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Ch 10 Lecture 3 Angular Overlap

I. Ligand Field Theory and Square Planar Complexes

A. Sigma Bonding

1) Group Theory MO Description for D4hsymmetry

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2) Choose dz2, dx2-y2, px, pyas

most likely orbitals from

metal ion

3) 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-orbitalgroups is called D

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B. p-bonding

1) dxydxzand dyzcan have p-bonding

2) p-orbitals of metal too small

C. Complete MO Diagram

1) s-bonding set filled by L electrons

2) p-donor set

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

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III. Tetrahedral Complexes and Ligand Field Theory

A. Sigma and Pi bonding

B. Results

1) 4 s-bonding orbitals are filled by ligand electrons

a) A1has no match with metal other than small s-orbital

b) T2matches dxy, dxz, dyzso these orbitals are raised in energyc) The dx2-y2an dz2orbitals are not involved so stay at same energy

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

2) The p-bonding interactions reinforce Dt

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III. Angular Overlap Theory

A. 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 LM orbitalorbital interactions

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

c) Overlap depends strongly on the angles of the orbitals to each otherd) We consider each ligands effect on each metal orbital and add them up

B. Sigma Donor Interactions

1) The strongest possible interaction for an octahedral complex is with dz2orbital

a) Most of its electron density is on the z-axisb) All other interactions are measured relative to those of dz2

c) Bonding MOs = mostly ligand; Antibonding MOs = mostly metal

d) Approximate the MOAO energy difference = es

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

a) Only sinteractions are available to NH3ligands

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

c) Metal d-orbitals

i. Add up the values for interaction down the table of ligand positionsii. dz2= (2 x 1) + (4 x ) = 3es

iii. dx2-y2= (2 x 0) + (4 x ) = 3es

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

d) Ligand Orbitalsi. Total interactions with all metal d-orbitals across the row

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

iii. Ligands #2--#5 = (1 x ) + (1 x ) = 1 es

e) Resultsi. 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 = ML bonds

v. Total of 12 esdestabilization (dz2, dx2-y2) and 12 esstabilization (L)

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C. p-acceptor interactions

1) p-acceptor interactions in octahedral

geometry

a) p-acceptor has empty p or p

MOs = CO, CN-, PR3

b) Strongest overlap is between

dxyand p*

c) p* is higher in energy than the

dxy, so dxybecomes stabilized

d) dxy, dxz, and dyzare all

stabilized by4ep, dz2and dx2-y2are unaffected

e) ep< es(not as good overlap)

f) Dois still t2geg* = 3es+ 4ep

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2) p-donor interactions

a) p-donors have reversed signs on the

interactions because now the pMO

is lower in energy than d-orbitals

b) The effected d-orbitals are raised in

energy by +4ep

c) If the ligand is a p-donor and a p-

acceptor, the p-acceptor part wins

out (Dois increased)

d) Dois still t2geg* = 3es- 4ep

e) dz2, dx2-y2has +3esonly from s-

bonding

f) dxy, dxz, dyzhas +4epfrom only p-

bonding

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D. Magnitudes of es, ep, and Do

1) Changes in ligand or metal result in changes in es, ep, and Do

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

3) Example: L = 6 H2O

a) Co

2+

has n = 3, high spin, but Co

3+

has n = 0, low spinb) Fe3+has n = 5 high spin, but Fe(CN)6

3+ has n = 1, low spin

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4) Tetrahedral Complexes: Dt NH3because it is more basic (stronger field ligand)

b) F- > Cl- > Br- > I- (basicity)3) p-donors

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

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

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

5) 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

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II. The Jahn-Teller Effect

A. 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 dz2and

dx2-y2orbital energies

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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 10

2

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 Preferences

A. Angular overlap calculations1) Square Planar vs. Octahedral: Only d8, d9, d10low spin complexes find this

geometry energetically favorable

2) Square Planar vs. Tetrahedral:

a) d0, d1, d2, d10complexes 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

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