Interelectronic repulsion distribution functions in the ground state of helium: slow convergence of CI wavefunctions

Abstract

The formalism of the pair electron distribution function has been used to study total and local interelectronic repulsion for the ground state of helium. A discussion of the distances that contribute most to electron repulsion is made, and plots of the local interelectronic repulsion are given for Hartree-Fock, explicitly correlated and configuration interaction wavefunctions, showing some interesting qualitative differences. A cusp effect in the limit r12=0 arises for the interelectronic repulsion distribution computed with the explicitly correlated wavefunction, but no cusp is observed for Hartree-Fock and configuration interaction wavefunctions.

Radial electron-pair densities and shell structure of atoms

“…Examples are given in figure 1 for the six rare-gas atoms He, Ne, Ar, Kr, Xe and Rn. For light atoms He [14][15][16]19], Be [17,18,22], Ne [20,21] and Ar [22], these maximum characteristics were also found in the literature. The atoms with two maxima are separated into three groups, as specified above, by Z.…”

“…where N(N − 1)/2 is the number of electron pairs. Since the radial densities were examined only for a few light atoms in the literature [8,9,[14][15][16][17][18][19][20][21][22], the present systematic study over 102 atoms should be useful to clarify their general characteristics. In the next section, our numerical procedure is summarized for the analysis of the radial densities.…”

Compact expressions for the electron–electron distribution function for the 2S states of three-electron systems

“…The coefficient a3(£'2'£'3) will have a dependence on the delta factors introduced in Eqs. (21) and (22). With the information in Table I i.e.,…”