Molecular orbital theory approach to bonding in transition metal complexes

Molecular orbital (MO) theory considers the overlap of atomic orbitals, of matching symmetry and comparable energy, to form molecular orbitals.

When atomic orbital wave functions are combined, they generate equal numbers of bonding and antibonding molecular orbitals.

The bonding MO is always lower in energy than the corresponding antibonding MO.

Electrons occupy the molecular orbitals in order of their increasing energy in accordance with the aufbau principal.

Bond-Order = Electrons in bonding MOs – Electrons in antibonding MOs 2

2pz

1s

2pz

2s

2pz*

2s*

1s*

2s*

2px,2py*

2px

2px,2py

2s

1s

2py

2px* 2py*

2pz*

1s*

Molecular Orbitals for Homonuclear Diatomic Species

Molecular orbital descriptions of dioxygen species.

2p

2p*

2p*

2p

1560

121~128 ~149

1150-1100 850-740

3O2

Tripletoxygen

Singletoxygen

Superoxide Peroxide

1O2 (1

Singletoxygen1O2 (1 2O2

1O22-

Bond-order2.01.5 1.0

vibrational stretching frequency (cm-1)

Bond-length (pm)

Molecular orbital approach to bonding in octahedral complexes, ML6

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Combinations of atomic orbitals Molecular Orbital

4s ± 1/√6(σ1 + σ2 + σ3 + σ4 + σ5 + σ6) a1g

4px ± 1/√2 (σ1 σ2)

4py ± 1/√2 (σ3 σ4) t1u

4pz ± 1/√2 (σ5 σ6)

3dx2 - y2 ± 1/2 (σ1 + σ2 σ3 σ4) eg

3dz2 ± 1/√12 (2 σ5 + 2 σ6 σ1 σ2 σ3 σ4)

3dxy

3dxz Non-bonding in σ complex t2g

3dyz

_______________________________________________________________________________________________

MO diagram for -bonded octahedral metal complex

a1g

a1g*

t1u*

t1u

eg*

t2g

eg

4p

4s

3d

6 ligandorbitals (

Metal ion, Mn+ Ligand, L[ML6]n+

o

12 electrons

dn electrons

a1g

a1g*

t1u*

t1u

eg*

t2g

eg

4p

4s

3d

6 ligandorbitals

Metal ion, Mn+ Ligand, L[ML6]n+

o

LMCTtransitions

MLCTtransitions

d-d transitions

ligand electrons

d electrons

Electronic Transitions in d4 Octahedral Metal Complex

Since the metal 4p and t2 orbitals are of the same symmetry, e → t2 transitions in Td complexes are less “d-d” than are t2g → eg transitions inOh complexes. They are therefore more allowed and have larger absorbtivity values (

M.O. Diagram for Tetrahedral Metal Complex

t2b

t2*

a1*

a1b

e

t2

4p

4s

3d 4 ligandorbitalsf illed with lone pair electrons ( )

t

ML4M 4 L

3d electrons

Metal-ligand -bonding interactions

t2g orbitals (dxy, dxz, dyz) are non-bonding in a -bonded octahedral complex

ligands of -symmetry overlap with the metal t2g orbitals to form metal-ligand -bonds.

-unsaturated ligands such as CO, CN- or 1,10-phenanthroline or sulfur and phosphorus donor ligands (SR2, PR3) with empty t2g-orbitals have the correct symmetry to overlap with the metal t2g orbitals.

C O

Metal- d

*

Ligand overlap-

*(t2g)

M

C=O

Metal- d Ligand -

P

R

RR

d(t2g) (t2g)

M

acceptor interactions have the effect of lowering the energy of the non-bonding t2g orbitals and increasing the magnitude oct.

ML6 Complex

ML6 Complex

6 Ligand orbitals

t2g(occupied)

eg*eg

*

t2g*

t2gb

Ligand(vacant)

his explains why -acceptor ligands like CO and CN- are strong field ligands, and why metal carbonyl and metal cyanide complexes are generally low-spin.

Metal- d Ligand -

L

p(t2g)

MLigand p (full)e.g. halide ion, X-

RO-

-interactions involving -donation of electron density from filled p-orbitals of halides (F- and Cl-) and oxygen donors, to the t2g of the

metal, can have the opposite effect of lowering the magnitude ofoct. In this case, the t2g

electrons of the -complex, derived from

the metal d orbitals, are pushed into the higher t2g* orbitals and

become antibonding. This has the effect of lowering oct.

(R)

ML6 Complex

ML6 Complex

6 Ligand orbitals

t2g(occupied)

eg*

t2g*

t2gb

Ligand(f illed)

eg*

Effect of ligand to metal donor interactions

-alkene organometallic complexes

HH

C

HH

C

Pt

Cl

Cl

Cl

Zeise’s Salt, K[PtCl3(C2H4)]

H

H

C

H

H

C

M

H

H

C

H

H

C

M

Metal Alkene ( Metal (t2g) Alkene ((dX2-y

2) donation -backbonding

L

L

L

L

L

L

C CHH

H HC C

HH

H H

-bonding MO (f illed) -antibonding MO

(empty)

*

acceptor interactions have the effect of lowering the energy of the non-bonding t2g orbitals and increasing the magnitude oct.

ML6 Complex

ML6 Complex

6 Ligand orbitals

t2g(occupied)

eg*eg

*

t2g*

t2gb

Ligand(vacant)

his lowering of the energy of the t2g orbitals also results in 9 strongly bonding M.O.’s well separated in energy from the antibonding orbitals

ML6 Complex

ML6 Complex

6 Ligand orbitals

t2g(occupied)

eg*eg

*

t2g*

t2gb

Ligand(vacant)

a1g

t1u

eg18 bonding electrons

6 -donor ligands (f illed)

Consequences of -bonding interactions between metal and ligand

Enhanced -splitting for -acceptor ligands makes -unsaturated ligands like CO, CN- and alkenes very strong-field ligands.

Stabilization of metals in low oxidation states. Delocalization of electron density from low oxidation state (electron-rich) metals into empty ligand orbitals by “back-bonding” enables metals to exist in formally zero and negative oxidation states (Fe(CO)5, Ni(CO)4

2-).

Accounts for organometallic chemistry of -Acid ligands

The application of the “18-electron rule” to predict and rationalize structures of many acidorganometallic compounds.

Electron donation by -unsaturated ligands

M

M

M

C C

M

AlkeneH2C=CH2

1,3-Butadiene C4H6

CyclopentadienylC5H5 (Cp)

BenzeneC6H6

CC

C

M

-Allyl C3H5

CH2=CH-CH2-

Ligand Hapticity, Electrons donated

CO M-CO 2

2

3

4

5

6

Ru

C C

CC

CO

O

OO

O Ru

5 CO 10

8

18

Ru(CO)5

6-C6H6

Mo

3 CO

6

6

6

18

Mo

C C

C

O O

O

Mo( C6H6)(CO)3

Examples of 18-electron organometallic complexes with -unsaturated (-acid) ligands

H H

Mo

C C

C

O O

O

C7H8

Mo

3 CO

6

66

18

W

C

CO

O

C5H5

5-C5H5

W

2 CO

3

54

6

18

W( C5H5)(5-C5H5)(CO)2

Fe Fe

C

CO

CO

CO

O

Fe 85-C5H5 5CO 22 -CO 2Fe-Fe 1 18

FeCl Fe 8

C3H5 33 CO 61 Cl 1 18

Fe( C3H5)(CO)3Cl

Scope of 16/18-electron rules for d-block organometallic compounds

Usually less than 18 electrons

Sc Ti VY Zr Nb

Usually18 electrons

Cr Mn FeMo Tc RuW Re Os

16 or 18Electrons

Co NiRh PdIr Pt

Fe

O

O of O2 (filled)

dz2 of Fe (empty)

O

O

Fe

of O2 (empty)

t2g (dxz,dyz) of Fe (filled)

*

*

Metal-ligand interactions involving bonding and antibonding molecular orbitals of O2