Accurate determination of the total electronic energy of the Be ground state

Abstract

New configuration-interaction (CI) ideas are tested and utilized to yield the most accurate determination to date of the Be nonrelativistic energy $E_{\mathrm{nr}}=-14.667358\mathrm{}\left(28\right)\mathrm{}$ a.u. Be, including a mass-polarization correction of -0.000030(3) estimated from literature data. A 650-term CI series gives a rigorous upper bound $E_u=-14.666902\mathrm{}$. The truncation error of the $10s9p8\mathrm{}d7f5\mathrm{}g3\mathrm{}h1i$ carefully optimized Slater-type orbital set is estimated largely from studies of apparent energy limits for each harmonic; it amounts to -0.000407(22). An additional -0.000019(2) energy error arises from truncating the full CI expansion. A relativistic energy correction $E_{\mathrm{expt}}-E_{\mathrm{nr}}=-0.001987\mathrm{}\left(30\right)\mathrm{}$ is predicted, which agrees well with an ab initio estimate of -0.001986 obtained by combining the Hartree-Fock quality results of Hartmann and Clementi with Pekeris's exact result for ${\mathrm{Be}}^{2+}$, thus including $K$-shell correlation effects in the relativistic correction. The correlation energy is determined with 0.03% of uncertainty, $E_c=-2.56604\mathrm{}\pm 0.00068$ eV. Particular attention is given to construction of basis sets, energy extrapolation procedures, and compact approximations to the full CI expansion. Comparisons with previous calculations are made, and it is pointed out how the present results may be improved.