Generalizing Hartree-Fock theory for nonrelativistic atomic ions to yield a ground-state electron density satisfying cusp and asymptotic conditions

Möller and Plesset in early work demonstrated quantitatively the high quality of the Hartree-Fock ground-state electron density ${\rho }_{\text{HF}}\left(\mathbf{r}\right)$. Therefore, Cordero, March, and Alonso recently proposed, for atoms, a fine-tuning of ${\rho }_{\text{HF}}\left(\mathbf{r}\right)$ to satisfy both the known asymptotic behavior of the density far from the nucleus, as well as the Kato cusp condition at the nuclei. Here we extend the diagonal density $\rho \left(\mathbf{r}\right)$ proposed by Cordero et al. to an off-diagonal idempotent one-particle density matrix. The orthonormal orbitals used in this construction are then to be found from the solution of generalized Hartree-Fock equations. We report calculations on the Be isoelectronic series of atomic ions with $Z$ from ${\text{Li}}^{-}$ to ${\text{Ca}}^{16+}$.

Figure 1

Optimal $\lambda$ (upper plot), obtained by means of Eq. (17) and comparison of computed correlation energies with corresponding literature data (lower plot) for the Be isoelectronic series of atomic ions considered in this work $\left(3\le Z\le 20\right)$. Data are in atomic units.

Figure 2

Plot of the energy relative to the Hartree-Fock energy as a function of the length scale parameter $\lambda$ for different Be-like atomic ions. Energies are in Hartree.

Figure 3

Plot of the radial density $4\pi r^2\rho \left(r\right)$ as a function of the distance from the nucleus for ${\text{Li}}^{-}$ ion. Data are in atomic units.

Figure 4

Plot of the radial density $4\pi r^2\rho \left(r\right)$ as a function of the distance from the nucleus for Be. Data are in atomic units.

Figure 5

Plot of the radial density $4\pi r^2\rho \left(r\right)$ as a function of the distance from the nucleus for ${\text{Ne}}^{6+}$ ion. Data are in atomic units.