Ch 10 Lecture 3 Angular Overlap

1. Ch 10 Lecture 3 Angular Overlap • Ligand Field Theory and Square Planar Complexes • Sigma Bonding • Group Theory MO Description for D4h symmetry

2. Choose dz2, dx2-y2, px, py as most likely orbitals from metal ion Three d-orbitals are not involved in s-bonding (dxy, dxz, dyz) 4) The s-bonding diagram is complex because the d-orbitals are split into three different groups. 5) The energy difference between the lowest 2 d-orbital groups is called D

3. p-bonding dxy dxz and dyz can have p-bonding p-orbitals of metal too small Complete MO Diagram s-bonding set filled by L electrons p-donor set Filled by L electrons if present F- p-orbitals or CN- p-orbitals Overall destabilizing on d-set Metal d-orbitals split into 4 groups d8 metals favor square planar due to large gap to high energy orbital (a2u)

5. Tetrahedral Complexes and Ligand Field Theory • Sigma and Pi bonding • Results • 4 s-bonding orbitals are filled by ligand electrons • A1 has no match with metal other than small s-orbital • T2 matches dxy, dxz, dyz so these orbitals are raised in energy • The dx2-y2 an dz2 orbitals are not involved so stay at same energy • Result is an inversion of the orbital sets from octahedral complexes • The p-bonding interactions reinforce Dt

7. Angular Overlap Theory • Development of the Theory • Ligand Field Theory shortcomings • Energy of interactions are ambiguous • Very complicated for multiple ligand types or non-standard geometries • Angular Overlap Theory • Estimate L—M orbital—orbital interactions • Combine all such interactions for the total picture of bonding • “Overlap” depends strongly on the angles of the orbitals to each other • We consider each ligand’s effect on each metal orbital and add them up • Sigma Donor Interactions • The strongest possible interaction for an octahedral complex is with dz2 orbital • Most of its electron density is on the z-axis • All other interactions are measured relative to those of dz2 • Bonding MO’s = mostly ligand; Antibonding MO’s = mostly metal • Approximate the MO—AO energy difference = es

9. Example: [M(NH3)6]3+ • Only s interactions are available to NH3 ligands • Lone pair can be thought of as isolated in N pz orbital • Metal d-orbitals • Add up the values for interaction down the table of ligand positions • dz2 = (2 x 1) + (4 x ¼ ) = 3es • dx2-y2 = (2 x 0) + (4 x ¾ ) = 3es • dxz,dxy,dzy,= 0 (no interactions with the ligands) • Ligand Orbitals • Total interactions with all metal d-orbitals across the row • Ligand #1 and #6 = (1 x 1) + 0 = 1 es • Ligands #2--#5 = (1 x ¼ ) + (1 x ¾ ) = 1 es • Results • Same pattern as LF Theory • 2 d-orbitals are raised in E • 3 d-orbitals are unchanged • All 6 ligand orbitals lowered E = M—L bonds • Total of 12 es destabilization (dz2, dx2-y2) and 12 es stabilization (L)

10. p-acceptor interactions 1) p-acceptor interactions in octahedral geometry a) p-acceptor has empty p or p MO’s = CO, CN-, PR3 b) Strongest overlap is between dxy and p* p* is higher in energy than the dxy, so dxy becomes stabilized d) dxy, dxz, and dyz are all stabilized by –4ep, dz2 and dx2-y2 are unaffected ep < es (not as good overlap) Do is still t2g—eg* = 3es + 4ep

11. p-donor interactions p-donors have reversed signs on the interactions because now the p MO is lower in energy than d-orbitals The effected d-orbitals are raised in energy by +4ep If the ligand is a p-donor and a p-acceptor, the p-acceptor part wins out (Do is increased) Do is still t2g—eg* = 3es - 4ep dz2, dx2-y2 has +3es only from s-bonding f) dxy, dxz, dyz has +4ep from only p-bonding

12. Magnitudes of es, ep, and Do • Changes in ligand or metal result in changes in es, ep, and Do • The number of unpaired electrons might then change as well • Example: L = 6 H2O • Co2+ has n = 3, high spin, but Co3+ has n = 0, low spin • Fe3+ has n = 5 high spin, but Fe(CN)63+ has n = 1, low spin

13. Tetrahedral Complexes: Dt <Do of a corresponding compound (fewer ligands) • Larger halide ligands decrease both es and ep • Smaller overlap with d-orbitals • Less electronegative ligands have less interaction • The Spectrochemical Series • A list of Strong-Field through Weak-Field ligands • s-donors only • en > NH3 because it is more basic (stronger field ligand) • F- > Cl- > Br- > I- (basicity) • p-donors • Halides field strength is lowered due to p-donor ability • For similar reasons H2O, OH-, RCO2- also are weak field ligands • p-acceptors increase ligand field strength: CO, CN- > phen > NO2- > NCS- • Combined Spectrochemical Series CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br - > I- Strong field, low spin p-acceptor s-donor only Weak field, high spin p-donor

14. The Jahn-Teller Effect • Unequal occupation of degenerate orbitals is forbidden • To obey this theorem, metal complexes with offending electronic structures must distort to “break” the degeneracy • Example: octahedral Cu(II) = d9 • The eg* set is unequally occupied • The result is a “tetragonal distortion” to remove the degeneracy of the dz2 and dx2-y2 orbital energies

15. First-row metal ions and the Jahn-Teller Effect • The effect is greater if eg* is the effected set, rather than t2g • Large J-T effects: Cr2+ (d4), high spin Mn3+ (d4), Cu2+ (d9) • Thermodynamic parameters can be effected: • [Cu(NH3)3]2+ + NH3 [Cu(NH3)4]2+ K4 = 1.5 x 102 • [Cu(NH3)4]2+ + NH3 [Cu(NH3)5]2+ K5 = 0.3 • [Cu(NH3)5]2+ + NH3 [Cu(NH3)6]2+ K6 ~ 0 • Four and Six Coordinate Preferences • Angular overlap calculations • Square Planar vs. Octahedral: Only d8, d9, d10 low spin complexes find this geometry energetically favorable • Square Planar vs. Tetrahedral: • d0, d1, d2, d10 complexes with strong field ligands prefer tetrahedral • d5, d6, d7 energies the same for weak field cases • The Trigonal Bipyramidal case of 5-coordinate complexes (D3h) Group Theory Approach yields three sets of d-orbitals