PNOsngbnd;CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane

摘要

It is shown that the convergence of the configuration expansion of a manyhyphen;electron wavefunction may be drastically improved without significantly complicating the energy matrix elements by using partially nonhyphen;orthogonal orbitals. The wavefunction thus obtained is the manyhyphen;electron analog to the natural orbital expansion of a twohyphen;electron wavefunction. The orbitals involved may be approximated by pseudonatural orbitals (``PNOsngbnd;CI''), and an efficient way of calculating these orbitals is presented. An approximate treatment of multiple substitutions is discussed yielding a coupled electron pair theory formulated within the CI scheme. These methods are applied to the ground state and three ionized states of methane. Including only double substitutions, the computed upper bound to the energy of the ground state is minus;40.4584 hartree, i.e. 0.057 above the experimental nonrelativistic energy. About 83percnt; of the total correlation energy is accounted for variationally, whereas the coupledhyphen;pair approximation yields 89percnt;. The ratio between intraorbital and interorbital valence shell correlation energy is calculated as 1.56 in the case of localized electrons. The equilibrium distance in CH4is found to be shifted from 2.046 bohr to 2.061 bohr due to correlation, and the harmonic frequency ngr;1is reduced from 3149 cmminus;1to 3037 cmminus;1. These results indicate that the anharmonicity corrections to the observed values have probably been over estimated. The correlation contributions to the ionization potentials are analyzed. The theoretical potentials differ from the observed values by 1percnt;ndash;2percnt;. The energy surface ofCH4plus;is investigated and is used to discuss the photoelectron spectrum of CH4. Contrary to previous work, the lowest minimum ofCH4plus;is found to have C2vsymmetry. In all applications the variational results are compared with those of the independenthyphen;pair and coupledhyphen;pair approaches, and it is concluded that the latter represents a definite improvement over the first two.