Atomic theorems

Abstract

The atomic statement of the principle of stationary action determines the theorems that establish the mechanics of an atom in a molecule. The atomic torque, power, and current theorems are derived. They, along with the atomic force, virial, and continuity theorems, provide a complete description of the behavior of matter at the atomic level, including the effects of electric and magnetic fields. The atomic power theorem, for example, enables one to determine the atomic or molecular source of the creation and dissipation of power in combustion or in an explosion. An atom in a molecule is an open system and an atomic equation of motion for an observable contains a component corresponding to the flux in its current density through the atomic surface. The differential form of each theorem yields an equation of motion for the corresponding property density in which the same surface flux appears as a divergence of the current density. The differential and integrated atomic theorems complement those for the total system, enabling one to relate the property to its atomic components and ultimately to a local contribution from each element in real space. © 1993 John Wiley & Sons, Inc.