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.
Skip Nav Destination
Article navigation
21 August 2020
Research Article|
August 18 2020
Full-quantum descriptions of molecular systems from constrained nuclear–electronic orbital density functional theory Available to Purchase
Xi Xu
;
Xi Xu
Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison
, 1101 University Avenue, Madison, Wisconsin 53706, USA
Search for other works by this author on:
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: [email protected]
Search for other works by this author on:
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: [email protected]
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
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
The Amsterdam Modeling Suite
Evert Jan Baerends, Nestor F. Aguirre, et al.
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Related Content
Molecular vibrational frequencies from analytic Hessian of constrained nuclear–electronic orbital density functional theory
J. Chem. Phys. (June 2021)
Constrained nuclear-electronic orbital density functional theory: Energy surfaces with nuclear quantum effects
J. Chem. Phys. (February 2020)
Assessment of electron–proton correlation functionals for vibrational spectra of shared-proton systems by constrained nuclear-electronic orbital density functional theory
J. Chem. Phys. (December 2024)
Modeling electronic absorption spectra with nuclear quantum effects in constrained nuclear–electronic orbital framework
J. Chem. Phys. (April 2025)
Nuclear–electronic orbital methods: Foundations and prospects
J. Chem. Phys. (July 2021)