Second and third derivatives of variational energy expressions: Application to multiconfigurational selfhyphen;consistent field wave functions

摘要

General analytical expressions are given for the second and third derivatives of constrained variational energy expressions. It is pointed out that variational energy expressions and oddhyphen;order derivatives have a distinct advantage over nonvariational (e.g., perturbative) energy expressions and evenhyphen;order derivatives. In particular, the firsthyphen;order wave function suffices to determine the derivatives of the variational energy up to third order. The coupledhyphen;perturbed multiconfigurational SCF (MChyphen;SCF) equations, obtained from the general results, are equivalent, with minor corrections, to the ones very recently presented by Osamura, Yamaguchi, and Schaefer. Explicit expressions are given for the second and third derivatives of the MChyphen;SCF energy. Computational implementation is briefly discussed.