The molecialar orbital theory describes the valence electrons as associated with all the nuclei concerned. The nuclei are in equilibrium positions in the stable molecule and electrons associated with all the nuclei can be described by wave functions. The energy states of electrons can be described in the combined states or molecular orbitals. The molecular orbitals are multicentred or delocalised. They are filled with the required number of electrons (each molecular orbital is usually filled with two electrons). Molecular orbitals may be obtained by the linear combination of atomic orbitals (LCAO method).
The molecular orbitals are assumed to possess the following characteristics:
(i) Each electron in the molecule is described by a wave function The value of (1) is such that the value of 1)2 at any point represents the probability of finding the electrons in unit volume around that point. The wave functions are called molecular orbitals. These molecular orbitals are polycentric so that the electron moves in the field of all the nuclei.
(ii) Each molecular orbital has its own energy.
(iii) Each electron has a definite spin \+ 2 or — —2i and Pauli’s exclusion principle is observed.
(iv) The appropriate form of the wave equation is quite complicated and cannot be used for exact solution except for hydrogen. Thus approximations are necessary. One of the approximations is that when an electron comes in the vicinity of one nucleus, the force arising on it is due to the nucleus and its other electrons. Both the wave equation and its solutions resemble those for the isolated atom, and the molecular orbital consists of a series of superposed self-consistent orbitals. This procedure is known as the linear combination of atomic orbitals (LCA0).
(v) The greater the overlap of atomic orbitals among themselves, more stable molecular orbitals (with least energy states) are obtained.
(vi) The energy of a molecular orbital is least when the combining atomic orbitals have equal or almost equal energy states. Atomic orbitals of low energy will not be able to overlap with other atomic orbitals and electrons carried by them will be non-bonding.
(vii) Each molecular wave function corresponds to a definite energy value. The sum of the individual energies of the molecular orbitals, after correction, represents the total energy of the molecule.
Let us now apply these factors to a simple homonuclear diatomic molecule such as hydrogen in which two identical atoms are linked by an electron pair bond.