Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems

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Abstract
A formalism for an efficient generation of spin‐symmetry adapted configuration interaction (CI) matrices of the N‐electron atomic or molecular systems, described by nonrelativistic spin‐independent Hamiltonians, is presented. The Gelfand and Tsetlin canonical basis for the finite dimensional irreducible representations of the unitary groups is used as an N‐electron CI basis. A simplified Gelfand‐type pattern pertaining to the N‐electron problem is introduced, which considerably simplifies the canonical basis generation and, more importantly, the calculation of representation matrices of the (infinitesimal) generators of the pertinent unitary group in this basis. The calculation of the CI matrices for the above mentioned systems is then straightforward, since any particle number conserving operator may be written as a sum of n‐degree forms in the unitary group generators. The computation of CI matrices for various Hamiltonians as well as the problems of the space‐symmetry adaptation of the Gelfand‐Tsetlin basis and of limited CI calculations are briefly discussed.