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Vibrational partition function

About: Vibrational partition function is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 24756 citations.


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TL;DR: It is concluded that using partition functions computed for molecules optimized in solution is a correct and useful approach for averaging over solute degrees of freedom when computing free energies of solutes in solution, and it is moreover recommended for cases where liquid and gas-phase solute structures differ appreciably or when stationary points present in liquid solution do not exist in the gas phase.
Abstract: We find that vibrational contributions to a solute’s free energy are in general insensitive to whether the solute vibrational frequencies are computed in the gas phase or in solution. In most cases, the difference is smaller than the intrinsic error in solvation free energies associated with the continuum approximation to solvation modeling, although care must be taken to avoid spurious results associated with limitations in the quantum-mechanical harmonic-oscillator approximation for very low-frequency molecular vibrations. We compute solute vibrational partition functions in aqueous and carbon tetrachloride solution and compare them to gas-phase molecular partition functions computed with the same level of theory and the same quasiharmonic approximation for the diverse and extensive set of molecules and ions included in the training set of the SMD continuum solvation model, and we find mean unsigned differences in vibrational contributions to the solute free energy of only about 0.2 kcal/mol. On the bas...

767 citations

Journal ArticleDOI
TL;DR: In this paper, a procedure that automatically identifies internal rotation modes and rotating groups during the normal mode vibrational analysis is outlined, and an improved approximation to the corrections for the thermodynamic functions is proposed.
Abstract: A procedure that automatically identifies internal rotation modes and rotating groups during the normal mode vibrational analysis is outlined, and an improved approximation to the corrections for the thermodynamic functions is proposed. The identification and the characterization of the internal rotation modes require no user intervention and make extensive use of the information imbedded in the redundant internal coordinates. Rigid-rotor internal rotation modes are obtained by fixing stretching, bending, and out-of-plane bending motions and solving the vibrational problem for the constrained system. Normal vibrational modes corresponding to internal rotations are identified by comparing them with the constrained modes. The atomic composition of the rotating groups is determined automatically and the kinetic energy matrix for internal rotation is given by either the constrained Wilson-G matrix or the Kilpatrick and Pitzer protocol. The potential periodicity, the rotating tops’ symmetry numbers, and the well-multiplicity are obtained using simple rules. These parameters can be altered by user input. An improved analytical approximation to the partition function for a one-dimensional hindered internal rotation has been developed that reproduces the accurate values tabulated by Pitzer and Gwinn to ±0.4% with a maximum error of 2.1%. This approximation is shown to behave better than previously available approximations over a wider range of regimes. The one-dimensional rotor treatment is generalized to give useful approximations to the multidimensional rotor thermodynamic functions that can be a good start for more thorough studies.

418 citations

Journal ArticleDOI
TL;DR: A method by which a quantum-mechanical partition function can be approximated from below by an effective classical partition function and the associated potential is obtained by a simple smearing procedure.
Abstract: We present a method by which a quantum-mechanical partition function can be approximated from below by an effective classical partition function. The associated potential is obtained by a simple smearing procedure. For a strongly anharmonic oscillator and a double-well potential, the lowest approximation gives a free energy which is accurate to a few percent, even at zero temperature.

370 citations

Journal ArticleDOI
TL;DR: In this article, a simple formula for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule is presented, which gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.
Abstract: A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.

338 citations

Journal ArticleDOI
TL;DR: In this paper, a simple application of Kubo's line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions in vibrational modes where vibrational dephasing processes are predominant in determining the shape of condensed phase band contour.
Abstract: A simple application of Kubo’s line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions. In vibrational modes where vibrational dephasing processes are predominant in determining the shape of the condensed phase band contour, the formalism shows that the vibrational correlation obeys a fast modulation mechanism (’’motional narrowing’’), e.g., in quinoline, tetravinyl tin, and isopropyl alcohol. However, even smaller molecules such as chloroform and methyl iodide show similar characteristics and only in exceptional cases (the uncoupled O–D stretch of D2O in H2O) is the modulation slow. This behavior is a consequence of the short modulation times (order of fractions of a picosecond) in the liquid which determine the phase loss of the vibrational amplitude after a brief period of a quasistatic distribution of molecular environments (’’rigid lattice’’) —times which can be approximately identified with the inverse average collision frequency. In order to compare theory and experiment quantitatively, the model requires that the vibrational second spectral moment must be measured in addition to the vibrational correlation function. Comparisons with vibrational memory functions, obtained from the correlation functions via the modified Langevin equation, corroborate the usefulness of the model.

287 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20233
202211
202110
202012
20195
20188