Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

Gidopoulos, N.I.; Gross, E.K.U.

doi:10.1098/rsta.2013.0059

Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

Gidopoulos, N.I.; Gross, E.K.U.

Authors

Dr Nikitas Gidopoulos nikitas.gidopoulos@durham.ac.uk
Associate Professor

E.K.U. Gross

Abstract

A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X(R), and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R. From the variational principle, we deduce formally exact equations for ΦR(r) and X(R). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.

Citation

Gidopoulos, N., & Gross, E. (2014). Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372(2011), Article 20130059. https://doi.org/10.1098/rsta.2013.0059

Journal Article Type	Article
Online Publication Date	Feb 10, 2014
Publication Date	Mar 13, 2014
Deposit Date	Sep 26, 2014
Publicly Available Date	Oct 2, 2014
Journal	Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.
Print ISSN	1364-503X
Electronic ISSN	1471-2962
Publisher	The Royal Society
Peer Reviewed	Peer Reviewed
Volume	372
Issue	2011
Article Number	20130059
DOI	https://doi.org/10.1098/rsta.2013.0059
Keywords	Beyond Born–Oppenheimer, Density functional theory, Non-adiabatic effects

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© 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, provided the original author and source are credited.