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