Determination of simple correlated wave functions for few-electron systems using a Jastrow factor

Abstract

Compact Jastrow-Slater-type correlated wave functions for three- and four-electron atoms and ions (Li, ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, Be, ${\mathrm{B}}^{+}$, and ${\mathrm{C}}^{2+}$) are proposed. The Jastrow factor we employed consists of one-body and two-body functions including only two variational parameters in total. We found that a one-body Jastrow function with one variational parameter, which is responsible for the screening effect around the nucleus, is effective for reproducing good total energies of the three- and four-electron atomic systems if hydrogenoid orbitals are adopted in the Slater determinant. On the other hand, a determinant composed of Hartree-Fock orbitals multiplied by the same Jastrow factor was found to give rather worse results than that composed of hydrogenoid orbitals. This result clearly indicates that analytic hydrogenoid orbitals coupled with the one-body Jastrow function are useful for describing simple wave functions and understanding the physical properties of these systems.