On the Use of the Quasi-Gaussian Entropy Theory in Systems of Polyatomic Flexible Molecules Andrea Amadei,* ,² Barbara Iacono, ‡ Simone Grego, ‡ Giovanni Chillemi, § M. E. F. Apol, ‡ Enrico Paci, ‡ Maurizio Delfini, ‡ and Alfredo Di Nola ‡,| Department of Chemical Sciences and Technology, UniVersity of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy, Department of Chemistry, UniVersity of Rome “La Sapienza”, Rome, Italy, and Inter-UniVersity Computing Consortium (CASPUR), UniVersity of Rome, “La Sapienza” Rome, Italy ReceiVed: August 2, 2000; In Final Form: December 4, 2000 In this article we show how the quasi-Gaussian entropy (QGE) theory can be used to treat systems of polyatomic flexible molecules, where the usual semirigid description is not always appropriate. We describe a completely general derivation of the QGE theory which does not make use of any semirigid approximation, and therefore it is very suited for large and flexible molecules. Using molecular dynamics simulations of flexible molecules in vacuo, we investigated the ability of the theory to describe intramolecular energy fluctuations and conformational equilibria of purely classical molecules in the ideal gas condition. Results show that the gamma state level of the theory and its generalization for treating conformational equilibria (multi-gamma state model) provide excellent theoretical models when applied to three polyatomic molecules of increasing conformational freedom. 1. Introduction Fluids involving polyatomic flexible molecules are often of great scientific and technological interest but usually exhibit very complex thermodynamics. In fact, the statistical mechanics of such systems is dictated by the intramolecular energy fluctuations and their coupling with the intermolecular interac- tions. In recent papers 1-4 we introduced a new statistical mechanical theory, the quasi-Gaussian entropy (QGE) theory, which is basically an extension of fluctuation theory. 5 We showed 6-10 that with this theory the fluid state thermodynamics can be reproduced with high accuracy for a large variety of typical fluids (not consisting of polyatomic flexible molecules) over a very large temperature-density range. In the QGE theory the fundamental expressions of statistical mechanics are refor- mulated in terms of the distribution function of the fluctuations of a macroscopic property and, by modeling such a distribution, a complete solution for the statistical mechanical behavior of the system can be obtained. With the use of a few physical- mathematical principles we can restrict the set of possible distributions to a subgroup of “quasi-Gaussian” distributions of increasing complexity. In the previous articles the QGE theory was derived and utilized in the three main statistical mechanical ensembles focusing on typical fluids, without specifically addressing the case of systems involving polyatomic flexible molecules. Such systems, where large conformational fluctua- tions can occur, require special care in the derivation of the theory based on the excess (ideal reduced) energy fluctuations, and present specific aspects to be investigated. Among them one of the most interesting is the calculation of conformational equilibria of a molecule in the gas phase and in solution which is in general still quite unfeasible, mainly because of the difficulty in estimating the free energies involved. Computer simulation techniques, such as molecular mechanics (MM), 11-17 molecular dynamics (MD), 18-23 and Monte Carlo (MC), 24 have been used extensively to calculate conformational equilibria, and specialized sampling techniques, such as umbrella sampling, thermodynamic perturbation (TP), and thermodynamic integra- tion (TI), coupled to MD or MC have been used both in gas and liquid phases to evaluate the Helmholtz free energy differences due to configurational changes. For small mole- cules, the internal energy evaluation is straightforward in the gas phase and still possible in solution using nonquantum mechanical approaches. More difficulties can arise in the calculation of the entropic contribution to the free energy, due to poor convergence of the calculations. 18 In addition, the prediction of the temperature dependence of conformational equilibria is still done on empirical basis, e.g. by perturbation expansions in temperature. In this paper we use a more general derivation of the QGE theory concerning the excess energy fluctuations, which is appropriate also for systems of polyatomic flexible molecules, we introduce a generalization of the gamma state model (the multi-gamma state model) to treat conformational equilibria, and we specifically investigate the properties of three flexible polyatomic molecules (amiridin, cyclohexane, and the alanine dipeptide) in the ideal gas condition using pure classical Hamiltonians to treat the intramolecular potential energy, and molecular dynamics simulations to obtain “experimental” data. 2. Theory The most general expression of the canonical partition function for a system of N molecules, with a purely classical * To whom correspondence should be addressed. E-mail: andrea. amadei@uniroma2.it. ² Department of Chemical Sciences and Technology. ‡ Department of Chemistry. § Inter-University Computing Consortium. | E-mail: dinola@degas.chem.uniroma1.it 1834 J. Phys. Chem. B 2001, 105, 1834-1844 10.1021/jp002805z CCC: $20.00 © 2001 American Chemical Society Published on Web 02/13/2001