General-model-space many-body perturbation theory: The(2s3p)P1,3states in the Be isoelectronic sequence

The energies of the $\left(2s3p\right){}_{}{}^{1,3}{}_{}{}^{}P$ states of the Be sequence ions N iv-Ne vii are calculated, with use of a general-model-space many-body perturbation theory (MBPT) to third order. The triplet states are described accurately by a one-configuration model ($P$) space including only $2s3p$, but the singlets are not; the singlet-triplet separation has the right sign (singlet below triplet) but is only 30% of experiment. Incorporation of the $2p3s$ configuration in the model space greatly improves the results. This incomplete, two-configuration model space yields virtually the same energies as the larger, complete model space required by other quasidegenerate MBPT methods, at one-fifth the computational cost.