Determination of Slater–Condon and Trees parameters in terms of the exact effective valence shell Hamiltonian

The empirical approximate Slater–Condon and Trees parameters of atomic spectra and semiempirical molecular electronic structure theories are expressed in terms of the matrix elements of the exact effective valence shell Hamiltonian (ℋv) for the snpm case. The nature of the configuration and occupation dependence of the Slater–Condon and Trees parameters is thereby made explicit by their representation in terms of exact configuration and occupation independent ℋv-matrix elements. Ab initio values of the latter for oxygen and nitrogen ions are utilized to provide ab initio Slater–Condon and Trees parameters for these systems.