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Inequalities Among 〈rn〉 Based on Gram Determinants

P. Csavinszky ; Department of Physics and Astronomy, University of Maine, Orono, Maine 04469-5709

Puni tekst: engleski pdf 12.146 Kb

str. 67-72

preuzimanja: 184



This paper considers determinantal inequalities based on 2 x 2 and 3x3 Gram determinants. The elements of these determinants are the expectation values (r'n), where r is the distance from the nucleus of a selected atom. The 2x2 Gram determinant involves m = -1, 0, 1, while the 3x3 Gram determinant involves m = -1, 0, 1, 2, 3. In the present work, for cal- culational purposes, it is assumed that the element (r) is unknown, while all the other elements of the 2x2 and 3x3 determinants are known.
Lower bounds of (r) are then calculated from the 2x2 and 3x3 determinantal inequalities for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculated lower-bound values of (r> are compared with the quantum-mechanical values of calculated by Boyd using the Roothaan-Hartree-Fock wave functions. It is found that the lower-bound value of (r) involving the 3x3 Gram determinant leads to a better agreement with the quantum-mechanical value of (r) than the lower-bound value of (r) involving the 2x2 Gram determinant. The implications of this finding are discussed.

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