Curve Crossing and Orthogonality of Molecular Orbitals

The approximate representation of states whose potential energy curves cross (or nearly cross) is discussed quantitatively, by comparing the energies and transition integrals of the 2sσ and 3dσ states of HeH 2+ calculated using various approximate molecular orbitals with the exact values. It is concluded that, whilst the usual methods of taking mixing with neighbouring states into account may lead to accurate values of the energies provided orthogonality is imposed, the oscillator strengths may be seriously in error, especially if they are associated with weak transitions.