A b i n i t i o effective valence shell Hamiltonian for the neutral and ionic valence states of N, O, F, Si, P, and S

Abstract

The effective valence shell Hamiltonian, ℋv, which acts within a finite valence space and exactly describes all the valence state energies, is applied to several atomic systems. The n=2 (L shell) ℋv of the first row atoms, N, O, and F and n=3 (M shell) s and p orbital ℋv of the second row atoms, Si, P, and S, are evaluated through second order using STO 5s4p2d and 6s5p3d basis sets, respectively. The calculations are equivalent to a (perturbative) Bk approximation which incorporates all excited configurations and which chooses the primary (valence) space as all the valence K2(2s)m(2p)n and K2L6(3s)m(3p)n configurations, respectively. Using the calculated matrix elements of ℋv, the energies of all the valence states of the neutrals and ions are simultaneously determined from a single ab initio calculation on only one charge state of each of these atomic systems. To understand the dependence of ℋv on the choice of core and valence orbitals, several sets of orbitals, obtained within the same primitive orbital basis, are tested. The nature of the orbital dependence is discussed. The best choices yield an average deviation of calculated excitation energies, ionization potentials and electron affinities from all the available corresponding experimental values of 0.3–0.4 eV for all the atoms. It is to be emphasized that these errors pertain to all charge states of the atom even though the Bk calculation is performed explicitly for only one of these charge states. Some features of the calculated ℋv are discussed in relation to semiempirical theories. In particular, three-electron parts of ℋv, which have no counterparts in semiempirical theories, are negative and contribute substantially to most excitation energies, ionization potentials and electron affinities. This implies that the parameters of semiempirical theories of valence must incorporate the effect of three-electron interactions in an average fashion similar to the way that the one-electron Fock operator describes the average influence of the two-electron interactions. A detailed description of this relationship between semiempirical parameters and ℋv matrix elements is given elsewhere.