A bond path: A universal indicator of bonded interactions

The quantum mechanics of proper open systems yields the physics that governs the local behavior of the electron density, rho(r). The Ehrenfest force F(r) acting on an element of rho(r) and the virial field upsilon(r) that determine its potential energy are obtained from equations of motion for the electronic momentum and virial operators, respectively. Each is represented by a "dressed" density, a distribution in real space that results from replacing the property in question for a single electron with a corresponding density that describes its average interaction with all of the remaining particles in the system. All bond paths, lines of maximum density linking neighboring nuclei in a system in stable electrostatic equilibrium, have a common physical origin in terms of F(r) and upsilon(r), regardless of the nature of the interaction. Each is homeomorphically mirrored by a virial path, a line of maximally negative potential energy density linking the same nuclei. The presence of a bond path and its associated virial path provide a universal indicator of bonding between the atoms so linked. There is no net force acting on an element of rho(r) or on an atom in a molecule in a stationary state, and upsilon(r) is attractive everywhere. Thus, contrary to what has appeared in the literature, no repulsive forces act on atoms linked by a bond path, nor on their nuclei. All atomic interactions, including these described as nonbonded and responsible for binding in condensed states of matter, result from a local pairing of the densities of opposite spin electrons. This local pairing, which varies throughout space and with the strength of the interaction, should be distinguished from the notion of an electron pair, as embodied in the Lewis model.