Topography of molecular scalar fields. I. Algorithm and Poincaré–Hopf relation
- 8 September 2003
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 119 (10) , 5037-5043
- https://doi.org/10.1063/1.1597652
Abstract
A new algorithm for locating the critical points (CP’s) of a three-dimensional molecular scalar field is discussed. The algorithm is based on a ray search from the surface extrema of appropriately defined atom-centered spheres. The algorithm is tested for molecular electrostatic potentials and electron densities of a few test molecules such as tetrahedrane, cubane, anthracene, diborane, etc. Furthermore, the Poincaré–Hopf relationship is examined for the set of CP’s thus obtained. A topological interpretation of the Euler characteristic of a given isosurface is employed for a stronger regional check on the number of CP’s enclosed in the isosurface.Keywords
This publication has 14 references indexed in Scilit:
- An improved algorithm to locate critical points in a 3D scalar field as implemented in the program MORPHYJournal of Computational Chemistry, 2003
- Clar's Aromatic Sextet Theory Revisited via Molecular Electrostatic Potential TopographyThe Journal of Organic Chemistry, 1999
- MORPHY, a program for an automated “atoms in molecules” analysisComputer Physics Communications, 1996
- Alteration of the Reactivity of a Tellurophene Within a Core‐Modified Porphyrin Environment: Synthesis and Oxidation of 21‐TelluraporphyrinAngewandte Chemie International Edition in English, 1995
- A robust algorithm to locate automatically all types of critical points in the charge density and its LaplacianChemical Physics Letters, 1994
- General atomic and molecular electronic structure systemJournal of Computational Chemistry, 1993
- Molecular electrostatics. A comprehensive topographical approachChemical Physics Letters, 1992
- Marching cubes: A high resolution 3D surface construction algorithmACM SIGGRAPH Computer Graphics, 1987
- On the similarity between molecular electron densities, electrostatic potentials and bare nuclear potentialsChemical Physics Letters, 1986
- Walking on potential energy surfacesThe Journal of Physical Chemistry, 1983