Abstract
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.
Highlights
The Born-Oppenheimer (BO) approximation [1,2] is among the most fundamental ingredients of modern condensed-matter theory
The BO approximation makes calculations computationally feasible, the motion of nuclear wave packets in the lowest BO potential energy surface provides us with an intuitive picture of many chemical reactions
The total wave function of the system is a single product of a nuclear wave function and the many-electron wave function which parametrically depends on the nuclear coordinates
Summary
The Born-Oppenheimer (BO) approximation [1,2] is among the most fundamental ingredients of modern condensed-matter theory. In this article we follow the first option: Our goal is to develop a Green’s function-based many-body theory for the complete system of electrons and nuclei where the Green’s functions are defined in terms of coordinates that refer to a body-fixed coordinate frame. First steps in this direction were taken with the formulation of a multicomponent density-functional theory [54,55,56] and with the derivation of a Green’s-function framework [57].
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