Optimization of Molecular Wavefunctions by Scaling

The conditions that a set of molecular electronic wavefunctions for different nuclear configurations be optimized by incorporation of scale factors, in general different for each wavefunction of the starting set, are derived. The relationship of these conditions to the quantum-mechanical virial theorem in Born—Oppenheimer approximation is pointed out. The quantitative effects of such optimization on a set of accurate wavefunctions for the hydrogen molecule and a partially optimized single-configuration molecular-orbital wavefunction for lithium fluoride are discussed. Expectation values and spectroscopic constants are investigated in detail. It is shown that as the total molecular energy decreases, the quantitative effects of scaling will become progressively smaller. A further conclusion is that, for sets of unscaled diatomic-molecule wavefunctions only partially optimized, curves for kinetic energy and potential energy of the system as a function of internuclear separation are more accurately obtained from the total molecular-energy curve by use of the virial theorem than by use of computed mean values.