Title: 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 (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 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 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 (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 HO^hf model and UM-N can capture no more than 50%. For a selected test set of C2 tomore » C8 linear and branched alkanes and species with different moieties, the enthalpies calculated using the HO^hf 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 HO^hf (2.69 cal mol^-1 K^-1) and UM-N (2.41 cal mol^-1 K^-1) models.« less

Authors:

Li, Yi-Pei ^[1]; Bell, Alexis T. ^[2]; Head-Gordon, Martin ^[3]

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+ Show Author Affiliations

1. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720-1462, United States
2. 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
3. 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:

Thu May 26 00:00:00 EDT 2016

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