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

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

p-bonding Complete MO Diagram 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)

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

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 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

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)

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

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

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

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

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

Four and Six Coordinate Preferences 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