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

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Abstract
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 odd‐order derivatives have a distinct advantage over nonvariational (e.g., perturbative) energy expressions and even‐order derivatives. In particular, the first‐order wave function suffices to determine the derivatives of the variational energy up to third order. The coupled‐perturbed multiconfigurational SCF (MC‐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 MC‐SCF energy. Computational implementation is briefly discussed.