Molecular gradients for the second-order generalized Van Vleck variant of multireference perturbation theory

Abstract

Recently, a revised second-order generalized Van Vleck perturbation theory (GVVPT2) for the description of molecular electronic structure has been reported [J. Chem. Phys. 117, 4133 (2002)] that is both state selective and of the “perturb-then-diagonalize” type of multireference perturbation theory (MRPT). Herein, formulas for analytic derivatives of the GVVPT2 energy with respect to nuclear perturbations are presented, as are illustrative calculations on model problems. Specifically, it is shown that the modification of the energy denominator, which addresses the so-called intruder-state problem of MRPT, is analytically differentiable with respect to nuclear perturbation and only requires use of matrices available, or directly obtainable, from the underlying multiconfigurational self-consistent field calculation. The developed formalism takes full advantage of the theoretical and computational characteristics of the GVVPT2 energy. In particular, the calculations are performed directly in a spin-adapted basis and utilize the recently introduced concept of macroconfigurations. Moreover, the full flexibility of the energy calculations with respect to arbitrariness of reference—i.e., no restriction to complete active space self-consistent field—is retained. Test calculations on N2 and O3 comparing the analytic derivatives with the results of finite-difference calculations corroborate the formulas and implementation.