Explicit form of Pauli potential for direct derivation of pair density from a two-particle differential equation for the quintet state of four electrons with harmonic interparticle interactions

Abstract

Recently, an analytic two-particle density matrix (2DM) has been derived for the quintet state of four electrons interacting via two-body harmonic forces. Here we use this 2DM to extract the exact pair density \(\Gamma (\mathbf{r}_1,\mathbf{r}_2)\). This is then employed in the known two-particle partial differential equation for the pair density amplitude to extract the Pauli potential \(v_P(\mathbf{r}_1,\mathbf{r}_2)\) for this quintet state.