Maclaurin expansion of electron-pair densities

Abstract

Maclaurin expansions of the spherically averaged electron-pair intracule (relative motion) h( u) and extracule (center-of-mass motion) d( R) densities are studied for wave functions expressed by a linear combination of Slater determinants. For small values of u and R, the densities h( u) and d( R) are expanded by even powers of u and R, respectively, and the derivatives h (2 m) (0) and d (2m)(0) are shown to satisfy an approximate relation d (2m)(0)/h (2m)(0)≅2 2m+3 for a particular case of Hartree–Fock wave functions, where m is a nonnegative integer. Maclaurin expansions of the radial densities H( u) and D( R) and of the cumulative distributions G( u) and C( R) are also discussed. Accurate Hartree–Fock values of h (2 m) (0) and d (2m)(0) ( m=0−3) are determined for the 53 atoms from He to Xe in their ground states.