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Title: Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules

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 setmore » of C2 to 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:
 [1] ;  [2] ;  [3]
  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:
Grant/Contract Number:
AC02-05CH11231
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
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
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
OSTI Identifier:
1418289