Clifford algebra unitary-group approach to many-electron system partitioning

Abstract

For the case of particle-number-conserving systems, the Clifford algebra unitary-group approach (CAUGA) is reformulated from the U(${2}^{n}$)\ensuremath{\downarrow}U(n) subduction viewpoint, providing a more direct physical insight into the structure of this formalism. This enables us to exploit a general system partitioning in the many-electron correlation problem for atomic and molecular systems within the CAUGA formalism. Several methods are given for the the CAUGA representation of both Gel'fand-Tsetlin and U(${\mathit{n}}_{1}$+${\mathrm{n}}_{2}$)\ensuremath{\supset}U(${\mathrm{n}}_{1}$)\ensuremath{\bigotimes}U(${\mathrm{n}}_{2}$) adapted partitioned bases, namely the permutation-orthogonalization method, the U(n) Clebsch-Gordan coefficient method, and the linear algebraic equation method. The flexibility offered by a general system partitioning for a physically meaningful configuration-interaction (CI) truncation and for a more efficient CI matrix element evaluation is illustrated on several examples.