Molecular dynamics configuration entropy

One of the most convincing tests of the AG relationship appeared in the work of Scala et al.92 for the SPC/E model of water,57 which is known to reproduce many of water s distinctive properties in its super-cooled liquid state qualitatively. In this study, the dynamical quantity used to correlate with the configurational entropy was the self-diffusivity D. Scala et al. computed D via molecular dynamics simulations. The authors calculated the various contributions to the liquid entropy using the methods described above for a wide range of temperature and density [shown in Figure 12(a-c)]. 

Liquids. V. On the Link between Molecular Dynamics and Configurational Entropy. 

Free volume Configurational entropy Coupling model Conventional thermodynamics Statistical thermodynamics Molecular dynamics Fox et al. (1955) Di Marzio (1964) Ngai et al. (1986)... 

This method avoids the convergence and accuracy problems of molecular dynamics or Monte Carlo simulations of systems containing explicit solvent molecules, by evaluating the electrostatic free energy of just one solute conformation surrounded by a dielectric continuum, and by adding the surface term and an estimate of the loss of the configurational entropy upon binding.77... 

Exact determination of entropy effects in enzymatic reactions is not an easy task even nowadays when sophisticated Monte Carlo and molecular dynamics methods are available for calculations (Warshel, 1991 Aqvist and Warshel, 1993). One way to examine the importance of entropy is to analyse the configuration space available to the system in its ground and transition states, both in the enzyme and in solution. The entropic contribution to the catalytic effect, relative to the uncatalysed solution can be expressed as... 

Fig. 12. Adam-Gibbs plots of the dielectric relaxation time of 2-methyltetrahydrofuran (2-MTHF) and 3-bromopentane (3-BP) versus (Tsconi) . The lines are VTF fits, 7 fus is the fusion temperature, and Tb is the temperature below which the VTF equation applies. /I ag and Avf are prefactors in the Adam-Gibbs and VTF equations, respectively. Tk is the calorimetri-cally determined Kauzmann temperature, and To is the VTF singular temperature, which were set equal in the VTF (line) fits. (Reprinted with permission from R. Richer and C. A. Angell. Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy. J. Chem. Phys. (1998) 108 9016. Copyright 1998, American Institute of Physics.)...

Richert, R., and Angell, C. A., Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy. J. Chem. Phys. 108, 9016 (1998). 

Molecular dynamics, like MC, is a dynamical procedure, but of a deterministic rather than stochastic nature. One starts from an arbitrary configuration and an initial set of particle velocities, and Newton s equations of motion of the system are integrated numerically as a function of time this time (unlike the MC time) corresponds to the real time. For fluids, MC and MD have comparable efficiency. For dense materials like proteins, MD is the more efficient because the random MC trial moves are rejected with high probability unless the moves are very small. The difficulty in obtaining the entropy with MC (discussed above) applies also to MD. 

J. Brady and M. Karplus, J. Am. Chem. Soc., 107, 6103 (1985). Configuration Entropy of the Alanine Dipeptide in Vacuum and in Solution A Molecular Dynamics Study. 

R. M. Levy, M. Karplus, J. Kushick, and D. Perahia, Macromolecules, 17, 1370 (1984). Evaluation of Configurational Entropy for Proteins Application to Molecular Dynamics Simulations of ct-Helix. 

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