Valence-Bond Studies of AH2 Molecules. I. BeH2

The valence-bond method is discussed and is compared with the molecular-orbital SCF method from a computational standpoint. A procedure is outlined for performing valence-bond calculations making use of the Prosser and Hagstrom biorthogonalization technique to evaluate the cofactors required when evaluating the energy using Löwdin's formula. A minimal basis set (STO) valence-bond calculation on BeH2 including all possible configurations which do not involve excitation of the Be 1s electrons is reported. This is compared with a molecular-orbital calculation using the same basis set. A valence-bond wavefunction neglecting ionic configurations is shown to give an energy better than the molecular-orbital wavefunction and almost as good as a ``full'' valence-bond calculation. The perfect pairing and Craig and Thirunamachandran's resonance approximation are examined. A scheme for performing semiempirical valence-bond calculations analogous to the Pople—Santry—Segal CNDO/2 MO method is described. Ionic configurations cannot be neglected in this ZDO approximation, but this is not a serious limitation. The method is very simple computationally. Hybrid and localized orbitals can be used.