Analysis of Electron Correlation in Two-Electron Systems. I. H−, He, and Li+

Abstract

Because they form the beginning of an isoelectronic series possessing electrons with antiparallel spins, H⁻, He, and Li⁺ lend themselves well to a study of electron correlation. The study is of three wavefunctions. Two introduce correlation: one by configuration interaction, the other by including Hylleraas‐type correlation factors. For comparison, the third function is based on the Hartree–Fock approach. The correlation within the wavefunctions is demonstrated by presenting two‐particle density difference maps, ${\mathrm{\Delta D(r}}_1{\mathrm{;\; r}}_2)$ , relative to the uncorrelated approach, and graphs of the radial density $\mathrm{D(r)}$ . Amongst the quantities calculated from the different treatments are $〈\cos {\gamma }_{12}〉$ , where ${\gamma }_{12}$ is the angle subtended by the electrons at the nucleus, ${\mathrm{〈r}}_1{\mathrm{·r}}_2〉$ , the coherent x‐ray scattering contribution $f_{00}\mathrm{(X)}$ , and ${\mathrm{〈r}}^n〉$ , where $\text{−\hspace{0.17em}2\hspace{0.17em}≤\hspace{0.17em}n\hspace{0.17em}≤\hspace{0.17em}4}$ . Results are compared throughout with those from a more accurate wavefunction. In addition, it was possible to study the effects of radial and angular correlation separately by producing the natural expansion for one of the correlated functions. The main conclusion is that as $Z$ increases, angular correlation replaces radial correlation in being more important. Further, s‐type correlation terms in the wavefunction cause the density to spread, whereas angular terms generally contract it. All such correlation effects tend to decrease with increasing $Z$ .