Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear–electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein, we develop the analytic Hessian for cNEO-DFT energy with respect to the change in nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicomponent cNEO coupled-perturbed Kohn–Sham (cNEO-CPKS) equations, which describe the response of electronic and nuclear orbitals to the displacement of nuclear (expectation) positions. With the analytic Hessian, the vibrational frequencies of a series of small molecules are calculated and compared to those from conventional DFT Hessian calculations as well as those from the vibrational second-order perturbation theory (VPT2). It is found that even with a harmonic treatment, cNEO-DFT significantly outperforms DFT and is comparable to DFT-VPT2 in the description of vibrational frequencies in regular polyatomic molecules. Furthermore, cNEO-DFT can reasonably describe the proton transfer modes in systems with a shared proton, whereas DFT-VPT2 often faces great challenges. Our results suggest the importance of nuclear quantum effects in molecular vibrations, and cNEO-DFT is an accurate and inexpensive method to describe molecular vibrations.
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28 June 2021
Research Article|
June 28 2021
Molecular vibrational frequencies from analytic Hessian of constrained nuclear–electronic orbital density functional theory
Special Collection:
2021 JCP Emerging Investigators Special Collection
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
Note: This paper is part of the 2021 JCP Emerging Investigators Special Collection.
J. Chem. Phys. 154, 244110 (2021)
Article history
Received:
April 29 2021
Accepted:
June 04 2021
Citation
Xi Xu, Yang Yang; Molecular vibrational frequencies from analytic Hessian of constrained nuclear–electronic orbital density functional theory. J. Chem. Phys. 28 June 2021; 154 (24): 244110. https://doi.org/10.1063/5.0055506
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