ML6 s-only bonding
“d0-d10 electrons”
anti bonding
“metal character”
non bonding
6 s ligands x 2e each
The bonding orbitals, essentially the ligand lone pairs,
12 s bondingwill
e
not be worked with further.
“ligand character”
π-bonding may be introduced
as a perturbation of the t2g/eg set:
Case 1 (CN-, CO, C2H4)
empty π-orbitals on the ligands
ML π-bonding (π-back bonding)
t2g (π*)
These are the SALC
formed from the p
orbitals of the ligands
that can interac with
the d on the metal.
t2g
eg
eg
Do
D’o
Do has increased
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(empty π-orbitals on ligands)
π-bonding may be introduced
as a perturbation of the t2g/eg set.
Case 2 (Cl-, F-)
filled π-orbitals on the ligands
LM π-bonding
eg
Do has decreased
eg
D’o
t2g (π*)
Do
Destabilization
t2g
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(filled π-orbitals)
Putting it all on one
diagram.
Strong field / low spin
Weak field / high spin
Spectrochemical Series
Purely s ligands:
D: en > NH3 (order of proton basicity)
 donating which decreases splitting and causes high spin:
D: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)
 accepting ligands increase splitting and may be low spin
D: CO, CN-, > phenanthroline > NO2- > NCS-
Merging to get spectrochemical series
CO, CN- > phen > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-
Strong field,
 acceptors
large D
low spin
s only
Weak field,
 donors
small D
high spin
Turning to Square Planar Complexes
z
y
x
Most convenient to use a local coordinate
system on each ligand with
y pointing in towards the metal. py to be used
for s bonding.
z being perpendicular to the molecular plane. pz
to be used for  bonding perpendicular to the
plane, ^.
x lying in the molecular plane. px to be used
for  bonding in the molecular plane, |.
ML4 square planar complexes
ligand group orbitals and matching metal orbitals
s bonding
 bonding (in)
 bonding
(perp)
ML4 square planar complexes
MO diagram
eg
s-only bonding
Sample bonding
Angular Overlap Method
An attempt to systematize the interactions for all geometries.
1
1
4
M
7
8
3
11
M
M
2
9
5
6
2
12
10
6
The various complexes may be fashioned out of the ligands
above
Linear: 1,6
Tetrahedral: 7,8,9,10
Trigonal: 2,11,12 Square planar: 2,3,4,5
T-shape: 1,3,5
Trigonal bipyramid: 1,2,6,11,12
Square pyramid: 1,2,3,4,5
Octahedral: 1,2,3,4,5,6
Cont’d
All s interactions with the ligands are stabilizing to the
ligands and destabilizing to the d orbitals. The interaction of a
ligand with a d orbital depends on their orientation with
respect to each other, estimated by their overlap which can be
calculated.
The total destabilization of a d orbital comes from all the
interactions with the set of ligands.
For any particular complex geometry we can obtain the
overlaps of a particular d orbital with all the various ligands
and thus the destabilization.
ligand
dz2
dx2-y2
dxy
dxz
dyz
1
1 es
0
0
0
0
2
¼
¾
0
0
0
3
¼
¾
0
0
0
4
¼
¾
0
0
0
5
¼
¾
0
0
0
6
1
0
0
0
0
7
0
0
1/3
1/3
1/3
8
0
0
1/3
1/3
1/3
9
0
0
1/3
1/3
1/3
10
0
0
1/3
1/3
1/3
11
¼
3/16
9/16
0
0
12
1/4
3/16
9/16
0
0
Thus, for example a dx2-y2 orbital is destabilized by (3/4 +6/16) es
= 18/16 es in a trigonal bipyramid complex due to s interaction.
The dxy, equivalent by symmetry, is destabilized by the same
amount. The dz2 is destabililzed by 11/4 es.
Coordination Chemistry
Electronic Spectra of Metal Complexes
Electronic spectra (UV-vis spectroscopy)
Electronic spectra (UV-vis spectroscopy)
hn
DE
The colors of metal complexes
Electronic configurations of multi-electron atoms
What is a 2p2 configuration?
n = 2; l = 1; ml = -1, 0, +1; ms = ± 1/2
Many configurations fit that description
These configurations are called microstates
and they have different energies
because of inter-electronic repulsions
Electronic configurations of multi-electron atoms
Russell-Saunders (or LS) coupling
For each 2p electron
n = 1; l = 1
ml = -1, 0, +1
ms = ± 1/2
For the multi-electron atom
L = total orbital angular momentum quantum number
S = total spin angular momentum quantum number
Spin multiplicity = 2S+1
ML = ∑ml (-L,…0,…+L)
MS = ∑ms (S, S-1, …,0,…-S)
ML/MS define microstates and L/S define
states (collections of microstates)
Groups of microstates with the same
energy are called terms
Determining the microstates for p2
Spin multiplicity 2S + 1
Determining the values of L, ML, S, Ms for different terms
1S
1P
Classifying the microstates for p2
Largest ML is +2,
so L = 2 (a D term)
and MS = 0 for ML = +2,
2S +1 = 1 (S = 0)
1D
Next largest ML is +1,
so L = 1 (a P term)
and MS = 0, ±1/2 for ML = +1,
2S +1 = 3
3P
Spin multiplicity = # columns of microstates
One remaining microstate
ML is 0, L = 0 (an S term)
and MS = 0 for ML = 0,
2S +1 = 1
1S
Largest ML is +2,
so L = 2 (a D term)
and MS = 0 for ML = +2,
2S +1 = 1 (S = 0)
1D
Next largest ML is +1,
so L = 1 (a P term)
and MS = 0, ±1/2 for ML = +1,
2S +1 = 3
3P
ML is 0, L = 0
2S +1 = 1
1S
Energy of terms (Hund’s rules)
Lowest energy (ground term)
Highest spin multiplicity
3P term for p2 case
3P
has S = 1, L = 1
If two states have
the same maximum spin multiplicity
Ground term is that of highest L
Determining the microstates for s1p1
Determining the terms for s1p1
Ground-state term
Coordination Chemistry
Electronic Spectra of Metal Complexes
cont.
Electronic configurations of multi-electron atoms
Russell-Saunders (or LS) coupling
For each 2p electron
n = 1; l = 1
ml = -1, 0, +1
ms = ± 1/2
For the multi-electron atom
L = total orbital angular momentum quantum number
S = total spin angular momentum quantum number
Spin multiplicity = 2S+1
ML = ∑ml (-L,…0,…+L)
MS = ∑ms (S, S-1, …,0,…-S)
ML/MS define microstates and L/S define
states (collections of microstates)
Groups of microstates with the same
energy are called terms
before we did:
p2
ML & MS
Microstate
Table
States (S, P, D)
Spin multiplicity
Terms
3P, 1D, 1S
Ground state term
3P
For metal complexes we need to consider
d1-d10
d2
3F, 3P, 1G, 1D, 1S
For 3 or more electrons, this is a long tedious process
But luckily this has been tabulated before…
Transitions between electronic terms will give rise to spectra
Selection rules
(determine intensities)
Laporte rule
g  g forbidden (that is, d-d forbidden)
but g  u allowed (that is, d-p allowed)
Spin rule
Transitions between states of different multiplicities forbidden
Transitions between states of same multiplicities allowed
These rules are relaxed by molecular vibrations, and spin-orbit coupling
Group theory analysis of term splitting
An e electron
superimposed
on a spherical
distribution
energies
reversed
because
tetrahedral
High Spin Ground States
Holes in d5
and d10,
reversing
energies
relative to
d1
dn
Free ion GS
Oct. complex
Tet complex
d0
1S
t2g0eg0
e0t20
d1
2D
t2g1eg0
e1t20
d2
3F
t2g2eg0
e2t20
d3
4F
t2g3eg0
e2t21
d4
5D
t2g3eg1
e2t22
d5
6S
t2g3eg2
e2t23
d6
5D
t2g4eg2
e3t23
d7
4F
t2g5eg2
e4t23
d8
3F
t2g6eg2
e4t24
d9
2D
t2g6eg3
e4t25
d10
1S
t2g6eg4
e4t26
dn
d10-n
dn
d5+n;
Holes: =
and neglecting spin =
same
splitting but reversed energies because positive.
Expect oct d1 and d6 to behave same as tet d4 and d9
Expect oct d4 and d9 (holes), tet d1 and d6 to be reverse of oct d1
A t2 hole in d5,
reversed energies,
reversed again
relative to
octahedral since tet.
d1  d6
d4  d9
Orgel diagram for d1, d4, d6, d9
Eg
or
E
T2g or T2
Energy
D
T2g or T2
Eg or E
D
d1, d6 tetrahedral
d4, d9 octahedral
0
d1, d6 octahedral
d4, d9 tetrahedral
ligand field strength
D
Orgel diagram for d2, d3, d7, d8 ions
Energy
A2 or A2g
T1 or T1g
T1 or T1g
P
T1 or T1g
T2 or T2g
F
T2 or T2g
T1 or T1g
A2 or A2g
d2, d7 tetrahedral
0
d2, d7 octahedral
d3, d8 octahedral
d3, d8 tetrahedral
Ligand field strength (Dq)
d2
3F, 3P, 1G, 1D, 1S
Real complexes
Tanabe-Sugano diagrams
Electronic transitions and spectra
Other configurations
d3
d9
d1
d2
d8
Other configurations
d3
The limit between
high spin and low spin
Determining Do from spectra
d1
d9
One transition allowed of energy Do
Determining Do from spectra
mixing
mixing
Lowest energy transition = Do
Ground state is mixing
E (T1gA2g) - E (T1gT2g) = Do
The d5 case
All possible transitions forbidden
Very weak signals, faint color
Some examples of spectra
Charge transfer spectra
Metal character
LMCT
Ligand character
Ligand character
MLCT
Metal character
Much more intense bands