Calculations on theS2ground state of Be ii

Extensive variational calculations on the ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ ground state of ${\mathrm{Be}}^{+}$ are reported. Using a 401-term expansion of Hylleraas-type functions, the nonrelativistic ground-state energy is determined to be -14.324 760 a.u., which is the lowest upper bound to the ground-state energy reported to date for this system. The Fermi contact interaction is determined to be 12.4980 a.u., which is in very close agreement with the experimental value of 12.503 88 a.u. The nuclear-magnetic shielding factor and the molar diamagnetic susceptibility are evaluated to be σ=1.415401 ×${10}^{\mathrm{-}4}$ a.u. and χ=-5.154 43×${10}^{\mathrm{-}6}$ ${\mathrm{cm}}^3$ ${\mathrm{mol}}^{\mathrm{-}1}$, respectively. The electron density at the nucleus, the moments 〈$r_i^n$〉, n=-1, 1, 2, and 3, and 〈$r_{\mathrm{ij}}^n$〉, n=-1, 1, and 2, are also reported. The specific mass shift (mass polarization contribution) is determined to be 2.758×${10}^{\mathrm{-}5}$ a.u. The rate of convergence of the calculation is discussed. The role of one versus two spin eigenfunctions in the basis set is discussed with respect to its bearing on the calculation of the Fermi contact interaction.