2009

Critical Points of the Electric Field from a Collection of Point Charges
TopologyBased Methods in Visualization II, Springer, 2009
Abstract
The electric field around a molecule is generated by the charge distribution of its constituents: positively charged atomic nuclei, which are well approximated by point charges, and negatively charged electrons, whose probability density distribution can be computed from quantum mechanics. For the purposes of molecular mechanics or dynamics, the charge distribution is often approximated by a collection of point charges, with either a single partial charge at each atomic nucleus position, representing both the nucleus and the electrons near it, or as several different point charges per atom. The critical points in the electric field are useful in visualizing its geometrical and topological structure, and can help in understanding the forces and motion it induces on a charged ion or neutral dipole. Most visualization tools for vector fields use only samples of the field on the vertices of a regular grid, and some sort of interpolation, for example, trilinear, on the grid cells. There is less risk of missing or misinterpreting topological features if they can be derived directly from the analytic formula for the field, rather than from its samples. This work presents a method which is guaranteed to find all the critical points of the electric field from a finite set of point charges. To visualize the field topology, we have modified the saddle connector method to use the analytic formula for the field.