The effect of dynamical correlation on the valence wavefunction of molecules: Dressed complete active space self-consistent field calculations

Abstract

Valence complete active space self-consistent field (CASSCF) calculations give the best representation of the non-dynamical (i.e. internal to the valence shell) correlation. Through a unitary transformation of the active MOs into orthogonal quasi-atomic orbitals, an orthogonal valence bond (OVB) reading of the wavefunction is possible; when applied to single (Li 2) and triple (N 2) bonds it shows the three major effects of the internal correlation, namely (i) the reduction of the fluctuation of the number of electrons per atom, (ii) the reduction of the fluctuation of the number of electrons per active atomic orbital, and (iii) the increase in the fluctuation of the atomic spin momentum. The effect of the dynamical (or external) correlation is included through a perturbative dressing (scaled on extensive variational calculations) of the CASCI matrix written in the OVB basis. The corrections are larger for ionic than for covalent situations, larger for the VB components where the atoms are excited, so that the resulting valence wavefunction is less contrasted than the undressed CASSCF wavefunction. CASSCF wavefunction exaggerates the amplitude of the internal (non-dynamical) correlation ordering effects. In an extreme case (Li 2 at short interatomic distances) the single determinantal HF wavefunction has larger overlap with the valence part of the exact wavefunction than the CASSCF wavefunction.