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An appraisal of Poincaré-Hopf relation and application to topography of molecular electrostatic potentials.

Authors
  • Roy, D
  • Balanarayan, P
  • Gadre, Shridhar R
Type
Published Article
Journal
The Journal of Chemical Physics
Publisher
American Institute of Physics
Publication Date
Nov 07, 2008
Volume
129
Issue
17
Pages
174103–174103
Identifiers
DOI: 10.1063/1.2999558
PMID: 19045329
Source
Medline
License
Unknown

Abstract

The Poincaré-Hopf relation is studied for molecular electrostatic potentials (MESPs) of a few test systems such as cyclopropane, cyclobutane, pyridine, and benzene. Appropriate spheres centered at various points, including the center of mass of the system under study, are constructed and the MESP gradient is evaluated on the corresponding spherical grid. The change in directional nature of MESP gradient on the surface of these spheres gives indication of the critical points of the function. This is used for developing a method for locating the critical points of MESP. The strategy also enables a general definition of the Euler characteristic (EC) of the molecule, independent of any region or space. Further, the effect of basis set and level of theory on the EC is discussed.

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