J. Phys. Chem. 1994, 98, 12945-12948
12945
Structure of trans-Rh(PH&(CO)X (X = F, C1) Using Hartree-FocMMBPT(2) and Density
Functional Theory
Edward A. Salter,? Andrzej Wierzbicki,*y*Jorge M. Seminario,s Norris W. Hoffman,*
Michael L. Easterling,* and Jeffry D. Madura*ft
Departments of Chemistry, Spring Hill College, Mobile, Alabama 36608, University of South Alabama,
Mobile, Alabama 36688, and University of New Orleans, New Orleans, Louisiana 70148
Received: July 25, 1994; In Final Form: September 21, 1994@
A study of trans-Rh(PH3)2(CO)X (X = F, Cl) using Hartree-FocWmany-body perturbation theory and density
functional methods is presented. We report optimized Hartree-Fock and MBPT(2) structures employing
effective core potentials with double-g plus polarization basis sets including f-type functions. Optimized
structures using density functional methods, including those with gradient-corrected exchange-correlation
functionals, are also reported. Both a b initio methods yield complexes which have a slightly distorted squareplanar structure with moderate bending of the phosphine ligands toward the halide. The predicted structure
of the chloro complex is compared with experimental data for truns-Rh(PPh3)2(CO)Cl.
Introduction
Ancillary ligands exert considerable influence on the stability
and reactivity of organotransition-metal c~mplexesl-~
in stoichiometric and catalytic transformations of organic compounds.
For example, the relative effects of halide a-donation and
n-donation appear to be important factors in the strength of
metal-halide and metal-phosphine bonds.4 Experimental and
computational studies comparing the chemistry of complexes
M-X differing only in the uninegative ligand X- (e.g., halide,
carboxylate, isocyanate, isothiocyanate) are therefore of interest.
We are particularly interested in the theoretical basis for the
relative anion a f f i i t i e ~ ~
of9trans-Rh(PPh3)2(CO)+
~
in the weakly
polar solvent dichloromethane: NCO- >> OAc- >> F- NCS> C1- > Br- > I-.
In this work, we present the results of a gas phase computational study of the model rhodium(1) Vaska complex shown
below, trans-Rh(PH&(CO)X (X = F, Cl).
co
I
Rh-PH3
H3P-
I
X
The structure is essentially that of a distorted 16-electron squareplanar complex formed from a ds central metal and four a-donor
ligands. In future work, we plan to study other anion ligands
in the model complex and perhaps the more chemically
significant PMe3-, PPh3-, and PCy3-based Vaska series.
We have computed optimized structures and harmonic
vibrational frequencies for the model complexes using density
functional theory (DFT) as implemented in the DMol,' deMoh8
and the Gaussian92/DFTg computational chemistry programs.
In recent years DFT has become an accessible and attractive
method for routine calculations on medium to large molec u l e ~ . ~ ~DFT
- ' ~ geometries and harmonic vibrational frequencies for many small molecules have been found to compare
favorably with experiment and with those of traditional HartreeFock (HF)16 methods and many-body perturbation theory
+ Spring Hill College.
* University of South Alabama.
@
(MBPT(2)).I7-l9 A harmonic vibrational frequency calculation, required to establish that a given structure is a local
minimum on the potential energy surface, costs roughly the same
for DFT methods as for the HF method, and DFT frequencies
are often more accurate than the more costly MBPT(2) frequencies. Electron correlation in DFT is incorporated in the density
functional itself.20 The inclusion of f-functions on the central
metal atom in transition-metal complexes is not expected to have
a significant effect on an optimum DFT structure because the
density does not require sophisticated basis sets as wave
functions do. Our DFT results for the model chloro complex
support this claim.
For comparison, we have also computed HF- and MBPT(2)-optimized structures for the model complexes using Gaussian92.*l Studies using HF methods have been conducted on
the oxidative addition of H2 to iridium(1) Vaska c o m p l e x e ~ ~ ~ ~ ~ ~
without f-type basis functions. We believe f-functions are
necessary for the proper correlation of the d electrons of the
central metal. In this work we have included f-functions on
the central rhodium atom for all HF and MBPT(2) calculations.
University of New Orleans.
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-3654/94/2098-12945$04.50/0
Computational Details
All-Electron Calculations. DMol and deMon calculations
were performed on an IBM RISC/6000 Model 350. We used
the double numerical with polarization (DNP) and the double-t
with valence polarization (DZVP) basis sets in DMol 2.2 and
deMon 1.0, respectively. DMol calculations for the fluoro
compound involved 141 basis functions and 104 electrons, while
calculations for the chloro compound involved 145 basis
functions and 112 electrons. The deMon calculations for the
compounds involved 152 and 156 basis functions, respectively.
The basis sets do not include f-functions on rhodium. The FINE
mesh option was chosen for the numerical integration of matrix
elements. The local electron gas exchange-correlationfunctional
of Vosko, Wilk, and
(VWN) was used in deMon, and
the ~onBarth-Hedin*~functional (vBH) was used in DMol.
Both VWN and vBH correspond to parametrizations for the
uniform electron gas, but they do not yield the same results in
practice. No symmetry constraints were imposed during the
geometry optimizations. Harmonic vibrational frequencies were
computed by finite difference of analytic first derivatives to
confirm that local minima had been found.
0 1994 American Chemical Society
Salter et al.
12946 J. Phys. Chem., Vol. 98, No. 49, 1994
Density functional calculations in GAUSSIAN92DFT were
carried out on a Cray C90. We employed the Becke exchange
functional26with the Lee, Yang, and Parr correlation functionalz7
(B-LYP) and with the local spin density correlation functional
of Vosko, Wilk, and
(B-VWN); we also used the Slater
exchange functionalz8 (free electron gas) with the VWN
correlation functional (S-VWN) for direct comparison with the
deMon and DMol results. S t u d i e ~have
~ ~ .shown
~ ~ that these
functionals yield harmonic frequencies with mean absolute errors
less than those of MBFT(2) and produce respectable geometries.
Single bonds between non-hydrogen atoms tend to be somewhat
too short, double bonds are approximately correct, and triple
bonds are too long.30 The double-5 plus polarization basis
(DZP) was used in all of these calculations; the basis
does not include f-functions on rhodium. B-LYP is the highest
quality DFT model used in our study; B-LYP is considered to
have the best overall performance, at least for small molecules
in the standard 6-31G* basis.30 As a test of the impact of
f-functions, we performed a B-LYP optimization on the chloro
structure with f-functions included (optimum exponent = 1.10).
The GAUSSIAN92DFT calculations for the fluoro complex
involved a total of 104 electrons and 144 contracted Gaussian
basis functions; the chloro complex involved a total of 112
electrons and 148 contracted Gaussian basis functions (155 when
augmented with f-functions). The default grid option was
chosen for the numerical integration of matrix elements. C2,
symmetry was imposed during the geometry optimizations
which employed analytic first derivatives in the Bemy optimization algorithm. Analytical harmonic vibrational frequencies
were computed.
Pseudopotential Calculations. The HF and MBFT(2)
optimizations were carried out using GAUSSIAN92 on a Cray
XMP. Effective core potentials of the LANL1DZ34)35
basis set
provided in GAUSSIAN92 were used; valence double-5 basis
sets36are placed on each atom while an effective core potential
is used to describe the core electrons of the Rh, C1, and P atoms.
We augmented the LANLlDZ basis with polarization functions
to properly describe the consequences of the full electronelectron interaction by including basis functions of higher
angular momentum; i.e., for the d electrons of rhodium,
f-functions are required. For basis set balance, an additional
unoptimized d-function was added to the rhodium atom as well.
The exponents of the polarization functions were determined
by optimization of the MBPT(2) energy for each atom or ion.
The polarization functions used were as follows: hydrogen, p
exponent = 0.70;37 carbon, d exponent = 0.62; oxygen, d
exponent = 1.27; fluorine, d exponent = 1.52; chlorine, d
exponent = 0.56; phosphorus, d exponent = 0.39; rhodium, f
exponent = 1.10, d exponent = 1.00 (unoptimized). An
approximate DZP basis set was thereby constructed, denoted
as LANLlDZfP, suitable for MBPT(2) calculations for the
complex. Fluoro complex calculations involved 48 electrons
and 128 contracted Gaussian functions; the chloro complex
calculations involved 46 electrons and 127 contracted Gaussian
functions. Analytical first derivatives were not available for
the augmented LANLlDZ basis in GAUSSIAN92, so the
Fletcher-Powell full optimization algorithm3*was employed
in these cases with CzVsymmetry imposed. Numerical second
derivatives were not computed due to the high computational
cost.
Results and Discussion
The structural parameters of trans-Rh(PH3)~(CO)X(X = F,
C1) (Figure 1) as determined by our set of computational models
are summarized in Table 1. For comparison, the experimental
'-./
Figure 1. Structure of trans-Rh(PH3)~(CO)X(X = F, Cl). Bond lengths
and angles are given in Table 1. Complexes are distorted square-planar.
PH3 groups are eclipsed; HI and )I4 are in the primary plane.
bond angles and bond lengths for tr~ns-Rh(PPh3)2(CO)Cl~~
are
included in Table 1. Both structures are distorted square-planar;
the phosphine groups are shown in an eclipsed conformation
in Figure 1 with C2, symmetry. The rotational conformations
of the phosphine groups (estimated barrier to rotations 0.5
kcavmol) caused difficulties with convergence, and optimizations often yielded structures with one or more imaginary
harmonic frequencies, as has been seen previously with similar
compounds.z2 The fluoro complex was particularly problematic: DMol optimization produced a staggered structure as a
stable point on the potential energy surface, while deMon
optimization failed to produce a stable structure. By imposing
CZ, symmetry in all GAUSSIAN calculations, we were able to
bypass these difficulties and obtain stable structures in an
eclipsed conformation, as confirmed by harmonic frequency
calculations. The major structural difference between the
compounds is the rhodium-halide bond distance; r(Rh-F) and
r(Rh-Cl) are predicted to be 1.92-2.04 and 2.39-2.43 A,
respectively. This is as expected, since fluoride and chloride
ionic radii are given as 1.36 and 1.8 1 A, respe~tively.~~
In both
the fluoro and chloro complexes, the phosphine ligands are bent
toward the halide (a(X-Rh-P) = 83-85') due to electrostatic
attraction; each model predicts the bending to be greater by at
most 2" in the fluoro complex. In tran~-Rh(PPh3)2(CO)Cl,of
course, the bulky PPh3 ligands require maximum separation
(a(P-Rh-P) = 180°).39 It is also evident from the crystal
structure that the phenyl groups are staggered and that the
complex is skewed square-planar. The experimental values for
a(P-Rh-C) are reported as 95" and 85"; the values for a(PRh-C1) are 93.6" and 86.4".39 This departure from squareplanar symmetry observed in the X-ray structure is most likely
due to the intermolecular interaction within the crystal.
The predicted bond lengths agree reasonably well with the
values based upon the X-ray crystal data for truns-Rh(PPh3)2(C0)Cl. The best overall agreement with experiment is obtained
with the three local spin density results denoted as VWNDNP,
VWNIDZVP, and S-VWNIDZP; differences in the optimum
structures are due to the minor differences in the basis sets
employed. The B-LYP model produces bond lengths which
are systematically longer than other DFT values and longer than
expected, considering the experimental values for trans-%(PPh3)2(CO)Cl. The Rh-C bond length is 0.10 A too long, as
given by the B-LYP model and 0.06 8, too long by the local
Structure of truns-Rh(PH3)2(CO)X
J. Phys. Chem., Vol. 98, No. 49, 1994 12947
TABLE 1: Optimized Structure of trans-Rh(PH3)z(CO)X (X = F, Clyl
HFLANLlDZ
+ P"
MP2LANLIDZ iF V B " P I . ~ VWNIDZVF'fa S-VWNIDZP" B-LYPIDZP'J
1.915
2.402
1.829
1.125
1.406
1.403
82.1
164.2
97.9
99.3
127.5
113.4
0.0
123.7
1.941
2.262
1.683
1.183
1.409
1.409
85.4
170.8
94.6
98.6
127.2
114.5
0.0
123.5
( 1.987)
(2.281, 2.287)
(1.8 19)
(1.170)
(1.430)
(1.427, 1.429)
(85.2, 80.6)
( 165.8)
(96.3,97.8)
2.402
2.386
1.832
1.123
1.407
1.401
84.6
169.2
95.4
99.6
124.6
114.5
2.388
2.25 1
1.688
1.180
1.410
1.408
86.2
172.4
93.8
98.6
125.3
115.4
0.0
122.6
2.343
2.280
1.830
1.166
1.428
1.425
83.6
167.3
96.4
98.4
125.3
115.9
0.0
123.1
0.0
122.5
(125.3)
(1 15.9)
2.351
2.283
1.830
1.168
1.429
1.426
84.1
168.2
95.9
99.2
125.0
115.2
0.0
123.1
1.969
2.276
1.814
1.174
1.422
1.422
83.6
167.1
96.4
99.1
126.5
114.4
0.0
123.6
2.039
2.363
1.861
1.185
1.422
1.421
83.4
166.8
96.6
98.9
125.8
115.0
0.0
123.2
2.345
2.277
1.822
1.172
1.424
1.421
84.0
169.7
95.1
99.4
124.3
115.3
0.0
122.7
2.433 (2.428)
2.363 (2.362)
1.871 (1.864)
1.183 (1.183)
1.423 ( 1.423)
1.420 (1.420)
85.3 (85.4)
170.6 (170.8)
94.7 (94.6)
99.0 (99.0)
123.3 (123.2)
116.2 (116.2)
0.0 (0.0)
122.1 (122.1)
exptk
2.382
2.322
1.77
1.14
(93.6, 86.4)
180
(95, 85)
Bond lengths in A, bond angles (a) and dihedral angles (d) in deg. Complexes have CZ, symmetry. HF energy = -250.612 44 au (F) and
-165.893 43 au (Cl). MBFT(2) (MP2) energy = -251.668 64 au (F) and -166.899 85 au (Cl). Values in parentheses denote parameters for
converged staggered fluoro complex. Only selected parameters are shown; two values indicate that CzVsymmetry is broken. DMol-vBH energy
= -5578.988 62 au (F) and -5938.492 78 au (Cl). f Fluoro complex did not converge to a local minimum. deMon-VWN energy = -5937.849 58
au (Cl). * S-VWN energy = -5580.590 27 au (F) and -5940.250 99 au (Cl). B-LYP energy = -5587.248 95 au (F) and -5947.587 33 au (Cl).
Values in parentheses denote f-functions included in the basis set for the chloro complex. B-LYP energy = -5947.590 71 au (Cl). Experimental
parameters for trans-Rh(PPh&(CO)CI (solid phase).39 The crystal structure does not possess CzVsymmetry. Two values are shown where symmetry
is broken.
approximation methods. All other DFT bond lengths deviate
from experiment by less than 0.05 8,. The inclusion of f-type
functions in the B-LYP model shortens the Rh-Cl and Rh-C
bonds by 0.005 and 0.007 A, respectively, providing a minor
improvement. Although the B-LYP model is the most sophisticated DFT model used, it apparently does not yield the best
structure for our particular case. We can not and do not
conclude that B-LYP will not be the best overall model in
general, and extensive calculations by other groups indicate this
to be the best overall
The HFLANLlDZfP bond lengths are in good agreement
with the expected values for the chloro com lex: r(Rh-P) and
r(Rh-C) are longer than expected by 0.06 . The usual bond
length expansion upon going from the HF model to the MBPT(2) level of theory is seen for r(P-H), r(C-0) (which expands
by 0.06 8, in both complexes), and r(Rh-F) in the fluoro
complex (which expands by 0.026 8,). The other metal-ligand
bonds in both complexes are contracted at the MBPT(2) level
instead. The correlation contraction is surprisingly large (0.14
8,) for the Rh-P and Rh-C bonds in both complexes; the final
result is that these MBPT(2) bond lengths are about 0.07 8,
shorter than expected. The correlation contraction of transitionmetal-neutral ligand bonds has been observed previously for
r(M-0) in V(H20)+ and Sc(H20)+; for the rest of the series
studied (Sc-Zn), the usual r(M-0) correlation expansion was
seen.41
Frequencies and intensities of the carbonyl stretch as predicted
by the various DFT models are presented in Table 2. In the
complexes, the C-0 bond distance is known to be longer and
the carbonyl stretching frequency is known to be lower than in
B
TABLE 2: Carbonyl Harmonic Stretching Frequencies for
trans-Rh(PH~)z(CO)X(X = F, Clyl
vBW
DNPb
VWNl
DZVF
S-VWNI
DZP
B-LYPIDZP
exptd
X=F
2006.64
2014.49
2031.97
(677.7)
2037.99
(711.3)
1929.87
(677.9)
1934.96
(704.4)
1971
X=C1
2034.96
(691.1)
2042.20
(717.0)
1980
Frequencies given in cm-'. Intensities shown in parentheses; units
are in W m o l . DMol intensities not available. For deMon the value
for the fluoro compound is from a structure with one imaginary
frequency and is shown here for comparison only. Experimental values
for the fundamental absorption band for trans-Rh(PPh3)z(CO)X in
CH~C~Z.~.~
the unbound CO molecule!2
The experimental values for the
carbon monoxide molecule are 1.128 32 8, and 2169.814 cm-'
(gas phase);43 the fundamental transition in CHzClz is 2143
cm11.44 The experimental values for the PPh3-based chloro
analogue are r(C0) = 1.14(2) 8, (solid phase)39 and, for the
fundamental transition, v(C0) = 1980 cm-' (CHzC12).6 The
fundamental transition for the PPh3-based fluoro complex is
1971 cm-' ( C H Z C ~ ~Because
).~
of the lower frequency, r(C0)is expected to be slightly longer in the fluoro complex. These
experimental observations are reflected in our computational
results in Tables 1 and 2. For example, the B-LYP model
predicts 2060.7 cm-' and 1.160 A for free carbon monoxide in
the gas phase. Our B-LYP calculations predict v(C0) as 1930
and 1935 cm-' for the fluoro and chloro model complexes: the
differences in frequency are comparable to what is observed in
experiment, with the fluoro value 5 cm-' lower than the chloro
Salter et al.
12948 J. Phys. Chem., Vol. 98, No. 49, 1994
TABLE 3: Estimated AE for the tran~-Rh(PH3)2(CO)Cl
-t
F- -- truns-Rh(PH&(CO)F C1- Exchange Reactiona
+
HF/
AE
LANLlDZ+P
MP2/
LANLlDZ+P
vBW
DNP
S - W /
DZP
B-LYPI
DZP
34.8
27.9
63.7
24.4
27.4
Energies given in kcal/mol. Absolute energies for complexes given
in Table 1. F- absolute energies: HF, -99.413 96 au; MBPT(2) (MP2),
-99.602 70 au; DMol-vBH, -99.258 54 au; S-VWN, -99.432 69 au;
B-LYP, -99.866 95 au. C1- absolute energies: HF, -14.750 38 au;
MBPTQ) (MP2), -14.878 40 au; DMol-vBH, -458.864 26 au; SVWN, -459.132 26 au; B-LYP, -460.248 99 au.
value. The chloro complex C-0 bond distance is predicted
by B-LYP to be 1.183 A; the fluoro value is, as expected, longer
by 0.002 A. Indeed, all computational models shown in Table
1 indicate the value of r(C-0) is slightly longer in the fluoro
complex, and all DFT models indicate v(C0) is 5-8 cm-I lower
in the fluoro complex (Table 2).
We report estimated AE values for the gas phase chloridefluoride exchange reaction in Table 3. The highest quality
calculations, MBPT(2) using the LANLlDZ+P basis and the
B-LYP method using a DZP basis, are in excellent agreement,
yielding 27.4 and 27.9 kcaymol, respectively.
Finally, we note that Mulliken population analysis45shows
the large charge separation between the rhodium and the halide
in our model complexes. The charge difference is, of course,
smaller in the chloro complex. For example, the B-LYP
Mulliken charges are given by 0.191 (rhodium) and -0.543
(fluorine) and by -0.010 (rhodium) and -0.407 (chlorine), in
the respective complexes. The electrostatic attraction between
the phosphine ligands and the halide is represented by Mulliken
charges as well. The charges of the hydrogen atoms near the
halide are 0.020 in the fluoro complex and 0.040 in the chloro
complex.
Conclusions
Our calculations for the model phosphine-based Vaska
complexes truns-Rh(PH&(CO)X (X = F, Cl) with the MBPT
and DFT methods demonstrate that DFT methods afford
energetics and structures of comparable quality to that of the
more costly MBPT(2) method. Also, vibrational frequencies
can be calculated using DFT methods at relatively low
computational cost. The intense carbonyl stretching frequency
of the fluoro compound is predicted to be 5-8 cm-' lower than
that of the chloro compound; experiment confirms a 9 cm-'
decrease for the PPh3-based analogues in CH2Cl2. The local
density approximation yields the overall most favorable structure
in comparison with experimental data for truns-Rh(PPh3)2(CO)C1. Little advantage in the structural description of the complex
is gained by including f-type functions in the B-LYP method.
We expect that considerably larger systems can be successfully
studied using DFT methods without f-type basis functions.
Results reported in this paper show that the local density
approximation is suitable for structures and the B-LYP method
produces reliable energetics. We are currently conducting
studies of several other rhodium(1) Vaska complexes.
Acknowledgment. We thank the following for support: the
University of South Alabama Research Committee for funding,
IBM for the loan of a RISC/6000 Model 350 workstation fitted
with a 1 GB hard drive, the Alabama Supercomputer Authority
for computer time, and Biosym Technologies for the loan of
DMol 2.2 and deMon 1.0. We are grateful to Don Odom of
IBM for his assistance in obtaining and setting up the IBM
workstation.
References and Notes
(1) Tolman, C. A. Chem. Rev. 1977,77,313.
(2) Collman, J. P.; Hegedus, L. S.; Norton, J. R.; Finke, R. G. Principles
and Applications of OrganotransitionMetal Chemistry;University Science
Books: Mill Valley, 1987.
(3) Parshall, G. W. Homogeneous Catalysis;Wiley: New York, 1980.
(4) Bryndza, H. E.; Domaille, P. J.; Paciello, R. A.; Bercaw, J. E.
Organometallics 1989,8, 379.
(5) Branan, D. M.; Hoffman, N. W.; McElroy, E. A.; Miller, N. C.;
Ramage, D. L.; Schott, A. F.; Young, S. H. Inorg. Chem. 1987,26, 2915.
(6) Araghizadeh, F.; Branan, D. M.; Hoffman, N. W.; Jones, J. H.;
McElroy, E. A.; Miller, N. A.; Ramage, D. L.; Salazar, A. B.; Young, S.
H. Inorg. Chem. 1988,27, 3752.
(7) DMol version 2.2; Biosym Technologies: San Diego, CA, 1992.
(8) deMon version 1.0;Biosym Technologies; San Diego, CA, 1992.
(9) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon,
M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.;
Stewart, J. J. P.; Pople, J. A. Gaussian 92DFT Revision G.2; Gaussian
Inc.: Pittsburgh, PA, 1993.
(10) Labanowski, J. K.; Andzelm, J. W. Density Functional Methods
in Chemistry; Springer-Verlag: New York, 1991.
(11) Parr, T. G.; Yang, W. Density-Functional Theory of Atoms and
Molecules; Oxford University FVess: New York, 1989.
(12) Folga, E.; Ziegler, T. J. Am. Chem. SOC. 1993,115, 636.
(13) Folga, E.; Ziegler, T. Organometallics 1993,12, 325.
(14)Woo, T.; Folga, E.; Ziegler, T. Organometallics 1993,12, 1289.
(15) Ziegler, T.; Folga, E.; Berces, A. J. J. Am. Chem. SOC. 1993,115,
636,
(16) Roothan, C. C. J. Rev. Mod. Phy. 1951,23, 69.
(17) Moller, C.; Plesset, M. S. Phys. Rev. 1934,46, 618.
(18) Purvis, G. D., III; Bartlett, R. J. J. Chem. Phys. 1982,76, 1910.
(19) Bartlett, R. J. Annu. Rev. Phys. Chem. 1981,32, 359.
(20) Seminario, J. M. Int. J. Quantum Chem., Symp., in press.
(21) Frisch, M. J.; Trucks, G. W.; Head-Gordon,M.; Gill, P. M.; Wong,
M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.;
Repolgle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J.
S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, J. D.; Baker, J.; Stewart,
J. J. P.; Pople, J. A. Gaussian 92 Revision C; Gaussian Inc.: Pittsburgh,
PA, 1992.
(22) Abu-Hasanayn, F.; Krogh-Jespersen, K.; Goldman, A. S. Inorg.
Chem. 1993,32, 4957.
(23) Sargent, A. L.; Hall, M. B. Inorg. Chem. 1992,31, 317.
(24) Vosko, S. H.; Wilk, L.; Nussair, M. Can. J. Phys. 1980,58,1200.
(25) vonBarth, U.; Hedin, L. J. Phys. 1972,C5, 1629.
(26) Becke, A. D. Phys. Rev. A 1988,38, 3098.
(27) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B. 1988,37, 785.
(28) Slater, J. C. Quantum Theory of Molecules and Solids. The SelfConsistent Field of Molecules and Solids; McGraw-Hill: New York, 1974;
VOl. 4.
(29) Andzelm, J.; Wimmer, E. J. Chem. Phys. 1992,96, 1280.
(30) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993,
98, 5612.
(31) Godbout, N.;Salahub, D. R.; Andzelm, J.; Wimmer, E. Can. J.
Chem. 1992, 70, 560.
(32) St-Amant, A.; Salahub, D. R. Chem. Phys. Lett. 1990,169, 387.
(33) St-Amant, A. Thesis, Universite de Montreal, 1992.
(34) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985,82, 270.
(35) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985,82, 284.
(36) Dunning, T. H.; Hay, P. J. Modern Theoretical Chemistry;
Plenum: New York, 1976.
(37) Redmon, L. T.; Purvis, G. D. I.; Bartlett, R. J. J. Am. Chem. SOC.
1979,101, 2856.
(38) Fletcher, R.; Powell, M. J. D. Comput. J. 1963,6 , 163.
(39) Dunbar, K. R.; Haefner, S. C. Inorg. Chem. 1992,31, 3676.
(40) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry,
4th ed.; Harper and Row: New York, 1993; pp A-90.
(41) Magnusson, E.; Moriarty, N. W. J. Comput. Chem. 1993,14,961.
(42) Nakamoto, K. Infrared and Raman Spectra of Inorganic and
Coordination Compounds, 4th ed.; Wiley: New York, 1986.
(43) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular
Structure IV, Constants of Diatomic Molecules, 2nd ed.; van Nostrand: New
York, 1979; Vol. 1, pp 520.
(44)Hoffman, N. W. Unpublished work. Sample prepared by saturating
dichloromethane with carbon monoxide. Spectrum taken by FT-IR.
(45) Mulliken, R. S. J. Chem. Phys. 1955,23, 1833.