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
Molecular orbital descriptions of dioxygen species.
Molecular orbital approach to bonding in octahedral complexes, ML6
______________________________________________________________________________________________________________________________
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)
4pz ± 1/√2 (σ5  σ6)
t1u
3dx2 - y2 ± 1/2 (σ1 + σ2  σ3  σ4)
3dz2
± 1/√12 (2 σ5 + 2 σ6  σ1  σ2  σ3  σ4)
eg
3dxy
3dxz
3dyz
t2g
Non-bonding in σ complex
_______________________________________________________________________________________________
MO diagram for s-bonded octahedral metal complex
M.O. Diagram for Tetrahedral 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 in Oh complexes. They are
therefore more allowed and have larger absorbtivity values (e)
Metal-ligand P-bonding interactions
 t2g orbitals (dxy, dxz, dyz) are non-bonding in a s-bonded octahedral
complex
 ligands of P-symmetry overlap with the metal t2g orbitals to form
metal-ligand P-bonds.
 P-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.
Pacceptor interactions have the effect of lowering the energy of
the non-bonding t2g orbitals and increasing the magnitude Doct.
This explains why P-acceptor ligands like CO and CN- are strong field ligands, and
why metal carbonyl and metal cyanide complexes are generally low-spin.
P-interactions involving P-donation of electron density from filled porbitals of halides (F- and Cl-) and oxygen donors, to the t2g of the
metal, can have the opposite effect of lowering the magnitude of
Doct. In this case, the t2g electrons of the s-complex, derived from the
metal d orbitals, are pushed into the higher t2g* orbitals and become
antibonding. This has the effect of lowering Doct.
M
Metal- d (t2g)
L
Ligand p (full)
e.g. halide ion, XRO-
Ligand - p
Effect of ligand to metal Pdonor interactions
P-alkene organometallic complexes
Zeise’s Salt, K[PtCl3(C2H4)]
Pacceptor interactions have the effect of lowering the energy of
the non-bonding t2g orbitals and increasing the magnitude Doct.
This 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
Consequences of P-bonding interactions between
metal and ligand
 Enhanced D-splitting for P-acceptor ligands makes P-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)42-).
 Accounts for organometallic chemistry of P-Acid ligands
 The application of the “18-electron rule” to predict and rationalize
structures of many Pacid organometallic compounds.
Electron donation by P-unsaturated ligands
Examples of 18-electron organometallic complexes with Punsaturated (P-acid) ligands
Scope of 16/18-electron rules for
d-block organometallic compounds
Usually less than
18 electrons
Usually
18 electrons
16 or 18
Electrons
Sc
Y
Cr
Mo
W
Co
Rh
Ir
Ti V
Zr Nb
Mn
Tc
Re
Fe
Ru
Os
Ni
Pd
Pt
Metal-ligand interactions involving bonding and
antibonding molecular orbitals of O2
 of O2 (empty)
*
of O2 (filled)
*
O
O
O
O
Fe
dz2 of Fe (empty)
Fe
t2g (dxz ,dyz ) of Fe (filled)