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Monotonicity properties of the atomic charge density function

✍ Scribed by J. C. Angulo; R. J. Yáñez; J. S. Dehesa; E. Romera

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
739 KB
Volume
58
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

The present knowledge of the monotonicity properties of the spherically averaged electron density p ( r ) and its derivatives, which comes mostly from Roothan-Hartree-Fock calculations, is reviewed and extended to all Hartree-Fock ground-state atoms from hydrogen ( Z = 1) to uranium ( Z = 92). In looking for electron functions with universal (i.e., valid in the whole periodic table) monotonicity properties, it is found that there exist positive values of ct so that the function g o ( r ; ct) = p( r ) / r a is convex, and g l ( r ; a) = -p'( r ) / r a is not only monotonically decreasing from the origin but also convex. This is, however, not the case for the function g J r ; a) = p " ( r ) / r " .

Additionally, the conditions which specify values for p such that the function gn( r; p ) = (l)"p'")(r)/r n = 0 , l in all neutral atoms below uranium. The last property is used to obtain inequalities of general validity involving three radial expectation values which generalize all the similar ones known to date, as well as other relationships among these quantities and the values of the electron density and its derivatives at the nucleus.

Wiley & Sons, Inc.

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