Application of the unitary group approach (UGA) to evaluate spin density for Configuration Interaction (CI) calculations in a basis of S$^{2}$ eigenfunctions

摘要

We present an implementation of the spin-dependent unitary group approach to calculate spin densities for CI calculations in a basis of spin symmetry-adapted functions. Using S$^{2}$ eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. In order to achieve this, we combine the method to calculate $U(n)$ generator matrix elements developed by Robb and Downward~[\onlinecite{downward_1977}] with the approach of Gould and Battle to calculate $U(2n)$ generator matrix elements~[\onlinecite{battle_1993}]. We also compare and contrast the spin density formulated in terms of the spin-independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one- and two-electron charge densities.