Hylleraas - configuration - interaction study of the 1 S ground state of neutral beryllium

Beryllium, with its four electrons and strong mixing of the 1s2 2s2 and 1s2 2p2 configurations, has long been the subject of investigation. The first reasonably accurate nonrelativistic calculations on the ground state were the configurationinteraction (CI) studies of Watson [1] and Weiss [2]. Szasz and Byrne [3] were the first to explicitly correlate the wave function by adding intrashell rij coordinates in a Hylleraas (Hy)-type wave function. Gentner and Burke [4] improved on Szasz and Byrne’s work by including intershell rij coordinates. Sims and Hagstrom [5] combined the Hy and CI methods in a Hylleraas-configuration-interaction (Hy-CI) [5] calculation in 1971 with a considerable improvement in the energy. Bunge did his first Be calculation in 1968 [6] and his CI calculations for Be improved steadily over the years, culminating in a benchmark calculation of over 2.6 million terms in 2010 [7]. A multiconfiguration Hartree-Fock (MCHF) correlation study of Be was presented by Froese Fischer and Saxena in 1974 [8] and then was further refined by Froese Fischer in 1993 [9], leading finally to a calculation of over 650 000 terms in 2010 [10]. While significant progress was being made in Hy treatments of three-electron systems, integral problems with the conventional Hy expansions [11–13] brought calculations to a halt as far as four-electron systems were concerned until finally, in 1998, Büsse et al. [14] overcame serious integral problems and made major improvements through the use of Hy-type doubly linked terms in the wave-function expansions. This was the first major Hy-type calculation of near microhartree accuracy. In 1995 the exponentially correlated Gaussian (ECG) method was introduced by Komasa et al. [15]. The relative simplicity of the resultant integrals led to a sequence of impressively accurate calculations, culminating in the work of Adamowitz and co-workers [16,17] which stands as the best work to date (our work is second only to theirs). Table I summarizes Be ground-state variational results listed in order of increasing accuracy. In this paper, we present preliminary results from a very large Hy-CI calculation (over 40 000 symmetry adapted expansion functions) for the Be ground state.