Variational principle and path integrals for atoms in molecules

Two things were done in this paper: (i) A generalization of Schwinger's variational principle to a subsystem was developed within the framework of quantum field theory and applied to the theory of atoms in molecules. This work generalizes the previous derivation given in the Schrödinger formulation. (ii) It is demonstrated that Feynman's path integral, when expressed in terms of the coherent‐state representation, can be constructed for a subsystem of a many‐electron system if a divergence term, which serves as a variational constraint in the definition of an atom in a molecule, is added to the Lagrangian. This formulation is equivalent to the atomic statement of the variational principle if the divergence term is suitably constructed. It is shown that the path integral can be expressed as a product of the individual atomic contributions to the steps along the paths with the action being determined by a corresponding sum of the atomic contributions to the action integral.