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Statistical thermodynamics of bond torsional modes: Tests of separable, almost-separable, and improved Pitzer–Gwinn approximations
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10.1063/1.2219441
/content/aip/journal/jcp/125/8/10.1063/1.2219441
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/8/10.1063/1.2219441

Figures

Image of FIG. 1.
FIG. 1.

The potential energy along the effective torsional coordinate for as given by Eq. (1) (solid curve) and the segmented reference potential (dashed curve) are plotted as a function of . The eigenvalue spectrum of the potential of Eq. (1) is also displayed.

Image of FIG. 2.
FIG. 2.

The C scheme moment of inertia (in ) for calculated as a function of the torsional coordinate with all other coordinates frozen at their equilibrium values (dotted line) and with all other coordinates optimized (solid line).

Tables

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Table I.

Glossy of acronyms.

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Table II.

Moments of inertia (in ) calculated by five approximate schemes for various isotopomers of .

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Table III.

Comparison of eigenvalues of the 1D effective torsional potential obtained with three different estimates of the reduced moment of inertia for (in and relative to the ground state) with the results of Koput et al. with the full-dimensional potential.

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Table IV.

Harmonic frequencies, zero-point energies (ZPE), anharmonic ZPE corrections, and tunneling splittings (all in ) for various isotopomers of .

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Table V.

Partition functions for the 1D torsional potential of calculated using various methods.

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Table VI.

isotope ratios for partition functions of the 1D torsional potential using various methods.

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Table VII.

Percentage errors for 1D. [Mean unsigned percentage errors (MU%E) and maximum percentage errors (Max%E) averaged over nine temperatures in the rage of for all seven isotopomers for 1D torsional partition functions with moments of inertia obtained from the C scheme at the minimum configuration. The results, for a given amount of data, are sorted in order of increasing MU%E.]

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Table VIII.

Mean unsigned percentage errors (MU%E) (averaged over seven temperatures in the range of for all seven isotopomers) and maximum percentage errors (Max%E) full-dimensional molecular partition functions for the torsional mode treated by various methods with moments of inertia obtained from the C scheme at the minimum configuration, and the other modes treated at the quantum HO level. The results, for a given amount of data, are sorted in order of increasing sum of MU%E and Max%E.

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Table IX.

Mean unsigned percentage errors (MU%E) (averaged over seven temperatures in the range for all seven isotopmers) and maximum percentage errors (Max%E) for full-dimensional molecular partition functions for methods that require the whole multidimensional surface.

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Table X.

Comparison of mean unsigned percentage errors in 1D and full-D for best methods in each class (for this purpose, “best” is defined as smallest MU%E or smallest Max%E).

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/content/aip/journal/jcp/125/8/10.1063/1.2219441
2006-08-23
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Statistical thermodynamics of bond torsional modes: Tests of separable, almost-separable, and improved Pitzer–Gwinn approximations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/8/10.1063/1.2219441
10.1063/1.2219441
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