Chemistry and the near-sighted nature of the one-electron density matrix

Two different macrospopic pieces of copper have different external potentials and, because of the unique functional relationship between the electron density and the external potential as demanded by density functional theory, should possess different electron density distributions. Experimentally, however, an atom in the bulk exhibits the same electron density in both samples and they possess identical sets of intensive properties. Density functional theory does not account for the fundamental observation underlying the theory of atoms in molecules: that what are apparently identical distributions of charge can be observed for an atom or a grouping of atoms in systems with different external potentials and that these atoms contribute essentially identical amounts to the energies and all other properties of the systems in which they occur. It is shown that, unlike the external potential, the kinetic energy density and the potential energy density, defined by the virial of the Ehrenfest force acting on electron density, are short-range functions. As recorded in the first article on atoms in molecules, they exhibit a local dependence on the electron density that causes them to faithfully mimic the transferability of the atomic charge distributions from one system to another. The electron, the kinetic energy, and the virial densities are all determined directly by the one-electron density matrix, a function termed near-sighted by Professor Kohn. It is this near-sighted property of the one-matrix that underlies the working hypothesis of chemistry—that of a functional group exhibiting a characteristic set of properties. The observations obtained from the theory of atoms in molecules and the atomic theorems it determines demonstrate the existence of a local relationship between the electron density and all properties of a system. © 1995 John Wiley & Sons, Inc.