Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

Ville J. Härkönen; Robert Van Leeuwen; E. K.U. Gross

doi:10.1103/PhysRevB.101.235153

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

Ville J. Härkönen^*, Robert Van Leeuwen, E. K.U. Gross

^*Corresponding author for this work

Institute of Chemistry

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	American English
Article number	235153
Journal	Physical Review B
Volume	101
Issue number	23
DOIs	https://doi.org/10.1103/PhysRevB.101.235153
State	Published - 15 Jun 2020

Bibliographical note

Funding Information:
V.J.H. thanks Dr. Ivan Gonoskov for useful discussions on various aspects of the present work. E.K.U.G. acknowledges financial support by the European Research Council Advanced Grant FACT (ERC-2017-AdG-788890).

Publisher Copyright:
© 2020 authors. Published by the American Physical Society.

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title = "Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation",

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.",

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AB - 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.

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Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

Abstract

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