Coulomb holes and expectation values. I. Explicitly correlated wavefunctions

We have examined, in depth, several wavefunctions for the two‐electron systems H⁻, He, Li⁺, and Be⁺⁺ already reported in the literature: three noncorrelated wavefunctions and ten explicitly correlated wavefunctions. For each wavefunction we calculated the two‐particle distribution function f(r₁₂) and from it obtained the Coulomb hole. The expectation values ${\mathrm{〈\; r}}^n{\text{〉, Δr, ρ(0), 〈 δ}}^3({\mathrm{r}}_1{\mathrm{)〉,\; 〈\; \delta }}^3({\mathrm{r}}_{12}{\mathrm{)〉,\; 〈\; r}}_{12}^n{\mathrm{〉,\; \Delta r}}_{12}\mathrm{,\; 〈}\cos {\gamma }_{12}\mathrm{〉,\; 〈}{\mathrm{r}}_1·{\mathrm{r}}_2{\mathrm{〉,\; 〈\; r}}_1{\mathrm{(r}}_1·{\mathrm{r}}_2\mathrm{)〉}$ , and α, the electric dipole polarizability, have also been evaluated. By comparing the results for different wavefunctions some insight was obtained into the roles played by different types of correlation factor.