1. Metal-ligand  interactions in an octahedral environment Six ligand orbitals of  symmetry approaching the metal ion along the x,y,z axes We can build 6 group orbitals of  symmetry as before and work out the reducible representation

2. s If you are given , you know by now how to get the irreducible representations  = A 1g + T 1u + E g

3. s Now we just match the orbital symmetries

4. 6  ligands x 2e each 12  bonding e “ligand character” “d 0 -d 10 electrons” non bonding anti bonding “metal character”

5. Introducing π-bonding 2 orbitals of π-symmetry on each ligand We can build 12 group orbitals of π-symmetry

6.  π = T 1g + T 2g + T 1u + T 2u The T 2g will interact with the metal d t 2g orbitals. The ligand pi orbitals do not interact with the metal e g orbitals. We now look at things more closely.

7. Anti-bonding LUMO(π) First, the CN- ligand

8. Some schematic diagrams showing how p bonding occurs with a ligand having a d orbital (such as in P), or a  * orbital, or a vacant p orbital.

9. 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.

10. 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.

11. 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

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

13. 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 -

14. 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

15. 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,  |.

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

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

18. A crystal-field aproach: from octahedral to tetrahedral Less repulsions along the axes where ligands are missing

19. A crystal-field aproach: from octahedral to tetrahedral A correction to preserve center of gravity

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

22. 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

23. 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.

24. ligand dz2dz2 d x 2 -y 2 d xy d xz d yz 11 e  0000 2¼¾000 3¼¾000 4¼¾000 5¼¾000 610000 7001/3 800 900 10001/3 11¼3/169/1600 121/43/169/1600 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 .