Electrostatic potentials at the nucleus for isoelectronic series of light atomic ions using the QMC method in relation to DFT

Abstract

The electrostatic potential at the nucleus is here calculated using the quantum Monte Carlo method. Both variational and diffusion-type data are presented for four different isoelectronic series of atomic ions, namely He, Li, Be and B. These results are then utilized to evaluate the ground-state energies of such atomic ions

Approaching the s-wave model ground state energy of He-like atomic ions: results from a model Hamiltonian

“…In Figure 1, we show the curves for H(ξ opt , λ opt ), s-wave energy and fully correlated energy as a function of the nuclear charge for He-like ions in the range of Z < 1. Fully correlated data are taken from our recent work [11]. The three curves touch the function corresponding to the hydrogenic ion at different Z consistently with the amount of correlation energy recovered, the energy of the hydrogenic ion being exact.…”

“…Figure1: Energy curves of He-like ions against the nuclear charge Z compared with the energy of corresponding hydrogenic ions. Curves are for fully correlated[11] calculations (A), for the s-wave model (B), for H(ξ opt , λ opt ) (C) and for Hartree-Fock (HF).…”

Variational quantum Monte Carlo results for N2, N2+ and C2– utilising the four-dimensional density of Bright Wilson

“…In the literature, there are few data of this type for N 2 . Here we mention the work of Finally, we have attempted a fit of VMC kinetic energy by using the equation (15). Our best fit leads to a value of 0.118(1) for λ, not very different from 1/9.…”

“…The above equation has been initially proposed for any polyatomic molecule [11] through a more general charging parameter ranging from 0 to 1, where 1 corresponds to the charging of all the nuclear charges to their final values. The Bright Wilson relation is formally exact but, as we pointed out in our previous work on atoms [15], it is not possible to compute the electronic potential at nuclear position when one or more electrons cannot be bound. This normally happens when the nuclear charge is smaller than a critical value at which the ionization potential goes to zero.…”