Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules
Abstract
The partition functions, heat capacities, entropies, and enthalpies of selected molecules were calculated using uncoupled mode (UM) approximations, where the fulldimensional potential energy surface for internal motions was modeled as a sum of independent onedimensional potentials for each mode. The computational cost of such approaches scales the same with molecular size as standard harmonic oscillator vibrational analysis using harmonic frequencies (HO^{hf}). To compute thermodynamic properties, a computational protocol for obtaining the energy levels of each mode was established. The accuracy of the UM approximation depends strongly on how the onedimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UMN), the accuracies of the calculated thermodynamic properties are not significantly improved versus the HO^{hf} model. Significant improvements can be achieved by constructing potentials for internal rotations and vibrations using the energy surfaces along the torsional coordinates and the remaining vibrational normal modes, respectively (UMVT). For hydrogen peroxide and its isotopologs at 300 K, UMVT captures more than 70% of the partition functions on average. By con trast, the HO^{hf} model and UMN can capture no more than 50%. For a selected test set of C2 tomore »
 Authors:

 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 947201462, United States
 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 947201462, United States; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
 Department of Chemistry, University of California, Berkeley, California 947201462, United States; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1418289
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Theory and Computation
 Additional Journal Information:
 Journal Volume: 12; Journal Issue: 6; Journal ID: ISSN 15499618
 Publisher:
 American Chemical Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Entropy; Enthalpy; Heat Capacity; Partition function; Anharmonicity; Rigid rotor; Harmonic oscillator; Internal rotor
Citation Formats
Li, YiPei, Bell, Alexis T., and HeadGordon, Martin. Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules. United States: N. p., 2016.
Web. doi:10.1021/acs.jctc.5b01177.
Li, YiPei, Bell, Alexis T., & HeadGordon, Martin. Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules. United States. doi:10.1021/acs.jctc.5b01177.
Li, YiPei, Bell, Alexis T., and HeadGordon, Martin. Thu .
"Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules". United States. doi:10.1021/acs.jctc.5b01177. https://www.osti.gov/servlets/purl/1418289.
@article{osti_1418289,
title = {Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules},
author = {Li, YiPei and Bell, Alexis T. and HeadGordon, Martin},
abstractNote = {The partition functions, heat capacities, entropies, and enthalpies of selected molecules were calculated using uncoupled mode (UM) approximations, where the fulldimensional potential energy surface for internal motions was modeled as a sum of independent onedimensional potentials for each mode. The computational cost of such approaches scales the same with molecular size as standard harmonic oscillator vibrational analysis using harmonic frequencies (HOhf). To compute thermodynamic properties, a computational protocol for obtaining the energy levels of each mode was established. The accuracy of the UM approximation depends strongly on how the onedimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UMN), the accuracies of the calculated thermodynamic properties are not significantly improved versus the HOhf model. Significant improvements can be achieved by constructing potentials for internal rotations and vibrations using the energy surfaces along the torsional coordinates and the remaining vibrational normal modes, respectively (UMVT). For hydrogen peroxide and its isotopologs at 300 K, UMVT captures more than 70% of the partition functions on average. By con trast, the HOhf model and UMN can capture no more than 50%. For a selected test set of C2 to C8 linear and branched alkanes and species with different moieties, the enthalpies calculated using the HOhf model, UMN, and UMVT are all quite accurate comparing with reference values though the RMS errors of the HO model and UMN are slightly higher than UMVT. However, the accuracies in entropy calculations differ significantly between these three models. For the same test set, the RMS error of the standard entropies calculated by UMVT is 2.18 cal mol1 K1 at 1000 K. By contrast, the RMS error obtained using the HO model and UMN are 6.42 and 5.73 cal mol1 K1, respectively. For a test set composed of nine alkanes ranging from C5 to C8, the heat capacities calculated with the UMVT model agree with the experimental values to within a RMS error of 0.78 cal mol 1 K 1 , which is less than onethird of the RMS error of the HOhf (2.69 cal mol1 K1) and UMN (2.41 cal mol1 K1) models.},
doi = {10.1021/acs.jctc.5b01177},
journal = {Journal of Chemical Theory and Computation},
number = 6,
volume = 12,
place = {United States},
year = {2016},
month = {5}
}
Web of Science