Spin-Free Computation of Matrix Elements. I. Group-Theoretical Computation of Pauling Numbers

Spin‐free wavefunctions may be symmetry adapted to a given irreducible representation of the symmetric group $S_N$ by a number of different operators. When matrix elements over these symmetry‐adapted wavefunctions are computed, one obtains terms which are group theoretical in nature and terms which are dynamical. In this paper we present formulas for computing the group‐theoretical coefficients for four types of projectors–spin‐free equivalent of the Löwdin projection operator, ${\xi }_Y$ ; structure projector (spin‐free equivalent of valence‐bond‐type functions), ${\kappa }_Y$ ; sequence‐adapted spin‐free equivalent of the Löwdin projection operator, ${\xi }_Y^G$ ; and sequence‐adapted structure projector, ${\kappa }_Y^G$ . We also give a formula relating the Pauling numbers for the different symmetry projectors to a reference projector.