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.

Acidity of Brønsted acids is explained in terms of the electrostatic potentials of the corresponding conjugate bases. The electrostatic potential distribution on the zero-flux surface of the strongest isolable carborane anions is seen to provide a good measure of their acidities. Increasing value of the lowest minimum in the electrostatic potential is observed to be a signature of increasing acidity.

Topographical analysis of the molecular electrostatic potential (MESP) along a reaction path is employed for bringing out sequential electronic reorganizations for 1,3-dipolar cycloadditions of ethyne to fulminic acid as well as diazomethane. A simple and consistent set of rules for portraying electronic mechanisms of chemical reactions using the MESP topography is applied for this purpose. The MESP topography at each point on the concerted reaction path is associated with a classical electronic structure yielding a clear picture of the electronic reorganization along the reaction path.

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.

The recognition of interaction between two molecules is analysed via the topography of their molecular electrostatic potentials (MESP). The point of recognition between two species is proposed to be the geometry at which there is a change in the nature of the set of MESP critical points of one of the molecules vis-a-vis with its MESP topography at infinite separation. These results are presented for certain model systems such as pyridine and benzene dimers, cytosine-guanine and adenine-thymine base pairs in various orientations of approach of the two species.