Relativistic corrections to atomic energies from quantum Monte Carlo calculations

Relativistic corrections to the ground-state energies of the He, ${\mathrm{Be}}^{2+}$, ${\mathrm{Ne}}^{8+}$, Be, and Ne atoms are calculated using first-order perturbation theory, yielding results accurate to order 1/${\mathit{c}}^2$, 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.