Accuracy of finite-difference harmonic frequencies in density functional theory
Abstract
Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors < 0.1 cm-1 as compared to results based on an analytic Hessian. For very small frequencies corresponding to nonbonded vibrations in noncovalent complexes (for which the harmonic approximation is questionable anyway), the finite-difference error can be larger, but even in these cases the errors can be reduced below 0.1 cm-1 by judicious choice of the displacement step size and a higher-order finite-difference approach. Finally, the surprising accuracy and robustness of the finite-difference results suggests that availability of the analytic Hessian is not so important in today's era of commodity processors that are readily available in largemore »
- Authors:
-
[1]
- The Ohio State Univ., Columbus, OH (United States)
- The Ohio State Univ., Columbus, OH (United States); Max-Planck-Inst. fur Kohlenforschung, Mulheim (Germany)
- Publication Date:
- Research Org.:
- The Ohio State Univ., Columbus, OH (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division; National Science Foundation (NSF)
- OSTI Identifier:
- 1604465
- Alternate Identifier(s):
- OSTI ID: 1401300
- Grant/Contract Number:
- SC0008850; CHE-1300603
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Chemistry
- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 19; Journal ID: ISSN 0192-8651
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; finite difference; harmonic frequencies; isotopic shifts; noncovalent interactions; density functional theory
Citation Formats
Liu, Kuan-Yu, Liu, Jie, and Herbert, John M. Accuracy of finite-difference harmonic frequencies in density functional theory. United States: N. p., 2017.
Web. doi:10.1002/jcc.24811.
Liu, Kuan-Yu, Liu, Jie, & Herbert, John M. Accuracy of finite-difference harmonic frequencies in density functional theory. United States. https://doi.org/10.1002/jcc.24811
Liu, Kuan-Yu, Liu, Jie, and Herbert, John M. Wed .
"Accuracy of finite-difference harmonic frequencies in density functional theory". United States. https://doi.org/10.1002/jcc.24811. https://www.osti.gov/servlets/purl/1604465.
@article{osti_1604465,
title = {Accuracy of finite-difference harmonic frequencies in density functional theory},
author = {Liu, Kuan-Yu and Liu, Jie and Herbert, John M.},
abstractNote = {Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors < 0.1 cm-1 as compared to results based on an analytic Hessian. For very small frequencies corresponding to nonbonded vibrations in noncovalent complexes (for which the harmonic approximation is questionable anyway), the finite-difference error can be larger, but even in these cases the errors can be reduced below 0.1 cm-1 by judicious choice of the displacement step size and a higher-order finite-difference approach. Finally, the surprising accuracy and robustness of the finite-difference results suggests that availability of the analytic Hessian is not so important in today's era of commodity processors that are readily available in large numbers.},
doi = {10.1002/jcc.24811},
journal = {Journal of Computational Chemistry},
number = 19,
volume = 38,
place = {United States},
year = {Wed May 10 00:00:00 EDT 2017},
month = {Wed May 10 00:00:00 EDT 2017}
}
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