The effects of triple and quadruple excitations in configuration interaction procedures for the quantum mechanical prediction of molecular properties

Abstract

The importance of including triple and quadruple excitations (relative to a single Hartree–Fock determinant) in ab initio electronic structure configuration interaction (CI) theory is investigated for several small molecules [HF, N2, CO, H2O, NH3, (3B1) CH2, and (1A1) CH2]. Specifically the effects of these high order electron correlations on equilibrium molecular geometries, dipole moments, harmonic vibrational frequencies, and infrared intensities are reported. Triple and quadruple excitations are generally found to affect the dipole moment, in an absolute sense, only slightly. In some cases, infrared intensities show a medium to large dependence on higher excitations. Molecular geometries, and subsequently the harmonic vibrational frequencies, however, are significantly more dependent upon these higher excitations. Quadruple excitations are found to be significantly more important than triple excitations for all closed shell systems except for CO, where the relative importance of triples to quadruples is roughly 2:3 in predicting for vibrational frequencies. On the other hand, it is found that triples and quadruples are of nearly equal importance for 3B1 CH2. The equilibrium bond length and molecular properties of the multiply bonded species CO and N2 show a larger absolute dependence on the higher than double excitations. Several additional levels of theory [e.g., all singles, doubles, and quadruples (CISDQ)] have been applied to HF and N2 in a more detailed investigation of the structure of the CI Hamiltonian matrix. It is concluded that only a very small subset of the triply and quadruply excited configurations account for nearly all of the higher excitation effects on harmonic frequencies.