Relativistic corrections to atomic energies from quantum Monte Carlo calculations

Abstract

Relativistic corrections to the ground-state energies of the He, Be +, Ne +, Be, and Ne atoms are calculated using first-order perturbation theory, yielding results accurate to order 1/c, where c is the velocity of light. Accurate nonrelativistic wave functions and variational and diffusion quantum Monte Carlo techniques are used to calculate the required expectation values. Our results agree with previous work for the two-electron cases, and in all cases we obtain excellent agreement with the experimental total energies. Our values for the expectation values of the relativistic correction to the Coulomb interaction (the Breit interaction) are considerably smaller than those calculated within Dirac-Fock theory, and therefore our calculations give a quantitative estimate of the importance of correlation effects in determining this contribution. PACS number(s): 31.15.p, 71.10.+x, 31.30.Jv

Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

“…[16] using VMC method for Z = 2, 4, 10 are introduced for comparison together with the exact Pekeris values [15]. It is clear from Table II that our results are in most cases better than those obtained using variational Monte Carlo in [16]. In general, the results are in good agreement with the corresponding exact data.…”

“…(3.3) to (3.8), we rstly identify the following quantity for any 3N -dimensional vector of electron coordinates R [16]:…”

“…In 1958, Pekeris [15] presented accurate calculations for the relativistic corrections of two electron atoms with nuclear charge up to Z = 10 using rst-order perturbation theory and a wave function with many parameters. Also, variational and diusion Monte Carlo techniques are used to calculate relativistic corrections to the ground state energies of He, Be 2+ , Ne 8+ , Be and Ne atoms using an accurate non-relativistic wave function and rst order perturbation theory [16]. In Ref.…”

A Quantum Monte Carlo Study of Lanthanum

“…The most common QMC techniques, for atoms and molecules, are the variational Monte Carlo (VMC) and the diffusion Monte Carlo (DMC). Accurate calculations for extremely light atoms using QMC methods are performed by a large number of researchers [1][2][3][4]. For the atoms heavier than Ne, the situation is more difficult.…”

Quantum Monte Carlo Calculations of the Energy of the Relativistic Homogeneous Electron Gas

“…Moreover, there is a considerable literature on relativistic effects in light atoms which we can use to check the validity of the perturbation theory and the accuracy of our QMC methods. Recently we used QMC methods to perform similar calculations of the relativistic energies of several atoms including the ten-electron neon atom [7], which yielded results of very high accuracy.Derivations of the perturbation to the nonrelativistic Schrödinger equation correct to order 1͞c 2 for a system of electrons in a static electric field have been given by Bethe and Salpeter [5] and Itoh [6]. After averaging over spins the terms with nonzero expectation values for the unpolarized HEG are, in Hartree atomic units,D…”