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Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis

Authors

  • Xiangzhu Li,

    1. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
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    • Department of Chemistry, Xiamen University, Xiamen, Fujian, China

  • Josef Paldus

    1. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
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    • Also at the Department of Chemistry and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo Campus, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.


Abstract

A detailed algorithm is described that enables an implementation of a general valence bond (VB) method using the Clifford algebra unitary group approach (CAUGA). In particular, a convenient scheme for the generation and labeling of classical Rumer–Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin-independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N-electron basis-set truncation than is possible with the standard Gel'fand–Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser–Parr–Pople (PPP)-type Hamiltonian and nonorthogonal overlap-enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.

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