Coordination Complex

[Co(NH3)6]Cl3

Crystal Field Theory: Octahedral Complexes

xz yz xy

z2 x2-y2

Non-sphericalsymmetry

CoN

H3

NH3H3N

H3N

3+

d

degenerate d atomic orbitals

degenerate d atomic orbitals

Metal ion, Mn+, and

six ligands, L, at an

infinite distance apart

Uniformly raised energies of

d orbitals in a hypothetical

spherical electrostatic field

If the electrostatic field

created by point charge

ligands is octahedral, then the

energy of electrons in d

orbitals that point directly at

the ligands will be higher in

energy compared to

barycenter and the electrons

in d orbitals that point

between the ligands will be

lower in energy compared to

the barycenter.

d atomic orbitals split into 2 levels

Do = hn = hc/l

I- < Br- < Cl- < F- < H2O < NH3 < en < CO ~ CN-

Weak field Ligand High field Ligand

High electrostatic interaction: large CF splitting.

Low electrostatic interaction: small CF splitting.

How do we understand this trend?

Ligand Field Theory

MO Theory (LCAO-MO) applied to Coordination Complexes

Remember Classical Example of the Dative Bond:

Ammonia Borane

Co

NH

3

NH3H3N

H3N

3+

Extend to:

Metal dx2-y2

NH3

Right symmetry for interaction

Metal dxy

Wrong symmetry for interaction

x

y

NH3x

So, (3dz2, & 3dx2-y2) & 2 lone pair orbitals

interact to form sigma bonds

dxy, dxz, dyz do NOT

y

Octahedral Case: Ligands along x, y, z axes

σ-bonding: Molecular Orbital Theory (LCAO-MO)

applied to Coordination Compounds: Ligand Field Theory

Metal Atom Orbitals (ligands along x, y, z axes)

(3dz2, & 3dx2-y2)

Ligands (6 lone pair orbitals)

SALC Approach

Step 1: Find the SALCs of the L’s for the type of bond (sigma, pi…)

that we are interested in.

Step 2: Reduce that representation into a sum of irreducible representation

of the point group of our molecule

Step 3: Find the orbitals of M that have the same symmetry

as the SALCs of the L’s

Step 4: Draw the MO by combine the orbitals of M with the SALCs of L

Ligand Field Theory: Oh Complexes

SALC(sigma)

6 0 0 2 2 0 0 0 4 2 = A1g + Eg + T1u

Reducible Representation Decompose into three

Irreducible Representations

Ligand Field Theory: Oh Complexes

SALC(sigma)

6 0 0 2 2 0 0 0 4 2 = A1g + Eg + T1u

Reducible Representation Decompose into three

Irreducible Representations

Ligand Field Theory: Oh Complexes

Show that sum of irreducible representations is equal to our generated reducible representation

SALC(sigma)

6 0 0 2 2 0 0 0 4 2 = A1g + Eg + T1u

Reducible Representation Decompose into three

Irreducible Representations

s orbital: A1g …matches with the A1g SALC = A1g + Eg + T1u

(px, py, pz) orbitals: T1u …matches with the T1u SALC = A1g + Eg + T1u

(dx2—y2 , dz2) orbitals: Eg …matches with the Eg SALC = A1g + Eg + T1u

(dxy, dxz, dyz) orbitals: T2g ...no match with any SALC = A1g + Eg + T1u

Ligand Field Theory: Oh Complexes