The use of projection operators in the configuration interaction problem

Abstract

Matrix elements of the many-particle Hamiltonian, for atomic, molecular, or nuclear wave function calculations, can be reduced from quadratic to linear forms by the use of totally antisymmetric basis functions which result from applying projection operators to single determinants. The projection operators select components with definite transformation properties under symmetry operations of the invariance group of the Hamiltonian. It is shown that the projected functions need to be known only up to an undetermined numerical factor in order to determine matrix elements between the corresponding normalized functions. A method is given for constructing such projected determinants from any orthonormal set of totally antisymmetric functions with the same transformation properties under the symmetry group. To complete the presentation of a self-contained, practicable, and reasonably efficient method for evaluating the general configuration interaction matrix element, a minimal set of linear equations are stated which determine the transformation coefficients that completely reduce the representation of an arbitrary symmetry group.