Symmetric Group Graphical Approach to the Configuration Interaction Method

Abstract

Some concepts of the graphical unitary group approach (GUGA) have been applied in a method of evaluation of matrix elements based on the permutational symmetry of the wavefunction. The new method seems to be simpler than both the original method of evaluation of matrix elements and the unitary group approach formulated in the Gelfand-Tsetlin basis. Introduction of a graphical representation of the orbital parts of the configuration state functions allows us to give explicit formulae for matrix elements of two-electron operators. The resulting formalism may be applied in the conventional and in the direct configuration interaction methods. The reference state may be taken as an arbitrary multiconfiguration function.