The nuclear-electronic orbital (NEO) framework enables the incorporation of nuclear quantum effects by treating both electrons and specific key nuclei quantum-mechanically. The conventional NEO method predicates on the controversial Born–Oppenheimer separation between classical and quantum nuclei, and its potential energy surface only depends on the coordinates of classical nuclei. In this paper, based on the fact that quantum nuclei are relatively localized, we develop the constrained nuclear-electronic orbital density functional theory (cNEO-DFT) by imposing a constraint on the expectation value of the quantum nuclear position. In this way, an extended NEO energy surface is obtained, which also depends on the quantum nuclear position. Compared to the potential energy surface obtained from conventional DFT, the extended NEO energy surface incorporates the nuclear quantum effects, which have notable impacts on the energy profile. Furthermore, cNEO-DFT can facilitate the location of NEO stationary states. It potentially can be used in geometry optimization, transition states search, and the calculation of reaction dynamics.
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28 February 2020
Research Article|
February 26 2020
Constrained nuclear-electronic orbital density functional theory: Energy surfaces with nuclear quantum effects
Xi Xu
;
Xi Xu
Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison
, 1101 University Avenue, Madison, Wisconsin 53706, USA
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Yang Yang
Yang Yang
a)
Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison
, 1101 University Avenue, Madison, Wisconsin 53706, USA
a)Author to whom correspondence should be addressed: yyang222@wisc.edu
Search for other works by this author on:
a)Author to whom correspondence should be addressed: yyang222@wisc.edu
J. Chem. Phys. 152, 084107 (2020)
Article history
Received:
December 23 2019
Accepted:
February 09 2020
Citation
Xi Xu, Yang Yang; Constrained nuclear-electronic orbital density functional theory: Energy surfaces with nuclear quantum effects. J. Chem. Phys. 28 February 2020; 152 (8): 084107. https://doi.org/10.1063/1.5143371
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