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 full-dimensional potential energy surface for internal motions was modeled as a sum of independent one-dimensional 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 one-dimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UM-N), 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 (UM-VT). For hydrogen peroxide and its isotopologs at 300 K, UM-VT captures more than 70% of the partition functions on average. By con trast, the HOhf model and UM-N 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 94720-1462, United States
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720-1462, United States; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Berkeley, California 94720-1462, United States; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1418289
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Theory and Computation
- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 6; Journal ID: ISSN 1549-9618
- 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, Yi-Pei, Bell, Alexis T., and Head-Gordon, Martin. Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules. United States: N. p., 2016.
Web. doi:10.1021/acs.jctc.5b01177.
Li, Yi-Pei, Bell, Alexis T., & Head-Gordon, Martin. Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules. United States. https://doi.org/10.1021/acs.jctc.5b01177
Li, Yi-Pei, Bell, Alexis T., and Head-Gordon, Martin. Thu .
"Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules". United States. https://doi.org/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, Yi-Pei and Bell, Alexis T. and Head-Gordon, Martin},
abstractNote = {The partition functions, heat capacities, entropies, and enthalpies of selected molecules were calculated using uncoupled mode (UM) approximations, where the full-dimensional potential energy surface for internal motions was modeled as a sum of independent one-dimensional 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 one-dimensional potentials of each modes are defined. If the potentials are determined by the energy as a function of displacement along each normal mode (UM-N), 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 (UM-VT). For hydrogen peroxide and its isotopologs at 300 K, UM-VT captures more than 70% of the partition functions on average. By con trast, the HOhf model and UM-N 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, UM-N, and UM-VT are all quite accurate comparing with reference values though the RMS errors of the HO model and UM-N are slightly higher than UM-VT. 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 UM-VT is 2.18 cal mol-1 K-1 at 1000 K. By contrast, the RMS error obtained using the HO model and UM-N are 6.42 and 5.73 cal mol-1 K-1, respectively. For a test set composed of nine alkanes ranging from C5 to C8, the heat capacities calculated with the UM-VT model agree with the experimental values to within a RMS error of 0.78 cal mol -1 K -1 , which is less than one-third of the RMS error of the HOhf (2.69 cal mol-1 K-1) and UM-N (2.41 cal mol-1 K-1) models.},
doi = {10.1021/acs.jctc.5b01177},
journal = {Journal of Chemical Theory and Computation},
number = 6,
volume = 12,
place = {United States},
year = {Thu May 26 00:00:00 EDT 2016},
month = {Thu May 26 00:00:00 EDT 2016}
}
Web of Science
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