Nonorthogonality corrections in the method of correlated basis functions |
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Authors: | Eugene Feenberg |
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Institution: | Department of Physics, Washington University, St. Louis, Missouri 63130 USA |
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Abstract: | A set of normalized linearly independent basis functions φ1, φ2, …, φj, … generates matrix representatives and of the Hamiltonian operator and the identity. An orthonormal basis , , …, , … generated by a Löwdin transformation is characterized by the distance in Hilbert space between and φj. The choice of positive definite minimizes these distances and maximizes the diagonal elements of . Again for positive definite and a finite basis, 1 ? j ? p, the analysis yields a general theorem on Trace (? p for all positive and negative integral values of n except n = ?1 and ? p for n = ?1).Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of . Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas. |
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