The document discusses molecular orbital theory and its application to transition metal complexes. It describes how atomic orbitals of matching symmetry combine to form molecular orbitals, with equal numbers of bonding and antibonding orbitals. Electrons fill the molecular orbitals starting with the lowest energy orbitals. Ligand interactions such as π-accepting and π-donating affect the splitting of orbitals and influence the metal's oxidation state.

1. Molecular orbital theory approach to
bonding in transition metal complexes

2.  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

4. Molecular orbital descriptions of dioxygen species.

5. 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
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6. MO diagram for s-bonded octahedral metal complex

8. 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)
M.O. Diagram for Tetrahedral Metal Complex

9. 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.

10. 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.

11. Metal- d Ligand-
L
p
(t2g)
M
Ligand p (full)
e.g. halide ion, X-
RO-
P-interactions involving P-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 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.

12. Effect of ligand to metal Pdonor interactions

13. P-alkene organometallic complexes
Zeise’s Salt, K[PtCl3(C2H4)]

15. 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

17. 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)4
2-).
 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.

18. Electron donation by P-unsaturated ligands

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

24. Scope of 16/18-electron rules for
d-block organometallic compounds
Usually less than
18 electrons
Sc Ti V
Y Zr Nb
Usually
18 electrons
Cr Mn Fe
Mo Tc Ru
W Re Os
16 or 18
Electrons
Co Ni
Rh Pd
Ir Pt

25. 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