Correlation study of Be1s22s2by a separated-pair numerical multiconfiguration Hartree-Fock procedure

A systematic procedure is proposed for obtaining a correlated multiconfiguration Hartree-Fock (MCHF) wave function for the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S$ ground state of Be. With $\Phi _{}^{\mathrm{MCHF}}{}_2{}^{}=a_1|1\mathrm{}{s}^{2}2s^2〉+a_2|1\mathrm{}{s}^{2}2p^2〉$ as a zero-order approximation, a first-order correction ${\Phi }^{\mathrm{}\left(1\right)\mathrm{}}$ is derived consisting of sums of the type $\Sigma {n\ge 3}^{}\Sigma {m\ge 3}^{}{c}_{nm}|\alpha \beta \mathrm{nlm}{l}^{\prime }{}_{}{}^1{}_{}{}^{}S〉$, where $\alpha ,\beta \subset \mathrm{}\{1s,2s,2p\}\mathrm{}$. By transforming the basis of radial functions a "reduced" form consisting of a single sum is obtained for each such double sum. A numerical MCHF procedure is used to compute the separated pair-correlated functions. These functions are then combined in a configuration-interaction calculation. For Be, 99.1% of the correlation was accounted for in 52 configurations, yielding a total energy of - 14.66587 a.u.