Natural orbitals from single and double excitation configuration interaction wave functions: their use in second-order configuration interaction and wave functions incorporating limited triple and quadruple excitations

Abstract

As an alternative to orbitals obtained from a molecular complete-active-space self-consistent-field (CASSCF) wave function, we have investigated the use of natural orbitals (NOs) obtained from configuration interaction (CI) wave functions including all single and double excitations (CISD) for use in multireference CI (MRCI) studies. The specific MRCI methods investigated are (1) second-order CI (SOCI), which includes all single and double excitations with respect to a full CI in the valence space and (2) a wave function that includes all single and double excitations out of a valence space CISD reference function. The latter wave function can also be described as a single–double–triple–quadruple excitation CI in which only two electrons are allowed to simultaneously reside outside of the valence space, ‘‘which we call CISD[TQ].’’ Comparison is made with CASSCF-SOCI and full CI results for NH2 (2B1), CH3 (2A″2), and SiH2 (1B1) at equilibrium bond distances (Re) 1.5 and 2.0Re, and with full CI results for the dissociation energy of N2. The dissociation energies of N2 and C2 are also obtained using large atomic natural orbital basis sets and the results compared to CASSCF-SOCI and internally contracted MRCI results. In all, the MRCI results with CISD NOs are very similar to the CASSCF-MRCI results, and at geometries where the reference wave function is dominant, the relatively compact CISD[TQ] method yields results that are very close to SOCI. In addition to their ease of generation, the CISD NOs offer the added advantage of allowing for truncation of the CI configuration list on an orbital basis by simply deleting high-lying virtual orbitals. The errors introduced by this truncation are almost quantitatively obtained at the CISD level of theory.