Accuracy of finitedifference 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 coupledperturbed 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 largescale parallelization. Not only for absolute frequencies but also for isotopic and conformerdependent frequency shifts in flexible molecules, we find that the finitedifference 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 finitedifference 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 higherorder finitedifference approach. Finally, the surprising accuracy and robustness of the finitedifference 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:

 The Ohio State Univ., Columbus, OH (United States)
 The Ohio State Univ., Columbus, OH (United States); MaxPlanckInst. 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) (SC22). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1604465
 Alternate Identifier(s):
 OSTI ID: 1401300
 Grant/Contract Number:
 SC0008850; CHE1300603
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Chemistry
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 19; Journal ID: ISSN 01928651
 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, KuanYu, Liu, Jie, and Herbert, John M. Accuracy of finitedifference harmonic frequencies in density functional theory. United States: N. p., 2017.
Web. doi:10.1002/jcc.24811.
Liu, KuanYu, Liu, Jie, & Herbert, John M. Accuracy of finitedifference harmonic frequencies in density functional theory. United States. doi:10.1002/jcc.24811.
Liu, KuanYu, Liu, Jie, and Herbert, John M. Wed .
"Accuracy of finitedifference harmonic frequencies in density functional theory". United States. doi:10.1002/jcc.24811. https://www.osti.gov/servlets/purl/1604465.
@article{osti_1604465,
title = {Accuracy of finitedifference harmonic frequencies in density functional theory},
author = {Liu, KuanYu 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 coupledperturbed 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 largescale parallelization. Not only for absolute frequencies but also for isotopic and conformerdependent frequency shifts in flexible molecules, we find that the finitedifference approach exhibits mean errors < 0.1 cm1 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 finitedifference error can be larger, but even in these cases the errors can be reduced below 0.1 cm1 by judicious choice of the displacement step size and a higherorder finitedifference approach. Finally, the surprising accuracy and robustness of the finitedifference 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 = {2017},
month = {5}
}
Web of Science
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