Electronic Structure of d-Metal Complexes : Ligand Field Theory and Jahn -Teller distortion

1. Electronic Structure of d-Metal Complexes :Ligand Field Theory andJahn-Teller distortion 201450098 김동현

2. Contents • Crystal Field Theory • Ligand Field Theory • Jahn-Teller distortion

3. Crystal Field Theory • the electron pairs on the ligands are viewed as point negative charges that interact with the d orbitals on the central metal. • The nature of the ligand and the tendency toward covalent bonding is ignored. • splitting of the d orbitals • The model can be used to understand, interpret and predict the magnetic behavior, colors and some structures of coordination complexes.

4. Ligands, viewed as point charges, at the corners of an octahedron affect the various dorbitals differently.

5. d - Orbital Splitting destabilized (higher energy) Stabilized (lower energy)

6. The colors exhibited by most transition metal complexes arises from the splitting of the d orbitals. • As electrons transition from the lower t2g set to the eg set, light in the visible range is absorbed.  Color depends on size of ∆o • The actual size of the gap varies with the metal

8. CFT limitation The complexes of cobalt (III) show the shift in color due to the ligand. (a) CN–, (b) NO2–, (c) phen, (d) en, (e) NH3, (f) gly, (g) H2O, (h) ox2–, (i) CO3 2–.

9. Ligand Field Theory • Crystal Field Theory completely ignores the nature of the ligand. As a result, it cannot explain the spectrochemical series. • Ligand Field Theory uses a molecular orbital approach.

10. Ligand • Bonding • πBonding p-donor p-acceptor

11. Bonding

12. Creation of a Molecular Orbital Diagram for an Octahedral Complex • The most basic approach considers sigma bonding only, since all ligands can act as sigma donors. • A set of group orbitals (SALCs) representing the six ligands is constructed from the 6 ligand orbitals. • Using a group theoretical approach, the symmetries of the ligand group orbitals can be shown to be a1g, t1u, and eg. • These group orbitals interact with the metal d, s, and p orbitals (which have symmetries of eg/t2g, a1g, and t1u, respectively) to form molecular orbitals.

13. The metal dxy, dxz, and dyz orbitals are of t2g symmetry. Because there is no ligand group orbital of suitable symmetry to interact with these orbitals, they form nonbonding molecular orbitals. • The molecular orbitals may then be filled with electrons, with two electrons coming from each of the ligands for a total of 12 electrons. • If the metal has any d-electrons, they will populate the t2g and eg* orbitals, as predicted by crystal field theory. • The difference between the t2g and eg* orbitals gives Δo, the crystal field splitting parameter.

14. totally symmetric a1g orbital. doubly degenerate eggroup Group orbitals for sigma bonding in an octahedral transition metal complex. triply degenerate t1u group s orbitals Group orbitals showing interaction with metal dx2-y2 and dz2 orbitals px, py, and pzorbitals

15. Molecular orbital diagram for an octahedral transition metal complex, considering only sigma bonding

16. π Bonding - π donor • A ligand with filled π orbitals acts as a π donor. • Halogens are an example of π donor ligands.

18. π Bonding - π Acceptor • CO is an example of a π acceptor ligand. • A ligand with empty π* orbitals can accept electron density from a metal d-orbital.

21. The Spectrochemical Series • list of Strong-Field through Weak-Field ligands CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br - > I- Weak field, high spin p-donor Strong field, low spin p-acceptor s-donor only

22. Ligand Field Strength Observations 1. ∆o increases with increasing oxidation number on the metal. Mn+2<Ni+2<Co+2<Fe+2<V+2<Fe+3<Co+3 <Mn+4<Mo+3<Rh+3<Ru+3<Pd+4<Ir+3<Pt+4 2. ∆oincreases down a group

23. 4 electron in metal d orbital

24. High Spin /Low Spin (d1 to d10) • Electron configurations for octahedral complexes, e.g. [M(OH2)6]+n • Only the d4 through d7 cases can be either high-spin or low spin

25. Ligand Field Stabilization Energy • A measure of the net stabilization of the complex relative to the free ion • Large negative values indicate a stable complex

26. Evaluating LFSE • Net stabilization = -2/5 Δoctfor each t2ge- • Net destabilization = +3/5 Δoctfor each ege- • For a high spin d7 case : LFSE = 5(-2/5 Δoct) +2(+3/5 Δoct) = -4/5 Δoct

27. Ligand Field Theory - Square planar

28. The square planar complex looks like the octahedral complex without ligands along the z axis. • This should result in lowering the energy of any orbital involving the z axis.

30. Ligand Field Theory - Tetrahedral

31. Tetrahedral Splitting Diagram • Relatively small field splitting: ΔT= (4/9)∆o • Tetrahedral complexes are almost always high spin because of the weak crystal field. That is, ΔT < P(pairing E)

33. Jahn-Teller distortion

34. High-spin Ni(II) – only one way of filling the eg level – not degenerate, no J-T distortion Cu(II) – two ways of filling eg level – it is degenerate, and has J-T distortion d9 d8 eg eg energy eg t2g t2g t2g Ni(II)

36. Thermodynamic parameters can be effected • [Cu(H2O)3(NH3)3]2+ + NH3[Cu(H2O)2(NH3)4]2+ K4 = 1.5 x 102 • [Cu(H2O)2(NH3)4]2+ + NH3[Cu(H2O)(NH3)5]2+ K5 = 0.3 • [Cu(H2O)(NH3)5]2+ + NH3[Cu(NH3)6]2+ K6 ~ 0

38. Reference • Miessler, Gary L.; Tarr, Donald A. Inorganic Chemistry Third Edition. Prentice Hall.  • University of California, Irvine, http://www.chem.uci.edu/~lawm/ Matt Law Research Group • Decock, Roger L.; Gray, Harry B. (1990). Chemical Structure and Bonding. Benjamin/Cummings.  • University of North Carolina Wilmington Lecture, Jahn-Teller distortion and coordination number four.

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