Molecular Potential Energies from Experimental Electric Field and Electrostatic Potential at Nuclei

In this paper, the molecular electrostatic potential energy V is first estimated from the electric field generated by an experimental electron density. Once the high resolution X-ray diffraction data are fitted against the Hansen-Coppens multipole model, the electric field E is analytically computed on every point inside and around the molecule by using our own software FIELD. The potential energy is then obtained by a numerical and robust integration of E²/2. The topological analysis of the electric field is carried out to reveal the specific contribution of atoms in a molecule. Application is made on a set of seven organic molecules of different sizes. The results are compared to those obtained from Politzer's empirical calculations of the molecular energy using the electrostatic potential values at the atomic nuclei (EPN) within the framework of the Thomas-Fermi approximation. In this context, the molecular energy estimates found for the chosen molecules are presented and discussed.