Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom.

Abstract

Explicitly correlated Gaussian functions are applied to extensive variational calculations of the $^{1}$S ground state of the beryllium atom. The convergence of the energy with respect to the basis-set expansion length is investigated. The nonrelativistic clamped-nuclei energy computed from a 1200-term wave function equals -14.667 355 hartree and is in error by about 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. This is the lowest variational upper bound to the beryllium ground-state energy reported to date and it shows that recent empirical estimates of the nonrelativistic energy of the Be atom lie slightly too high. Several expectation values, including powers of interparticle distances and the Dirac \ensuremath{\delta} function, are computed. The nuclear magnetic shielding constant, the magnetic susceptibility, the specific mass shifts, the transition isotope shift, and the electron density at the nucleus position are evaluated.