We develop a full-quantum formulation of constrained nuclear–electronic orbital density functional theory (cNEO-DFT). This formulation deviates from the conventional Born–Oppenheimer framework, and all nuclei and electrons are treated on an equal footing within the molecular orbital picture. Compared to the conventional DFT, the ground state energy in full-quantum cNEO-DFT inherently includes all vibrational zero-point energies. We also derived and implemented the analytic gradient of the full-quantum cNEO-DFT energy with respect to the quantum nuclear expectation positions. With the analytic gradient, the geometry optimizations are performed, which naturally include the nuclear quantum effects and describe the geometric isotope effects. The full-quantum cNEO-DFT is tested on a series of small molecules and the transition states of two hydrogen transfer reactions. The results are compared with those from conventional DFT, DFT-VPT2, and NEO-DFT with only key protons treated quantum mechanically. It is found that the nuclear quantum effects have notable impacts on molecular equilibrium geometries and transition state geometries. The full-quantum cNEO-DFT can be a promising method for describing the nuclear quantum effects in many chemical processes.
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21 August 2020
Research Article|
August 18 2020
Full-quantum descriptions of molecular systems from constrained nuclear–electronic orbital density functional theory
Xi Xu
;
Xi Xu
Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison
, 1101 University Avenue, Madison, Wisconsin 53706, USA
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Yang Yang
Yang Yang
a)
Theoretical Chemistry Institute and Department of Chemistry, 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. 153, 074106 (2020)
Article history
Received:
May 18 2020
Accepted:
July 23 2020
Citation
Xi Xu, Yang Yang; Full-quantum descriptions of molecular systems from constrained nuclear–electronic orbital density functional theory. J. Chem. Phys. 21 August 2020; 153 (7): 074106. https://doi.org/10.1063/5.0014001
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