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

The natural spin orbital (NSO) representation of the single-density configu ration interaction (SDCI) is an infinite set of partially occupied one-part icle states. The occupation probabilities are related to the CI expansion c oefficients. The correlation one-density, the difference between the Hartre e-Fock (HF) and CI one-densities, with the virial theorem, gives the electr on correlation energy from one-particle energies alone. NSO occupation prob abilities are related to NSO one-particle energies, and it is shown that th e 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 the y will allow systematic calculation of correlation energies from HF eigenva lues and one-particle energies. (C) 1999 Elsevier Science B.V. All rights r eserved.