Molecular Orbital Occupation and Bond Order

The electrons in an atom occupy the atomic orbitals from the lowest energy upwards, according to the aufbau principle, and Hund’s rule.

In molecules, the electrons occupy the molecular orbitals according to the same criteria. The electronic configuration of a molecule can therefore be written in the same way as an atomic electronic configuration, but using the molecular orbitals.

The electronic configuration of N2, for example, is (1σg)2(2σu)2(1πu)4(3σg)2.

If we look at the configuration of N2, we see that the 3σg orbital contains two electrons, and is the highest energy orbital to contain electrons: it is known as the Highest Occupied Molecular Orbital (HOMO). The next highest energy orbital is the 2πg orbital, but this contains no electrons: it is known as the Lowest Unoccupied Molecular Orbital (LUMO).

Electronic transitions are often observed which correspond to transitions between the HOMO and the LUMO, and are responsible for many of the properties of a molecule. Together, they are known as the frontier orbitals, and they control much of the chemistry of a molecule.

Bond Order

An understanding of the electronic configuration of a molecule, or the molecular orbital diagram, can help to explain the strengths, and lengths, of bonds.

The bond order for a pair of atoms in a molecule is defined as:

Bond Order = 0.5 x (the number of electrons in bonding orbitals – the number of electrons in antibonding orbitals)

The variation in bond order can be demonstrated for the oxygen ions in the table below.

Bond Order in oxygen species
Species Electronic Configuration Number of electrons in bonding orbitals Number of electrons in antibonding orbitals Bond Order
O2+ (1σg)2(2σu)2(3σg)2(1πu)4(2πg)1 6 1 2.5
O2 (1σg)2(2σu)2(3σg)2(1πu)4(2πg)2 6 2 2
O2 (1σg)2(2σu)2(3σg)2(1πu)4(2πg)3 6 3 1.5
O22- (1σg)2(2σu)2(3σg)2(1πu)4(2πg)4 6 4 1

The decrease in bond order down this series is reflected in an increase in the bond length.

The bond order is also a good way of linking the molecular orbital electronic configuration to the Lewis structure for a molecule. O2 has a bond order of three, and this corresponds to the Lewis structure