臺灣博碩士論文加值系統

兩相熱力學模型是一種新穎的方法，能夠利用分子動態模擬的結果，快速且準確地算出純物質系統的熱力學性質，特別是熵及自由能。此方法主要將原子速度的自相關函數，經由傅立葉轉換得到原子振動的狀態密度。將系統振動視為簡諧運動，透過量子統計學即可獲得系統的熵和自由能。由於低頻率震動多為非簡諧，因而兩相熱力學模型將狀態密度分解成類固體以及類氣體部份，這樣的方式可以處理類氣體部份的非簡諧運動效應。對於純物質在所有不同的相態，兩相熱力學模型都能有效地提供熱力學資訊。本研究主要拓展兩相熱力學模型理論，使其能夠運用於混和物系統，以及結構柔軟性的分子。本論文包含兩個部分。第一部分，我們說明兩相熱力學模型在計算混和物系統的熱力學性質的理論與方法我們使用Lennard-Jones (LJ)混和物系統的過剩吉布斯自由能(excess Gibbs free energy)來做驗證，並選用了大範圍的狀態點(1 ≤ T* ≤ 3, 0.5 ≤ P* ≤ 2.5, 1 ≤ σBB/σAA ≤ 2, and 1≤ εBB/εAA ≤2)，以及探討改變非對角線上的LJ作用力參數的影響。其結果與Widom insertion 還有 thermodynamic integration (TI) 所得到的一致。我們的結果說明了兩相熱力學模型可以被使用於多成份系統當中。第二部分，我們建立兩相熱力學模型在計算具有分子內轉動的系統之理論與方法。一般來說，兩面角的轉矩在低溫時是簡諧振動、中溫時是受阻轉動、高溫時是自由旋轉。此依溫度改變的非簡諧效應可以透過將轉矩的狀態密度拆成類固體(簡諧運動)以及類氣體(自由旋轉)部份來處理。而轉矩的熵和自由能可以依據上面所得到的部分各自計算再相加而得。此研究選用了乙烯以及甲醇來探討，並涵蓋了大範圍的溫度條件。結果顯示，於20ps之內，兩相熱力學模型依然可以得到收斂的熱力學性質，並且其值落於Pitzer and Gwinn 和Truhlar 所提出的方法之間，此證明了兩相熱力學模型也可以用來計算具構型變化的複雜分子之熱力學性質。

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.

誌謝i
摘要ii
Abstractiii
Table of Contentsv
Figuresvii
Tablesix
Chapter 1 Introduction1
Chapter 2 Method and Theory4
2.1 The Vibrational Density of States4
2.2 Thermodynamic Properties from Two-Phase Thermodynamic (2PT) Model……4
2.3 The Partial Molar Volume……………………………9
2.4 Density of States (DoS) for internal rotations12
2.5 Two phase thermodynamic model for hindered rotors14
2.6 Weighting functions of free rotor15
2.7 Reduced moment of inertia16
Chapter 3 Computational Details18
3.1 MD conditions for Lennard-Jones binary mixtures18
3.2 MD conditions for ethane and methanol20
Chapter 4 Thermodynamic Properties of Mixture Fluids from 2PT23
4.1 The density of state distribution23
4.2 Thermodynamic properties for mixtures from 2PT model…………………24
4.3 Energy-cross term effect of 2PT model………………………33
4.4 Fluidicity parameter and partial molar volume in binary mixtures……………33
4.5 Convergence of 2PT mixture properties34
Chapter 5 Thermodynamic Properties of Molecules with Internal Rotations from 2PT……38
5.1 The density of state of Cartesian and internal coordinates……………38
5.2 Vibrational entropies of methanol and ethane……40
5.3 Convergence of 2PT internal properties……………52
Chapter 6 Conclusions…………………………………………………………………………54
Appendix 1…………………………………………………………………………………………56
Appendix 2…………………………………………………………………………………………58
References…………………………………………………………………………………………59

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