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Singer polymals. I. Evaluation of matrix elements
Author(s) -
Poshusta R. D.
Publication year - 1978
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560130104
Subject(s) - matrix (chemical analysis) , hamiltonian (control theory) , hamiltonian matrix , symmetry (geometry) , mathematics , physics , mathematical physics , mathematical analysis , quantum mechanics , symmetric matrix , chemistry , geometry , eigenvalues and eigenvectors , mathematical optimization , chromatography
Hamiltonian matrix elements between pairs of explicitly correlated Singer polymals are derived. A new method for 1/ r 12 matrix elements is found which avoids the 6 by 6 matrix inversion required at each quadrature point in the old method. The new formula requires about half the computer time of the old one. The electron repulsion and nuclear attraction matrix elements are shown to be related to incomplete elliptic integrals. Simplified formulas are derived for the special cases of cylindrical symmetry, spherical symmetry, and single‐center expansions. An upper bound approximation formula for the purpose of neglecting matrix elements is derived. These bounds may be useful for single‐center expansions but are found to be too high for the general case.