Comparison of two-electron densities reconstructed from one-electron density matrices

We consider approximate reconstruction of spinless and spin-resolved two-electron charge densities, intracule densities, and extracule densities utilizing only the one-electron reduced density matrix. Using large basis set, configuration interaction density matrices for the ground state of Be, we compare the two-electron densities obtained using several proposed reconstruction functionals ("natural orbital functionals") for the two-electron density and density matrix. We also analyze the intracule and extracule densities obtained from these reconstructions. Several of the proposed natural orbital functionals are found to produce unphysical negative values for the pair density when two parallel-spin electrons approach one another. Ancillary results from this study include new, simplified formulas for the intracule and extracule densities, and a mathematical justification for an approximate relation between atomic intracule and extracule densities that has previously been reported on the basis of extensive Hartree-Fock calculations. (C) 2002 Wiley Periodicals, Inc.