On the Sanibel coefficients in the expansion of spin-projected slater determinants

Authors

  • Per-Olov Löwdin

    1. Department of Quantum Chemistry, Uppsala University, Box 518, 75120 Uppsala, Sweden
    2. Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, U.S.A.
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Abstract

Every Slater determinant D may be uniquely analyzed in terms of spin components Dl = OlD which are pure spin eigenfunctions, so that S2Dl = l(l+1)D. Every component Dl = OlD may in turn be written as a sum of symmetric combinations of Slater determinants, Tk = [αμ−kβk‖αkβν−k], and the coefficients cmath image in the expansion OlD = ∑kcmath imageTk are known as the “Sanibel coefficients.” By using the relation S2Dl = l(l+1)D, a recursion formula for the coefficients cmath image is derived, which is then explicitly solved in the special case when Sz has the pure quantum number m = 0.

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