Exploring the Gradient Paths and Zero Flux Surfaces of Molecular Electrostatic Potential

The gradient vector field of molecular electrostatic potential, ∇V(r), has remained relatively unexplored in molecular quantum mechanics. The present article explores the conceptual as well as practical aspects of this vector field. A three-dimensional atomic partition of molecular space has been achieved on the basis of zero flux surfaces (ZFSs) of ∇V(r). Such ZFSs may completely enclose some of the atoms in the molecule, unlike what is observed in density-based atomic partitioning. The demonstration of this phenomenon is elucidated through typical examples, e.g., N2, CO, H2O, H2CO, OF(•), :CH2, and NH3BF3, where the electronegative atoms or group of atoms (group electronegativity) exhibits a closed ZFS of ∇V(r) around them. The present article determines an explicit reason for this phenomenon and also provides a necessary and sufficient condition for such a closed ZFS of ∇V(r) to exist. It also describes how the potential-based picture of atoms in molecules differs from its electron density-based analogue. This work further illustrates the manifestation of anisotropy in the gradient paths of MESP of some molecular systems, with respect to CO, (•)OH, H2O, and H2CO, and points to its potential in understanding the reactivity patterns of the interacting molecules.