Graphical techniques in the configuration interaction approach based on pure slater determinants

A graphical approach to the configuration interaction in the basis of pure Slater determinants is presented. The formulation based on the spin‐separated two‐slope graph ( SSTSG ), enabling the selection of determinants with the fixed M s value, has a direct relation to the well‐known concept of the group‐function product. The commonly used excitation criterion and the spatial (Abelian) symmetry properties are analyzed in terms of the graph's internal structure. The Slater formulae for the Hamiltonian matrix elements between determinants, in the particle‐hole formalism and in the spin‐separated form, are related to different classes of loops within graphs. Some aspects of implementation within both the matrix‐element‐driven ( ME ) and integral driven ( ID , direct) CI algorithms are discussed. The presented formulation, of a general complete active space ( CAS ) CI type, is a basis of the Graphical Determinantal Configuration Interaction ( GDCI ) computer program.