Atoms in molecules from the exact one-electron wave function

Abstract

Use of the electron amplitude (i.e., the square root of the electron density) in place of the electron density in Bader's topological theory of atoms in molecules, is shown to lead to identical definitions of bond paths and interatomic surfaces. The concepts of regions of charge concentration and depletion, derived from the Laplacian of the electron density, become the concepts of classically allowed and forbidden regions of space when derived from the Laplacian of the electron amplitude, because the latter is the wave function in the exact Schrödinger equation for (any) one electron in the many-electron molecule. However, the domains of corresponding regions are different, the size and depth of a classically allowed region always being larger than the corresponding region of charge concentration; in some cases there is no region of charge concentration corresponding to a classically allowed region. The surface between the outermost allowed and forbidden regions of space provides a definition of the size and shape of the molecule. This definition of the outermost surface of the electronic charge cloud (the molecular envelope) is exact apart from quantum mechanical tunelling. Hence it is proposed as a basis for molecular graphics; i.e., as the unique, non-arbitrary, and, in principle, exact definition of the size and shape of a molecule. Key words: electron density, quantum chemistry, molecular graphics.