Molecular orbital theory, or MO theory, is a method of explaining bonding between atoms in terms of electrons being spread out around a molecule rather than localized around the atoms, in contrast to valence bonding theory, or VB theory. Electrons in atoms are arranged in orbitals within subshells within shells. As a general rule, it is the electrons in the orbitals within the outermost shell that are involved in chemical bonding, although there are exceptions to this. An orbital can contain a maximum of two electrons, which must have opposite spins. In molecular orbital theory, when two atoms form a chemical bond, the atomic orbitals of the bonding electrons combine to produce molecular orbitals with similar rules regarding the number and spin of the electrons.
Electrons, like all subatomic particles, can behave as waves. Instead of occupying a definite point in space at a given time, an electron is spread out over all its possible locations around the atomic nucleus and its position can only be expressed in terms of probability. An equation developed by the physicist Erwin Schrodinger can be used to determine the “wave function” of an atomic orbital, giving the likelihood of finding an electron at different locations around the nucleus in terms of an electron density distribution. Molecular orbital theory explains atomic bonding by adding the wave functions of the atomic orbitals involved in bonding to give the wave functions for molecular orbitals enclosing the entire molecule.
Since the wave function equation gives both positive and negative values, known as phases, two molecular orbitals are produced. In the first, the atomic orbitals are added in phase — positive-to-positive and negative-to-negative. The second type is one where they are out of phase — negative-to-positive and positive-to-negative.
The in phase addition gives a molecular orbital with the electron density concentrated in the space between the nuclei, bringing them closer together and resulting in a configuration at a lower energy than the two original atomic orbitals combined. This is known as a bonding orbital. The out of phase addition results in the electron density being concentrated away from the space between the nuclei, pulling them further apart and producing a configuration with a higher energy level than the atomic orbitals. This is known as an anti-bonding orbital. Electrons from the atomic orbitals involved in bonding will prefer to fill the lower energy bonding molecular orbitals.
To determine the nature of the bond between two atoms, the “bond order” is calculated as: (bonding electrons – anti-bonding electrons)/2. A bond order of zero indicates that no bonding will take place. In comparison, a bond order of 1 indicates a single bond, with 2 and 3 indicating double and triple bonds, respectively.
As a very simple example, the bonding of two hydrogen atoms can be described in terms of molecular orbital theory. Each atom has just one electron, normally in the lowest energy orbital. The wave functions of these orbitals are added, giving a bonding and an anti-bonding orbital. The two electrons will fill the lower energy bonding orbital, with no electrons in the anti-bonding orbital. The bond order is therefore (2 – 0)/2 = 1, giving a single bond. This is in agreement with VB theory and with observation.
The interaction of two atoms of the next element in the periodic table, helium, gives a different result as there are two electrons in an orbital in each helium atom. When the wave functions are added, a bonding and an anti-bonding orbital are produced, as with hydrogen. This time, however, there are four electrons involved. Two electrons will fill the bonding orbital and the other two will have to fill the higher energy anti-bonding orbital. The bond order this time is (2 – 2)/2 = 0, so no bonding will take place. Again, this agrees with VB theory and with observation: helium does not form molecules.
Molecular orbital theory also correctly predicts double and triple bonds for oxygen and nitrogen molecules, respectively. In most cases, MO theory and valence bonding theory are in agreement; however, the former better explains molecules where the bond order lies between a single and a double bond, and the magnetic properties of molecules. The main disadvantage of molecular orbital theory is that, except for very simple cases such as those above, the calculations are much more complicated.