6 s ligands x 2e each

1. anti bonding “metal character” non bonding 12 s bonding e “ligand character” ML6s-only bonding “d0-d10 electrons” The bonding orbitals, essentially the ligand lone pairs, will not be worked with further. 6 s ligands x 2e each

2. Do Do has increased D’o Stabilization 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) These are the SALC formed from the p orbitals of the ligands that can interac with the d on the metal. t2g (π*) t2g eg eg t2g t2g (π) ML6 s-only ML6 s + π (empty π-orbitals on ligands)

3. D’o Do has decreased Do Destabilization Stabilization 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 eg t2g (π*) t2g t2g t2g (π) ML6 s-only ML6 s + π (filled π-orbitals)

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

5. 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) p accepting ligands increase splitting and may be low spin D: CO, CN-, > phenanthroline > NO2- > NCS-

6. Merging to get spectrochemical series CO, CN- > phen > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I- Weak field, p donors small D high spin Strong field, p acceptors large D low spin s only

7. Turning to Square Planar Complexes 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 p bonding perpendicular to the plane, p^. x lying in the molecular plane. px to be used for p bonding in the molecular plane, p|.

8. ML4 square planar complexes ligand group orbitals and matching metal orbitals s bonding p bonding (in) p bonding (perp)

9. Sample π- bonding ML4 square planar complexes MO diagram eg s-only bonding

10. 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 Square pyramid: 1,2,3,4,5 Octahedral: 1,2,3,4,5,6 Tetrahedral: 7,8,9,10 Square planar: 2,3,4,5 Trigonal bipyramid: 1,2,6,11,12

11. 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.

12. 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.

13. Coordination Chemistry Electronic Spectra of Metal Complexes

14. Electronic spectra (UV-vis spectroscopy)

15. Electronic spectra (UV-vis spectroscopy) hn DE

16. The colors of metal complexes

18. Many configurations fit that description Electronic configurations of multi-electron atoms What is a 2p2 configuration? n = 2; l = 1; ml = -1, 0, +1; ms = ± 1/2 These configurations are called microstates and they have different energies because of inter-electronic repulsions

19. Electronic configurations of multi-electron atoms Russell-Saunders (or LS) coupling 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) For each 2p electron n = 1; l = 1 ml = -1, 0, +1 ms = ± 1/2 ML/MS define microstates and L/S define states (collections of microstates) Groups of microstates with the same energy are called terms

20. Determining the microstates for p2

21. Spin multiplicity 2S + 1

22. Determining the values of L, ML, S, Ms for different terms 1S 1P

23. 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 One remaining microstate ML is 0, L = 0 (an S term) and MS = 0 for ML = 0, 2S +1 = 1 1S Classifying the microstates for p2 Electrons must have different quantum numbers 1+ 1+ illegal 1+ 1- is same as 1- 1+ (indistinguishable) Spin multiplicity = # columns of microstates

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

25. 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

26. Determining the microstates for s1p1

27. Determining the terms for s1p1 Ground-state term

28. Coordination Chemistry Electronic Spectra of Metal Complexes cont.

29. Electronic configurations of multi-electron atoms Russell-Saunders (or LS) coupling 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) For each 2p electron n = 1; l = 1 ml = -1, 0, +1 ms = ± 1/2 ML/MS define microstates and L/S define states (collections of microstates) Groups of microstates with the same energy are called terms

30. ML & MS Microstate Table States (S, P, D) Spin multiplicity Terms 3P, 1D, 1S Ground state term 3P before we did: p2

31. d2 3F, 3P, 1G, 1D, 1S For metal complexes we need to consider d1-d10 For 3 or more electrons, this is a long tedious process But luckily this has been tabulated before…

32. Transitions between electronic terms will give rise to spectra

33. 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

34. Group theory analysis of term splitting

35. 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 A t2 hole in d5, reversed energies, reversed again relative to octahedral since tet. Holes: dn = d10-n and neglecting spin dn = d5+n; 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

36. Eg or E T2gor T2 D T2g or T2 Egor E d1, d6 octahedral d1, d6 tetrahedral d4, d9 octahedral d4, d9 tetrahedral d1 d6 d4 d9 Orgel diagram for d1, d4, d6, d9 Energy D D 0 ligand field strength

37. Orgel diagram for d2, d3, d7, d8 ions Energy A2 or A2g T1 or T1g T1 or T1g P T2 or T2g T1 or T1g F T2 or T2g T1 or T1g A2 or A2g d2, d7 tetrahedrald2, d7 octahedral d3, d8 octahedral d3, d8 tetrahedral 0 Ligand field strength(Dq)

38. 3F, 3P, 1G, 1D, 1S Real complexes d2

39. Tanabe-Sugano diagrams

40. Electronic transitions and spectra

41. d3 d9 d1 d2 d8 Other configurations

42. d3 Other configurations The limit between high spin and low spin

43. Determining Do from spectra d1 d9 One transition allowed of energy Do

44. mixing mixing Determining Do from spectra Lowest energy transition = Do

45. Ground state is mixing E (T1gA2g) - E (T1gT2g) = Do

46. The d5 case All possible transitions forbidden Very weak signals, faint color

47. Some examples of spectra

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