Coordination Chemistry Electronic Spectra 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
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
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…
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
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