The Rotational Entropy of Nonrigid Polyatomic Molecules

Eidinoff, Maxwell L.; Aston, J. G.

doi:10.1063/1.1749684

Cited by 57 publications

(28 citation statements)

References 4 publications

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“…where the i ϭ 0 term of the Fourier expansion is absorbed in the normalization constant C. Let (1) , (2) , . .…”

Section: The Methodsmentioning

confidence: 99%

“…For this reason, internal rotations usually contribute a major part to the overall entropy of internal molecular motion. Although the pioneering work on the methods of evaluation of entropy of internal rotation was done already in the 1930s and 1940s, [1][2][3] the subject at present is still very much alive; 4 -9 significant efforts have been also devoted to the methods of evaluation of total conformational entropy of macromolecules.…”

Section: Introductionmentioning

confidence: 99%

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Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

et al. 2003

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A method of statistical estimation is applied to the problem of one-dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical-mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the "marginal" statistical-mechanical properties corresponding to a given internal rotational degree of freedom are reduced. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal-rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.

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“…where the i ϭ 0 term of the Fourier expansion is absorbed in the normalization constant C. Let (1) , (2) , . .…”

Section: The Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

et al. 2003

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“…The rotating subgroups of atoms can then be determined and the reduced moments of inertia for internal rotation can be computed, with or without approximations. [7][8][9][10][15][16][17][18][19][20][21] Making this rotor identification procedure automatic for a general molecule can be complicated and can involve many special cases, since it would require first the identification of rings and multiple bonds. Most of the problem, however, resides in the identification of the internal rotation modes.…”

Section: ͑1͒ ͑2͒mentioning

confidence: 99%

“…The treatment of a vibrational mode as an internal rotation has been studied by many authors over the years and most of the mathematical details have long been documented. [15][16][17][18][19][20][21] The primary task is to find which subgroups of the molecule are rotating so that one can define the kinetic energy matrix of the rotating system. Then, one needs to identify which of the vibrational modes are internal rotations.…”

Section: Identification Of Rotational Modesmentioning

confidence: 99%

Identification and treatment of internal rotation in normal mode vibrational analysis

Ayala¹,

Schlegel²

1998

The Journal of Chemical Physics

461

548

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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 Ϯ0.4% 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.

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“…However, the quantum number i varies here within the limits (-to, m). The conventional formula for the partition function qo of free internal rotation [20,21], was widely applied to calculations of thermodynamic functions, but it is being more and more neglected that it has approximative character; and, moreover, the intervals of I, and T values in which the qo approximation can reliably be applied were ignored. Consequently, there exist in literature several cases in which the formula (10) was applied to such situations where it led to negative values of the contribution of free internal rotation to the overall entropy, this fact not being noted by the authors.…”

Section: Free Internal Rotationmentioning

confidence: 99%

Limiting behavior of partition functions of models with quadratically dependent energy spectra and consequences regarding theoretical study of chemical reactivity

Zdeně

Slanina²

1985

Int J of Quantum Chemistry

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The conventional partition functions of models with quadratically dependent energy spectra ( e . g . , translation in a box or free internal rotation), which are widely used in literature, exhibit an incorrect limit behavior in the region of low temperatures and/or small values of the characterizing molecular parameter. In particular, this leads to the absurd value -2 for the contribution of these motions to the entropy term at these limit conditions. This incorrect behavior appears to be due to the replacement of rigorous summation by integration in conventional derivation of these partition functions. The derived improved practical formulas with the correct limit behavior indicate that it will be necessary to carry out quite substantial nunierical corrections in the case of many reactivity characteristics reported in the literature. Particularly, the improved formulas should be applied with (small) molecular complexes at the typical temperatures of their observation, e.g., van der Waals molecules with free internal rotation. Simultaneously discussed is the possibility of application of the functional relation valid for a rigorous partition function of the considered type of energy spectrum. The reasoning in the case of the translational partition function indicates that, in principle, it can depend on the vessel shape. Possible consequences for thermodynamics of the ideal gas are analyzed.

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The Rotational Entropy of Nonrigid Polyatomic Molecules

Cited by 57 publications

References 4 publications

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

Identification and treatment of internal rotation in normal mode vibrational analysis

Limiting behavior of partition functions of models with quadratically dependent energy spectra and consequences regarding theoretical study of chemical reactivity

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