Correlation study of Be1s22s2pP1by a separated-pair numerical multiconfiguration Hartree-Fock procedure

A procedure for obtaining a correlated multiconfiguration Hartree-Fock (MCHF) wave function, similar to the one used for the $1s^{2}2s^2$ groud state of Be, is applied to the $1s^{2}2s2p{}_{}{}^1{}_{}{}^{}P$ state. With ${\Phi }^{\mathrm{MCHE}}=a_1|1\mathrm{}{s}^{2}2s2p〉+a_2|1\mathrm{}{s}^{2}2p3d〉$ as a zero-order approximation, a first-order correction is derived which includes the effects of one- and two-electron replacements. Contributions from replacements from a particular pair of electrons were determined separately by a numerical MCHF procedure. The "pair correlation functions" were combined in a final configuration-interaction calculation with 52 configurations. The approximation yielded a total energy of -14.47085 a.u. which accounts for 97.5% of the correlation energy. A further first-order correction improved the correlation energy to 98.0%.