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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 MB) str. 67-72 preuzimanja: 158* citiraj
APA 6th Edition
Csavinszky, P. (1994). Inequalities Among 〈rn〉 Based on Gram Determinants. Croatica Chemica Acta, 67 (1), 67-72. Preuzeto s https://hrcak.srce.hr/136896
MLA 8th Edition
Csavinszky, P.. "Inequalities Among 〈rn〉 Based on Gram Determinants." Croatica Chemica Acta, vol. 67, br. 1, 1994, str. 67-72. https://hrcak.srce.hr/136896. Citirano 19.04.2021.
Chicago 17th Edition
Csavinszky, P.. "Inequalities Among 〈rn〉 Based on Gram Determinants." Croatica Chemica Acta 67, br. 1 (1994): 67-72. https://hrcak.srce.hr/136896
Harvard
Csavinszky, P. (1994). 'Inequalities Among 〈rn〉 Based on Gram Determinants', Croatica Chemica Acta, 67(1), str. 67-72. Preuzeto s: https://hrcak.srce.hr/136896 (Datum pristupa: 19.04.2021.)
Vancouver
Csavinszky P. Inequalities Among 〈rn〉 Based on Gram Determinants. Croatica Chemica Acta [Internet]. 1994 [pristupljeno 19.04.2021.];67(1):67-72. Dostupno na: https://hrcak.srce.hr/136896
IEEE
P. Csavinszky, "Inequalities Among 〈rn〉 Based on Gram Determinants", Croatica Chemica Acta, vol.67, br. 1, str. 67-72, 1994. [Online]. Dostupno na: https://hrcak.srce.hr/136896. [Citirano: 19.04.2021.]

Sažetak
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.

Hrčak ID: 136896

URI
https://hrcak.srce.hr/136896

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