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Unitary group tensor operator algebras for many-electron systems: II. One- and two-body matrix elements

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Abstract

Relying on our earlier results in the unitary group Racah-Wigner algebra, specifically designed to facilitate quantum chemical calculations of molecular electronic structure, the tensor operator formalism required for an efficient evaluation of one- and two-body matrix elements of molecular electronic Hamiltonians within the spin-adapted Gel'fand-Tsetlin basis is developed. Introducing the second quantization-like creation and annihilation vector operators at the unitary group [U(n)] level, appropriate two-box symmetric and antisymmetric irreducible tensor operators as well as adjoint tensors are defined and their matrix elements evaluated in the electronic Gel'fand-Tsetlin basis as single products of segment values. Using these tensor operators, the matrix elements of one- and two-body components of a general electronic Hamiltonian are found. Explicit expressions for all relevant quantities pertaining to at most two-column irreducible representations that are required in molecular electronic structure calculations are given. Relationships with other approaches and possible future extensions of the formalism to partitioned bases or spin-dependent Hamiltonians are discussed.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Xiangzhu Li & Josef Paldus

  2. Department of Chemistry and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo Campus, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Josef Paldus

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  1. Xiangzhu Li
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  2. Josef Paldus
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On leave from: Department of Chemistry, Xiamen University, Xiamen, Fujian, PR China.

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Li, X., Paldus, J. Unitary group tensor operator algebras for many-electron systems: II. One- and two-body matrix elements. J Math Chem 13, 273–316 (1993). https://doi.org/10.1007/BF01165571

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  • DOI: https://doi.org/10.1007/BF01165571

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