The structure of atoms is discussed in terms of the occupation of atomic orbitals by the electrons in that atom. Similarly, the structure of a molecule can be discussed in terms of molecular orbitals.

The electronic structure of an atom is based on the approximation that the overall wavefunction describing the atom is the product of the wavefunctions for the individual electrons. This is the orbital approximation. This is also made in molecules, so we need to consider how the molecular orbitals are constructed, and the wavefunction for the molecule is then the product of the individual wavefunctions for the electrons in these molecular orbitals.

Another approximation is made in constructing the molecular orbitals: this is that the molecular orbitals can be constructed from weighted combinations of the atomic orbitals of the constituent atoms making up the molecule.

This stems from the observation that when an electron is near the nucleus of one atom, its wavefunction is similar to that of an atomic orbital associated with that atom, and when the electron is near to the nucleus of another atom, its wavefunction is similar to that of an atomic orbital associated with the second atom. The overall wavefunction is therefore some combination of the two atomic orbitals. This approximation is known as the linear combination of atomic orbitals (LCAO) approximation.

Mathematical implications of the approximations in molecular orbital theory
orbital approximation
LCAO

In H₂, the individual 1s atomic orbitals combine in two ways.

The first is with both coefficients, c_A and c_B equal to 1, and this leads to a molecular orbital containing the two atomic electrons at a lower energy than the original atomic orbitals. This is known as a bonding orbital, as the electrons in this orbital have an enhanced probability of being found in the internuclear region compared to the original atomic orbitals.

Another combination has c_A equal to 1 and c_B equal to -1. This results in a molecular orbital at higher energy than the original atomic orbitals, and it is known as an antibonding orbital, and now the electrons have a reduced probability of being found in the internuclear region compared to the atomic orbitals.

The choice to consider the molecular orbitals as composed of the two atomic 1s orbitals is known as the basis set: the two 1s orbitals as the basis orbitals. In general, a basis set containing N orbitals will produce a set of N molecular orbitals.