利用分子動力學模型快速計算複雜系統的熵與自由能

賴品光

doi:10.6342/NTU.2013.01194

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利用分子動力學模型快速計算複雜系統的熵與自由能

Rapid Determination of entropy and free energy of complex fluids from Molecular Dynamic Simulation

賴品光 , Masters　　Advisor：林祥泰　　

英文 DOI： 10.6342/NTU.2013.01194

兩相熱力學模型；熵；混和物；分子內轉動；分子動態模擬； Two phase thermodynamic model ； entropy ； mixture ； internal rotation ； molecular dynamic simulation

Abstract │ Reference (55) │ Altmetrics

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The two-phase thermodynamic (2PT) model is a new method which utilizes the results from molecular dynamic simulation to determine thermodynamic properties rapidly and accurately, especially entropy and free energy. In this method, the vibrational density of states (DoS), obtained from the Fourier transform of the velocity autocorrelation function, treated as harmonic oscillator, is combining with quantum statistics to determine the entropy and free energy. As low frequency vibration is usually non-harmonic, the calculated DoS is decomposed into a solid-like and a gas-like component through the fluidicity parameter, allowing for treatments for the anharmonic effects in fluids. The 2PT method has been shown to provide reliable thermodynamic properties of pure substances over the whole phase diagram with only about 20ps MD trajectory. This research aims to generalize the 2PT method to mixture system and conformational flexible molecules. In this thesis, there are two aspects to be addressed. In the first part we show how the 2PT method can be used for mixtures with the same degree of accuracy and efficiency. We have examined the 2PT determined excess Gibbs free energies of Lennard-Jones (LJ) mixtures over a wide range of conditions (1 ≤ T* ≤ 3, 0.5 ≤ P* ≤ 2.5, 1 ≤ σBB/σAA ≤ 2, and 1≤ εBB/εAA ≤2), including the change of the off-diagonal LJ interactions. The 2PT determined values are in good agreement with those from Widom insertion or thermodynamic integration (TI). Our results suggest that the 2PT method can be a powerful method for understanding thermodynamic properties in more complicated multicomponent systems. In the second part, the two-phase thermodynamic (2PT) model is generalized to determine the thermodynamic properties of molecules with internal rotations. In general, the dihedral torsion changes from harmonic vibrations at low temperatures, to hindered rotation at intermediate temperatures, and to free internal rotor at high temperatures. We show that anharmonic effects and its temperature dependence of dihedral torsion can be quantified by separating the torsional density of states (DoS) into a solid-like (harmonic vibration) and a gas-like (free rotation) component. The thermodynamic properties, including the entropy and free energy, associated with torsional motions can then be obtained by applying suitable quantum statistics to the corresponding components of the DoS. We examined the calculation of internal rotation energy of ethane and methanol over a wide range of temperatures. We found that the 2PT method can provide converged internal rotation entropy from a short, about 20 ps, trajectory of molecular dynamic simulation. The 2PT determined entropy is found to fall between those based on the theoretical models by Pitzer and Gwinn and by Truhlar. Our results suggest that the 2PT method can be a powerful method for understanding thermodynamic driving forces for conformation changes of complicated molecular structures.

Reference ( 55 ) 〈TOP〉

1. Widom, B. Some Topics in the Theory of Fluids. The Journal of Chemical Physics 1963, 39 (11), 2808-2812.
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2. Bennett, C. H. Efficient estimation of free energy differences from Monte Carlo data. Journal of Computational Physics 1976, 22 (2), 245–268.
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3. Torrie, G. M.; Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. Journal of Computational Physics 1977, 23 (2), 187-199.
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4. Kofke, D. A. Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation. Molecular Physics 1993, 78 (6), 1331-1336.
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5. Schafer, H.; Daura, X.; Mark, A. E.; van Gunsteren, W. F. Entropy calculations on a reversibly folding peptide: Changes in solute free energy cannot explain folding behavior. Proteins: Structure, Function, and Bioinformatics 2001, 43 (1), 45-56.
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