Ch 10 Lecture 3 Angular Overlap

I. Ligand Field Theory and Square Planar ComplexesA. Sigma Bonding

1) Group Theory MO Description for D4h symmetry

2) Choose dz2, dx2-y2, px, py as most likely orbitals from metal ion

3) Three d-orbitals are not involved in -bonding

(dxy, dxz, dyz)

4) The -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

B. -bonding1) dxy dxz and dyz can have -bonding

2) p-orbitals of metal too small

C. Complete MO Diagram1) -bonding set filled by L electrons

2) -donor set

a) Filled by L electrons if present F- p-orbitals or CN- -orbitals

b) Overall destabilizing on d-set

3) Metal d-orbitals split into 4 groups

4) d8 metals favor square planar due to large gap to high energy orbital (a2u)

III. Tetrahedral Complexes and Ligand Field TheoryA. Sigma and Pi bonding

B. Results

1) 4 -bonding orbitals are filled by ligand electrons

a) A1 has no match with metal other than small s-orbital

b) T2 matches dxy, dxz, dyz so these orbitals are raised in energy

c) The dx2-y2 an dz2 orbitals are not involved so stay at same energy

d) Result is an inversion of the orbital sets from octahedral complexes

2) The -bonding interactions reinforce t

III. Angular Overlap TheoryA. Development of the Theory

1) Ligand Field Theory shortcomings

a) Energy of interactions are ambiguous

b) Very complicated for multiple ligand types or non-standard geometries

2) Angular Overlap Theory

a) Estimate L—M orbital—orbital interactions

b) Combine all such interactions for the total picture of bonding

c) “Overlap” depends strongly on the angles of the orbitals to each other

d) We consider each ligand’s effect on each metal orbital and add them up

B. Sigma Donor Interactions

1) The strongest possible interaction for an octahedral complex is with dz2 orbital

a) Most of its electron density is on the z-axis

b) All other interactions are measured relative to those of dz2

c) Bonding MO’s = mostly ligand; Antibonding MO’s = mostly metal

d) Approximate the MO—AO energy difference = e

2) Example: [M(NH3)6]3+

a) Only interactions are available to NH3 ligands

b) Lone pair can be thought of as isolated in N pz orbital

c) Metal d-orbitals

i. Add up the values for interaction down the table of ligand positions

ii. dz2 = (2 x 1) + (4 x ¼ ) = 3e

iii. dx2-y2 = (2 x 0) + (4 x ¾ ) = 3e

iv. dxz, dxy, dzy, = 0 (no interactions with the ligands)

d) Ligand Orbitals

i. Total interactions with all metal d-orbitals across the row

ii. Ligand #1 and #6 = (1 x 1) + 0 = 1 e

iii. Ligands #2--#5 = (1 x ¼ ) + (1 x ¾ ) = 1 e

e) Results

i. Same pattern as LF Theory

ii. 2 d-orbitals are raised in E

iii. 3 d-orbitals are unchanged

iv. All 6 ligand orbitals lowered E = M—L bonds

v. Total of 12 e destabilization (dz2, dx2-y2) and 12 e stabilization (L)

C. -acceptor interactions1)-acceptor interactions in octahedral

geometry

a) -acceptor has empty p or MO’s = CO, CN-, PR3

b) Strongest overlap is between dxy and *

c) * is higher in energy than the dxy, so dxy becomes stabilized

d) dxy, dxz, and dyz are all stabilized by –4e, dz2 and dx2-y2 are unaffected

e) e < e (not as good overlap)

f) o is still t2g—eg* = 3e + 4e

2) -donor interactions

a) -donors have reversed signs on the interactions because now the MO is lower in energy than d-orbitals

b) The effected d-orbitals are raised in energy by +4e

c) If the ligand is a -donor and a -acceptor, the -acceptor part wins out (o is increased)

d) o is still t2g—eg* = 3e - 4e

e) dz2, dx2-y2 has +3e only from -bonding

f) dxy, dxz, dyz has +4e from only -bonding

D. Magnitudes of e, e, and o

1) Changes in ligand or metal result in changes in e, e, and o

2) The number of unpaired electrons might then change as well

3) Example: L = 6 H2O

a) Co2+ has n = 3, high spin, but Co3+ has n = 0, low spin

b) Fe3+ has n = 5 high spin, but Fe(CN)63+ has n = 1, low spin

4) Tetrahedral Complexes: t <o of a corresponding compound (fewer ligands)

5) Larger halide ligands decrease both e and e

a) Smaller overlap with d-orbitals

b) Less electronegative ligands have less interaction

E. The Spectrochemical Series

1) A list of Strong-Field through Weak-Field ligands

2) -donors only

a) en > NH3 because it is more basic (stronger field ligand)

b) F- > Cl- > Br- > I- (basicity)

3) -donors

a) Halides field strength is lowered due to -donor ability

b) For similar reasons H2O, OH-, RCO2- also are weak field ligands

4) -acceptors increase ligand field strength: CO, CN- > phen > NO2- > NCS-

5) Combined Spectrochemical SeriesCO, CN- > phen > NO2

- > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br - > I-

Strong field, low spin-acceptor

-donor only Weak field, high spin-donor

II. The Jahn-Teller EffectA. Unequal occupation of degenerate orbitals is forbidden

1) To obey this theorem, metal complexes with offending electronic structures must distort to “break” the degeneracy

2) Example: octahedral Cu(II) = d9

a) The eg* set is unequally occupied

b) The result is a “tetragonal distortion” to remove the degeneracy of the dz2 and dx2-y2 orbital energies

B. First-row metal ions and the Jahn-Teller Effect

1) The effect is greater if eg* is the effected set, rather than t2g

2) Large J-T effects: Cr2+ (d4), high spin Mn3+ (d4), Cu2+ (d9)

3) Thermodynamic parameters can be effected:

a) [Cu(NH3)3]2+ + NH3 [Cu(NH3)4]2+ K4 = 1.5 x 102

b) [Cu(NH3)4]2+ + NH3 [Cu(NH3)5]2+ K5 = 0.3

c) [Cu(NH3)5]2+ + NH3 [Cu(NH3)6]2+ K6 ~ 0

III. Four and Six Coordinate PreferencesA. Angular overlap calculations

1) Square Planar vs. Octahedral: Only d8, d9, d10 low spin complexes find this geometry energetically favorable

2) Square Planar vs. Tetrahedral:

a) d0, d1, d2, d10 complexes with strong field ligands prefer tetrahedral

b) d5, d6, d7 energies the same for weak field cases

IV. The Trigonal Bipyramidal case of 5-coordinate

complexes (D3h)

Group Theory Approach yields three sets of d-orbitals