
O.00CO
0.0227
0.635
0.0000
0.OCO
0.2546
0.0008
0.0000
0.0000
0.0227
0.6385
0.0000
0.0000
O0.2548
0.0008
0.0000
0.0000
0.1281
0.0227
0.0000
0.0000
0.0000
0.0000
0.2548
0.0002
0.0227
0.1281
0.0000
0.0000
0.0000
0.0000
0. 2548
0.0002
0.1946
0.0227
0.2548
0.0003
0. 0000
0.0000
0. 0000
0.0000
O.1946
0.0227
0.2548
0.0003
0. 0000
0.0000
0.0000
0.0000
15
0. 0000
0. 0466
0.0005
0.0002
0.0000
0. 000
0.0000
0. 0000
0.0000
0. 0000
0.2991
0.0039
0.0014
0.0000
0.2991
0.0039
0.0014
0. 0000
0.2991
0.0032
0.0017
0.0000
0.2991
0.0032
0.0017
0.0004
0.3628
0.0032
0.0014
0.0004
0. 3628
0.0032
0.0014
29
30
0.0000
0.0000
0.0000
0.0000
0.0524
0.0000
0.0228
0.0000
0.0000
0.0023
0.0000
0.0000
0.0000
0.0023
0.0000
0.0000
-0.0000
0.5127
0.0000
0.0000
0.0007
0.5127
0.0000
0.0000
0.0007
0.4462
0.0006
0.0000
0.0000
0.4462
0.0006
0.0000
-0.0000
0.0000
0.0019
0.1022
0.0107
0.0000
0.0000
0.0000
0.0000
0.0000
0.8357
0.0000
-0.0008
0.0002
0.8357
0.0000
-0.0008
0.0002
0.0874
0.0000
0.0021
-0.0001
0.0874
0.0000
0.0021
-0.0001
0.0155
-0.0000
0.0021
0.0002
0.0155
-0.0000
0.0021
0.0002
-178-
TABLE XIX
MC182- Orbital
Occupations and Atomic Charges
ATo
Ce t L6
I
Ct(
1.323642
2 -0.553918
3 -C.553917
4 -0.553920
5 -0.553920
6 -0.553920
7 -0.553920
-¥cv
Y
e,
NET CARGES
OsC
OS~t6
Ir C{f-
1.1 82747
0.887297
-0.470732
-0.470733
-0.505733
-0.505735
-0.467116
-0.467116
-0. 514633
-0. 514 6 3 9
-0.537471
-0.537472
-0. 539199
-0.539200
wo.
?t Ct640.685256
-0.447519
-0.447520
-0.447520
-0.447522
-0.447520
-0 .447520
ORBITAL CHARGES
1
2
3
4
5
6
7
8
9
10
1
12
13
14
15
16
17
18
19
044412-62
0.204276
0 2042T6
0.204276
0 J6 51-443
1 106462
OJ651442
1.16461
IJo64'62
1 928286
1 973156
1.679319
1 .973156
1.928286
1J973156
1679319
lj973156
r. 928287
1'973156
20
1 0973157
23
24
1.975943
1.634910
1.976038
1.927756
1.998634
1.976071
1.962601
1.597450
1. 997393
1.913289
1.962601
1.597450
1.997393
1.913304
1.997375
1.997391
1J973156
11973157
1.998634
I *92 287
1.927836
1.913304
1.997375
1.997392
1.597663
1.913150
1.976420
1.961220
t. 928287
1.679319
29
14973158
1.679319
1.9973I57
1' 928287
IJ679319
1.J9731-57
1.973156
or 6, k c~t
t14 .
0.254733
0.254694
0.689237
1.089796
0.691196
1.999998
1.090277
1.927749
1.975943
1.634910
1.976037
1.927748
0.530787
0.291943
0.291119
0.291034
0.784508
1.141868
0.781450
1.999998
1.999997
1.913289
1.635010
25
26
27
28
30
31
32
33
0. 254192
1J679319
21
22
0.493131
1.927756
1.976072
1. 635010
1.636313
1.998629
1.927837
1.636313
1.976420
1.998629
1. 597663
1.595361
1.997385
1. 913150
0.574989
0.335091
0.335091
0.335091
0.867245
1.999997
0.867245
1.999998
1.999998
1.910892
1.996849
1.542930
1.996849
1.910893
1.996849
1.542930
1.996849
1.910893
1. 996849
1.996848
1.542930
1.910893
1.996850
1.996849
1.542930
1.910893
1.542930
1.996848
1. 996849
1.910893
1.595362
1.542930
1.997384
1.996848
1.961221
1.996848
-180-
TABLE XX
MC12-
Molecular Properties
Rel2ReC
OSCe2-
IrCl 622
t~B
Ptcl.'-
-9.98
-10.87
-11.31
-11.85
eg ()£ev.]
4.91
3.39
4.11
4.30
t2g (ev.)
2.91
2.04
1.65
(1.17)
Metal Charge
1.52
1.18
0.89
o.69
Metal-Cl Bond Order
o.438
o.454
O.475
0o.475
o.435
o.445
o.484
o.508
0.003
0.009
-0.009
-0.033
Et2g
(ev.)
tag
t2 u
-
a Bond Order
Bond Order
T
,
c1
% Metal in T2g MO
89
90
85
81
eqQ:
Calc.
32
38
44
51
Obs. .1112
27.8
33.8
41.6
52.0
C1 Occupation
5s
1.93
1.93
1.91
1.91
3Pa
1.68
1.65
1.60
1.54
3pr
3.94
3.95
3.96
3.99
CHAPIER VI
REFERENCES
1.
J. H. van Vleck, J. Chem. Phys., 2, 22 (1934).
2.
J. C. Slater, Phys. Rev., 36, 57 (1930).
3.
F. Herman and S. Skillman, Atomic Structure Calculations,
Prentice-Hall, Englewood Cliffs, N.J., 1963.
4.
R. E. Watson and A. J. Freeman, Phys. Rev., 123, 521 (1961);
120, 1125
5.
(1960).
Tables of Interatomic Distances and Configuration in
Molecules and Ions, The Chemical Society, London, 1958.
6.
C. E. Moore, Atomic Energy Levels, U.S. National Bureau of
Standards Circular 467, 1949 and 1952.
7.
R. S. Mulliken, J. Chem. Phys., 23, 1833 (1955).
8.
Ibid., 23, 1841 (1955).
9.
I. Prigogine, Ed., Advances in Chemical Physics, Vol. V.,
pgs. 33-147, Interscience, N.Y., 1963.
10.
lla.
Chapter II of this thesis.
R. Ikeda, D. Nakamura and M. Kubo, J. Fys.
Chem., 69, 2101
(1965).
llb.
12.
Idem., Bull Chem. Soc. Japan, 36, 1056 (1963).
D. Nakamura, Y. Kurita, K. Ito and M. Kubo, J. Am. Chem. Soc.,
82, 5783 (1960).
13.
C. J. Jorgensen, Absorption Spectra and Chemical Bonding in
Complexes, Pergamon Press, Oxford, 1962, p. 134.
-182-
14.
Idem., Progress in Inorganic Chemistry, Vol 4, F. A. Cotton,
Ed.,
Interscience,
N.Y.,
(1963);
p. 73.
15.
J. Owen and K. W. H. Stevens, Nature, 171, 836 (1953).
16.
B. N. Figgis, Introduction to Ligand Fields, McGraw-Hill,
N.Y., 1966.
17.
C. H. Townes and B. P. Dailey, J. Chem. Phys., 17, 782 (1949).
18.
T. P. Das and E. L. Hahn, Nuclear Quadrupole Resonance
Spectroscopy, Academic Press, N.Y., 1958.
-183-
AC KNOWLEDGEMENT
My admiration and gratitude goes to Professor F. Albert Cotton
for his inspiring interest and valuable quidance in the planning
of this research.
Thanks goes to Professor J. S. Wood who has
contributed crystallorgaphic advice;
rofessor Roald Hoffman,
Professor George Koster, and Dr. Pieter Ros for assistance and
guidance in the molecular orbital calculations.
My appreciation goes to the M.I.T. Computation Center and to
Miss Marilyn A. Milan for her aid in the preparation of this manuscript.
My sincere thanks goes to Professor Alan Davison and the group
members for their friendship.
I would like to express my gratitude to the N.I.H. for granting
me a pre-doctorlalfellowship.
Finally, I would like to express my affection for my parents
and particularly for my wife, Sara.
Without her love, encouragement,
and enduring patience, this thesis would not have been possible.
BIOGRAPHICAL
Charles
B. Harris was born on April 24, 1940, in
New York City.
Michigan.
SKETCH
He attended public schools in Grosse Pointe,
On September 9, 1961, he married the former
Sara Ann Mikesell of Allen Park, Michigan.
In June 1963, he
graduated with honors from the University of Michigan with a
B.S. in Chemistry.
In the Summer of 1963 he was presented an
N.S.F. award in Chemistry.
As an undergraduate he did research
in the fields of biochemistry and biophysics.
In the Fall of 1963
he entared graduate school at Massachusetts Institute of Technology
and was awarded an N.I.H. pre-doctoral fellowship in February 1965.
He wao elected to Sigma Xi in May 1966, and received an A.E.C.
post-doctoral fellowship for the period June 1966, through
August 1967, for work under the supervision of Professor F. A. Cotton.