6  ligands x 2e each 12  bonding e “ligand character” “d 0 -d 10 electrons” non bonding anti bonding “metal character” ML 6  -only bonding The bonding orbitals, essentially the ligand lone pairs, will not be worked with further.

t 2g egeg ML 6  -only ML 6  + π Stabilization (empty π-orbitals on ligands) oo ’o’o  o has increased π-bonding may be introduced as a perturbation of the t 2g /e g set: Case 1 (CN -, CO, C 2 H 4 ) empty π-orbitals on the ligands M  L π-bonding (π-back bonding) t 2g (π) t 2g (π*) egeg These are the SALC formed from the p orbitals of the ligands that can interac with the d on the metal.

t 2g egeg ML 6  -only ML 6  + π π-bonding may be introduced as a perturbation of the t 2g /e g set. Case 2 (Cl -, F - ) filled π-orbitals on the ligands L  M π-bonding (filled π-orbitals) Stabilization Destabilization t 2g (π) t 2g (π*) egeg ’o’o oo  o has decreased

Strong field / low spinWeak field / high spin Putting it all on one diagram.

Spectrochemical Series Purely  ligands:  en > NH 3 (order of proton basicity)  donating which decreases splitting and causes high spin:  : H 2 O > F > RCO 2 > OH > Cl > Br > I (also proton basicity)  accepting ligands increase splitting and may be low spin  : CO, CN -, > phenanthroline > NO 2 - > NCS -

Merging to get spectrochemical series CO, CN - > phen > en > NH 3 > NCS - > H 2 O > F - > RCO 2 - > OH - > Cl - > Br - > I - Strong field,  acceptors large  low spin  only Weak field,  donors small  high spin

Turning to Square Planar Complexes Most convenient to use a local coordinate system on each ligand with y pointing in towards the metal. p y to be used for  bonding. z being perpendicular to the molecular plane. p z to be used for  bonding perpendicular to the plane,  . x lying in the molecular plane. p x to be used for  bonding in the molecular plane,  |.

ML 4 square planar complexes ligand group orbitals and matching metal orbitals  bonding  bonding (in)  bonding (perp)

ML 4 square planar complexes MO diagram  -only bonding Sample  - bonding e g

A crystal-field approach: from octahedral to sq planar Less repulsions along the axes where ligands are missing

A crystal-field aproach: from octahedral to sq planar A correction to preserve center of gravity

The Jahn-Teller effect Jahn-Teller theorem: “there cannot be unequal occupation of orbitals with identical energy” Molecules will distort to eliminate the degeneracy

Angular Overlap Method An attempt to systematize the interactions for all geometries. 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 dz2dz2 d x 2 -y 2 d xy d xz d yz 11 e  ¼¾000 3¼¾000 4¼¾000 5¼¾ / /3 11¼3/169/ /43/169/1600 Thus, for example a d x 2 - y 2 orbital is destabilized by (3/4 +6/16) e  = 18/16 e  in a trigonal bipyramid complex due to  interaction. The d xy, equivalent by symmetry, is destabilized by the same amount. The d z 2 is destabililzed by 11/4 e .

Coordination Chemistry Electronic Spectra of Metal Complexes

Electronic spectra (UV-vis spectroscopy)

EE h

The colors of metal complexes

Electronic configurations of multi-electron atoms What is a 2p 2 configuration? n = 2; l = 1; m l = -1, 0, +1; m s = ± 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 m l = -1, 0, +1 m s = ± 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 M L = ∑m l (-L,…0,…+L) M S = ∑m s (S, S-1, …,0,…-S) M L /M S define microstates and L/S define states (collections of microstates) Groups of microstates with the same energy are called terms

Determining the microstates for p 2

Spin multiplicity 2S + 1

Determining the values of L, M L, S, Ms for different terms 1S1S 1P1P

Classifying the microstates for p 2 Spin multiplicity = # columns of microstates Next largest M L is +1, so L = 1 (a P term) and M S = 0, ±1/2 for M L = +1, 2S +1 = 3 3 P One remaining microstate M L is 0, L = 0 (an S term) and M S = 0 for M L = 0, 2S +1 = 1 1 S Largest M L is +2, so L = 2 (a D term) and M S = 0 for M L = +2, 2S +1 = 1 (S = 0) 1 D

Largest M L is +2, so L = 2 (a D term) and M S = 0 for M L = +2, 2S +1 = 1 (S = 0) 1 D Next largest M L is +1, so L = 1 (a P term) and M S = 0, ±1/2 for M L = +1, 2S +1 = 3 3 P M L is 0, L = 0 2S +1 = 1 1 S

Energy of terms (Hund’s rules) Lowest energy (ground term) Highest spin multiplicity 3 P term for p 2 case If two states have the same maximum spin multiplicity Ground term is that of highest L 3 P has S = 1, L = 1

Determining the microstates for s 1 p 1

Determining the terms for s 1 p 1 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 m l = -1, 0, +1 m s = ± 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 M L = ∑m l (-L,…0,…+L) M S = ∑m s (S, S-1, …,0,…-S) M L /M S define microstates and L/S define states (collections of microstates) Groups of microstates with the same energy are called terms

before we did: p2p2 M L & M S Microstate Table States (S, P, D) Spin multiplicity Terms 3 P, 1 D, 1 S Ground state term 3 P

For metal complexes we need to consider d 1 -d 10 d2d2 3 F, 3 P, 1 G, 1 D, 1 S 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 States dndn Free ion GSOct. complexTet complex d0d01S1St 2g 0 e g 0 e0t20e0t20 d1d12D2Dt 2g 1 e g 0 e1t20e1t20 d2d23F3Ft 2g 2 e g 0 e2t20e2t20 d3d34F4Ft 2g 3 e g 0 e2t21e2t21 d4d45D5Dt 2g 3 e g 1 e2t22e2t22 d5d56S6St 2g 3 e g 2 e2t23e2t23 d6d65D5Dt 2g 4 e g 2 e3t23e3t23 d7d74F4Ft 2g 5 e g 2 e4t23e4t23 d8d83F3Ft 2g 6 e g 2 e4t24e4t24 d9d92D2Dt 2g 6 e g 3 e4t25e4t25 d 101S1St 2g 6 e g 4 e4t26e4t26 Holes: d n = d 10-n and neglecting spin d n = d 5+n ; same splitting but reversed energies because positive. A t 2 hole in d 5, reversed energies, reversed again relative to octahedral since tet. Holes in d 5 and d 10, reversing energies relative to d 1 An e electron superimposed on a spherical distribution energies reversed because tetrahedral Expect oct d 1 and d 6 to behave same as tet d 4 and d 9 Expect oct d 4 and d 9 (holes), tet d 1 and d 6 to be reverse of oct d 1

Energy ligand field strength d 1  d 6 d 4  d 9 Orgel diagram for d 1, d 4, d 6, d 9 0   D d 4, d 9 tetrahedral or T 2 or E T 2g or E g or d 4, d 9 octahedral T2T2 E d 1, d 6 tetrahedral EgEg T 2g d 1, d 6 octahedral

F P Ligand field strength (Dq) Energy Orgel diagram for d 2, d 3, d 7, d 8 ions d 2, d 7 tetrahedral d 2, d 7 octahedral d 3, d 8 octahedral d 3, d 8 tetrahedral 0 A 2 or A 2g T 1 or T 1g T 2 or T 2g A 2 or A 2g T 2 or T 2g T 1 or T 1g

d2d2 3 F, 3 P, 1 G, 1 D, 1 S Real complexes

Tanabe-Sugano diagrams

Electronic transitions and spectra

Other configurations d1d1 d9d9 d3d3 d2d2 d8d8

d3d3 The limit between high spin and low spin

Determining  o from spectra d1d1 d9d9 One transition allowed of energy  o

Lowest energy transition =  o mixing Determining  o from spectra

Ground state is mixing E (T 1g  A 2g ) - E (T 1g  T 2g ) =  o

The d 5 case All possible transitions forbidden Very weak signals, faint color

Some examples of spectra

Charge transfer spectra LMCT MLCT Ligand character Metal character Ligand character Much more intense bands