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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1420511