Post on 20-Dec-2015
6 ligands x 2e each
12 bonding e“ligand character”
“d0-d10 electrons”
non bonding
anti bonding
“metal character”
ML6 -only bonding
The bonding orbitals, essentially the ligand lone pairs, will not be worked with further.
t2g
eg
t2g
ML6
-onlyML6
+ π
Stabilization
(empty π-orbitals on ligands)
o
’oo has increased
π-bonding may be introducedas a perturbation of the t2g/eg set:
Case 1 (CN-, CO, C2H4)empty π-orbitals on the ligands
ML π-bonding (π-back bonding)
t2g (π)
t2g (π*)
eg
These are the SALC formed from the p
orbitals of the ligands that can interac with the d on the metal.
t2g
eg
t2g
ML6
-onlyML6
+ π
π-bonding may be introducedas a perturbation of the t2g/eg set.
Case 2 (Cl-, F-) filled π-orbitals on the ligands
LM π-bonding
(filled π-orbitals)
Stabilization
Destabilization
t2g (π)
t2g (π*)
eg’o
o
o has decreased
Strong field / low spin Weak field / high spin
Putting it all on one diagram.
Spectrochemical Series
Purely ligands:
en > NH3 (order of proton basicity)
donating which decreases splitting and causes high spin:: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)
accepting ligands increase splitting and may be low spin
: 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 low spin
onlyWeak field, donors small high spin
Turning to Square Planar Complexes
y
x
zMost convenient to use a local coordinate system on each ligand with
y pointing in towards the metal. py to be used for 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 complexesligand group orbitals and matching metal orbitals
bonding
bonding (in)
bonding (perp)
ML4 square planar complexesMO diagram
-only bonding Sample- bonding
eg
Angular Overlap Method
An attempt to systematize the interactions for all geometries.
M
1
65
4 2
3
M
109
78
M 2
6
1
12
11
The various complexes may be fashioned out of the ligands above
Linear: 1,6
Trigonal: 2,11,12
T-shape: 1,3,5
Tetrahedral: 7,8,9,10
Square planar: 2,3,4,5
Trigonal bipyramid: 1,2,6,11,12
Square pyramid: 1,2,3,4,5
Octahedral: 1,2,3,4,5,6
Cont’d
All 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-y2dxy dxz dyz
1 1 e 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) e
= 18/16 e in a trigonal bipyramid complex due to interaction. The dxy, equivalent by symmetry, is destabilized by the same
amount. The dz2 is destabililzed by 11/4 e.
Coordination ChemistryElectronic Spectra of Metal Complexes
Electronic spectra (UV-vis spectroscopy)
Electronic spectra (UV-vis spectroscopy)
Eh
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 microstatesand they have different energies
because of inter-electronic repulsions
Electronic configurations of multi-electron atomsRussell-Saunders (or LS) coupling
For each 2p electron n = 1; l = 1
ml = -1, 0, +1ms = ± 1/2
For the multi-electron atomL = total orbital angular momentum quantum numberS = 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
Spin multiplicity = # columns of microstates
Next largest ML is +1,so L = 1 (a P term)
and MS = 0, ±1/2 for ML = +1,2S +1 = 3
3P
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
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
If two states havethe same maximum spin multiplicity
Ground term is that of highest L
3P has S = 1, L = 1
Determining the microstates for s1p1
Determining the terms for s1p1
Ground-state term
Coordination ChemistryElectronic Spectra of Metal Complexes
cont.
Electronic configurations of multi-electron atomsRussell-Saunders (or LS) coupling
For each 2p electron n = 1; l = 1
ml = -1, 0, +1ms = ± 1/2
For the multi-electron atomL = total orbital angular momentum quantum numberS = 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
MicrostateTable
States (S, P, D)Spin multiplicity
Terms3P, 1D, 1S
Ground state term3P
For metal complexes we need to considerd1-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
High Spin Ground Statesdn Free ion GS Oct. complex Tet complex
d0 1S t2g0eg
0 e0t20
d1 2D t2g1eg
0 e1t20
d2 3F t2g2eg
0 e2t20
d3 4F t2g3eg
0 e2t21
d4 5D t2g3eg
1 e2t22
d5 6S t2g3eg
2 e2t23
d6 5D t2g4eg
2 e3t23
d7 4F t2g5eg
2 e4t23
d8 3F t2g6eg
2 e4t24
d9 2D t2g6eg
3 e4t25
d10 1S t2g6eg
4 e4t26
Holes: dn = d10-n and neglecting spin dn = d5+n; same splitting but reversed energies because positive.
A t2 hole in d5, reversed energies,
reversed again relative to
octahedral since tet.
Holes in d5 and d10,
reversing energies relative to
d1
An e electron superimposed on a spherical
distribution energies reversed because
tetrahedral
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
Energy
ligand field strength
d1 d6 d4 d9
Orgel diagram for d1, d4, d6, d9
0
D
d4, d9 tetrahedral
or T2
or E
T2g or
Eg or
d4, d9 octahedral
T2
E
d1, d6 tetrahedral
Eg
T2g
d1, d6 octahedral
F
P
Ligand field strength (Dq)
Energy
Orgel diagram for d2, d3, d7, d8 ions
d2, d7 tetrahedral d2, d7 octahedral
d3, d8 octahedral d3, d8 tetrahedral
0
A2 or A2g
T1 or T1g
T2 or T2g
A2 or A2g
T2 or T2g
T1 or T1g
T1 or T1g
T1 or T1g
d2
3F, 3P, 1G, 1D, 1S
Real complexes
Tanabe-Sugano diagrams
Electronic transitions and spectra
Other configurations
d1 d9
d3
d2 d8
d3
Other configurations
The limit betweenhigh spin and low spin
Determining o from spectra
d1d9
One transition allowed of energy o
Lowest energy transition = o
mixing
mixing
Determining o from spectra
Ground state is mixing
E (T1gA2g) - E (T1gT2g) = o
The d5 case
All possible transitions forbiddenVery weak signals, faint color
Some examples of spectra
Charge transfer spectra
LMCT
MLCT
Ligand character
Metal character
Metal character
Ligand character
Much more intense bands