Atoms in molecules without boundaries: analyses via electrostatic potentials at nuclei

This prefatory review begins with historical background relating to the emergence of the electrostatic potential into the field of chemistry and related fields, leading then into the major focus of this paper: electrostatic potentials at nuclei. The electrostatic potential at the nucleus of an atom, whether it be in the free state or in a neutral molecule or in an ionic molecular species, is qualitatively a characteristic property of the atom. It changes remarkably little from one molecular environment to another. As has been shown earlier by Politzer, the energies of atoms and molecules can be expressed both approximately and rigorously in terms of the electrostatic potentials at their nuclei. For example, molecular energies can be written entirely as summations over atomic contributions, with no explicit interatomic terms. This provides a basis for estimating the energy of an atom in a molecule and supports the validity of the atoms-in-molecules concept, however without the necessity of boundaries for the atoms. This has been further substantiated by a recent paper entitled “Atoms do exist in molecules: Analysis using electrostatic potentials at nuclei”, where the authors have shown that the electrostatic potential created by the electrons of all the other atoms at a particular nucleus in a molecular species, not including those associated with that particular atom itself, is almost identical in magnitude to the potential due to the other nuclei. The significance of this will be discussed, with an emphasis on atoms in molecules without boundaries.