ISSN:
0020-7608
Schlagwort(e):
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Chemie und Pharmazie
Notizen:
This article considers two types of 2 × 2, 3 × 3, 4 × 4, and 5 × 5 determinantal inequalities. One type involves Gram determinants, while the other type involves determinants based on a theorem by Pólya and Szegö. The elements of the first type of determinants are 〈rn〉, while the elements of the second type of determinants are c 〈rn〉, where c = 3 + n, and r is the distance from the nucleus of an atom. Both types of determinantal inequalities are used to obtain lower-bound (LB) estimates of 〈1/r〉 for atoms of spherical symmetry. The inequalities involving Gram determinants have been applied previously by the author to atoms of spherically symmetric charge distributions, such as He, Ne, Ar, Kr, Xe; Li, Na, K, Rb; Be, Mg, Ca, Sr. In the resent article, the inequalities involving determinants based on the Pólya and Szegö theorem are applied to the same atoms. It is found that in both cases the LB values of 〈1/r〉, for all atoms considered, appear to converge to the quantum mechanical (QM) values of Boyd, who calculated them with the Roothan-Hartree-Fock wave functions of Clementi and Roetti. It is also found that the LB values of 〈1/r〉, using determinants based on the Pólya-Szegö theorem, converge “faster” to the QM values of 〈1/r〉 than do the LB values of 〈1/r〉 based on Gram determinants. © 1995 John Wiley & Sons, Inc.
Zusätzliches Material:
3 Tab.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1002/qua.560560834
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