Coordination Chemistry Bonding in transition-metal complexes

1. Coordination Chemistry Bonding in transition-metal complexes

2. Crystal field theory: an electrostatic model The metal ion will be positive and therefore attract the negatively charged ligands But there are electrons in the metal orbitals, which will experience repulsions with the negatively charged ligands

3. Ligand/d orbital interactions Orbitals point at ligands (maximum repulsion) Orbitals point between ligands (less pronounced repulsion)

4. The two effects of the crystal field

5. Splitting of d orbitals in an octahedral field eg 3/5 Do Do 2/5 Do t2g Do is the crystal field splitting E(t2g) = -0.4Do x 3 = -1.2Do E(eg) = +0.6Do x 2 = +1.2Do

6. The magnitude of the splitting (ligand effect) Weak field Strong field The spectrochemical series CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-

7. The magnitude of the splitting (metal ion effect) Weak field Strong field • increases with increasing formal charge on the metal ion • increases on going down the periodic table

8. Do ≈ M ∑ nlLl x 103 The splitting constant must depend on both the ligand and the metal. Predicts value of D (cm-1) nl is # of ligands Ll

9. d1 d2 d4 d3 Placing electrons in d orbitals Strong field Weak field Strong field Weak field

10. When the 4th electron is assigned it will either go into the higher energy eg orbital at an energy cost of D0 or be paired at an energy cost of P, the pairing energy. d4 Strong field = Low spin (2 unpaired) Weak field = High spin (4 unpaired) P < Do P > Do Notes: the pairing energy, P, is made up of two parts. 1) Coulombic repulsion energy caused by having two electrons in same orbital

11. Pairing Energy, P • The pairing energy, P, is made up of two parts. • Coulombic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of Pc for each doubly occupied orbital. • Exchange stabilizing energy for each pair of electrons having the same spin and same energy. Stabilizing contribution of Pe for each pair having same spin and same energy • P = sum of all Pc and Pe interactions

12. d5 d6 d7 1 u.e. 5 u.e. 0 u.e. 4 u.e. 1 u.e. 3 u.e. d8 d9 d10 1 u.e. 1 u.e. 2 u.e. 0 u.e. 0 u.e. 2 u.e. Placing electrons in d orbitals

13. Positive favors high spin. Neg favors low spin.

14. Enthalpy of Hydration of hexahydrate

15. Splitting of d orbitals in a tetrahedral field t2 Dt e Dt = 4/9Do Always weak field (high spin)

16. Magnetic properties of metal complexes Diamagnetic complexes very small repulsive interaction with external magnetic field no unpaired electrons Paramagnetic complexes attractive interaction with external magnetic field some unpaired electrons

17. Measured magnetic moments include contributions from both spin and orbital spin. In the first transition series complexes the orbital contribution is small and usually ignored.

18. Coordination Chemistry: Molecular orbitals for metal complexes

19. The symmetry of metal orbitals in an octahedral environment A1g T1u

20. The symmetry of metal orbitals in an octahedral environment T2g Eg

21. s The symmetry of metal orbitals in an octahedral environment

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

23. s If you are given G, you know by now how to get the irreducible representations G = A1g + T1u + Eg

24. Now we just match the orbital symmetries s

25. anti bonding “metal character” non bonding 12 s bonding e “ligand character” “d0-d10 electrons” 6 s ligands x 2e each

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

27. Gπ = T1g + T2g + T1u + T2u

28. Anti-bonding LUMO(π) The CN- ligand

29. Some schematic diagrams showing how p bonding occurs with a ligand having a d orbital (P), a p* orbital, and a vacant p orbital.

30. 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

31. 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) t2g (π*) t2g eg eg t2g t2g (π) ML6 s-only ML6 s + π (empty π-orbitals on ligands)

32. 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)

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

34. 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) Adding in water, hydroxide and carboxylate D: H2O > F > RCO2 > OH > Cl > Br > I p accepting ligands increase splitting and may be low spin D: CO, CN-, > phenanthroline > NO2- > NCS-

35. 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

36. 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|.

37. ML4 square planar complexes ligand group orbitals and matching metal orbitals

38. π- bonding ML4 square planar complexes MO diagram s-only bonding

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

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

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

43. 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

44. 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.

45. 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.