Effective valence shell interactions in carbon, nitrogen, and oxygen atoms

Abstract

We present the first numerical results of the canonical tranformation formalism for generating the valence shell effective interactions. Considering the valence space to be formed as the antisymmetrized direct product of 2s and 2p type orbitals we have computed all the matrix elements of the two‐body valence shell interactions for isolated carbon, nitrogen, and oxygen atoms. Explicit forms for the core, valence, and excited orbitals are the hydrogenlike functions defined by an effective nuclear charge. We compare our results with the semiempirical ’’electron–electron repulsion parameters’’ finding that for reasonable values of the effective charge—essentially a choice of the core and valence spaces—good agreement with the parameters deduced from atomic spectra data is obtained. Not only do the general features of semiempirical theory such as the reduction of the average strength of the two‐body interaction appear, but also the somewhat more subtle effects such as the relative ordering of the diagonal matrix elements emerge. The nonlocal nature of the effective interactions is noted and its implications for the usual semiempirical schemes are discussed.