Abstract
Exploiting our earlier results [J. Math. Chem. 4 (1990) 295–353 and 13 (1993) 273–316] on the unitary group U(n) Racah-Wigner algebra, specifically designed for quantum chemical calculations of molecular electronic structure, and the related tensor operator formalism that enabled us to introduce spin-free orbital equivalents of the second quantization-like creation and annihilation operators as well as higher rank symmetric, antisymmetric and adjoint tensors, we consider the problem of U(n) basis partitioning that is required for group-function type approaches to the many-electron problem. Using the U(n) ⊃ U(n 1) × U(n 2),n =n 1 +n 2 adapted basis, we evaluate all required matrix elements of U(n) generators and their products that arise in one- and two-body components of non-relativistic electronic Hamiltonians. The formalism employed naturally leads to a segmented form of these matrix elements, with many of the segments being identical to those of the standard unitary group approach. Relationship with similar approaches described earlier is briefly pointed out.
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M.D. Gould, X. Li and J. Paldus, to be published.
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Li, X., Paldus, J. Unitary group tensor operator algebras for many-electron systems. III. Matrix elements in U(n 1 +n 2) ⊃ U(n 1) × U(n 2) partitioned basis. J Math Chem 14, 325–355 (1993). https://doi.org/10.1007/BF01164475
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DOI: https://doi.org/10.1007/BF01164475