Electron correlation and natural orbitals: fractional orbital occupancy numbers, configuration interaction expansion coefficients and one-particle energies

Abstract

The natural spin orbital (NSO) representation of the single-density configuration interaction (SDCI) is an infinite set of partially occupied one-particle states. The occupation probabilities are related to the CI expansion coefficients. The correlation one-density, the difference between the Hartree–Fock (HF) and CI one-densities, with the virial theorem. gives the electron correlation energy from one-particle energies alone. NSO occupation probabilities are related to NSO one-particle energies, and it is shown that the two-particle energies of the occupied orbitals relate to the two-particle energies of the virtual orbitals. Numerical results from SDCI calculations on C and Ne show the approximations to be remarkably accurate and that they will allow systematic calculation of correlation energies from HF eigenvalues and one-particle energies.