The theory of atoms in molecules is extended to the case where the molecule is in the presence of an electromagnetic field. This theory is based upon a generalization of quantum mechanics to an open system, as obtained through a corresponding extension of Schwingerrsquo;s principle of stationary action. The extension of this principle is possible only if the open system satisfies a particular boundary condition, one which is expressed as a constraint on the variation of the action integral. This is the condition that it be bounded by a surface of zero flux in the gradient vector field of the charge density, the definition of an atom in a molecule. It is shown that this boundary constraint again suffices to define an atom as a quantum subsystem when the molecule is in the presence of an electromagnetic field. The mechanics of an open system and its properties are determined by the fluxes in corresponding vector current densities through its surface. As in the fieldfree case, the obtainment of these currents from the variation of the action integral is a direct result of the variation of the atomic surface and of the imposition of the variational constraint on its boundary. The currents in this case consist of a paramagnetic and a diamagnetic contribution, currents whose presence are a necessary requirement for the description of the properties of a system in the presence of external fields. The variational statement of the Heisenberg equation of motion obtained from the principle of stationary action is used to derive the Ehrenfest force and virial theorems for an atom in a molecule in the presence of external electric and magnetic fields. In this case, there are forces acting on the interior of the atom which arise from the magnetic pressures acting on its surface. It is shown that the molecular electric polarizability and magnetic susceptibility, like other properties, are rigorously expressible as a sum of atomic contributions.
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