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Estimation of the absolute internal‐rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations
Author(s) -
Darian Eva,
Hnizdo Vladimir,
Fedorowicz Adam,
Singh Harshinder,
Demchuk Eugene
Publication year - 2005
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20198
Subject(s) - moment of inertia , degrees of freedom (physics and chemistry) , chemistry , molecule , dihedral angle , kinetic energy , monte carlo method , entropy (arrow of time) , torsion (gastropod) , computational chemistry , statistical physics , classical mechanics , physics , molecular physics , thermodynamics , mathematics , quantum mechanics , hydrogen bond , medicine , statistics , surgery
A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two‐dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic‐simulation sample of the atomic configurations of the molecule. The torsional‐angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal‐rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis ‐stilbene are found to be much more strongly correlated than those in trans ‐stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 651–660, 2005