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  • 學位論文

利用分子動力學模型快速決定系統的絕對熵值

Rapid Determination of Absolute Entropy from Molecular Dynamic Simulations

指導教授 : 林祥泰

摘要


兩相熱力學模型是一種利用分子動力學模擬所得之原子及系統的資訊,進而快速並準確地的決定系統的熱力學性質,尤其是絕對熵值及自由能方面。兩相熱力學模型假設系統內之原子皆在震動並且藉由原子的震動速度的自相關函數經由傅立葉轉換後可得原子震動的狀態密度。另外,若是將該原子震動形式考慮為簡諧震動,即可套用量子統計力學去計算出熵與自由能。由於低頻率的震動多為非簡諧震動,兩相熱力學模型因而將狀態密度拆解成類固體及類氣體部分,並將類固體部分考慮為簡諧震動,類氣體則為非簡諧震動。分別套用量子統計學及硬球模型於類固體及類氣體部分後,兩相熱力學模型即可搭配分子動態模擬計算出氣態及液態系統的熱力學性質。結果顯示,兩相熱力學模型在預測純物質系統及混合物系統的熱力學性質上皆有高的準確度。然而Desjarlais博士最近發現兩相熱力學模型總會高估液態金屬的熵值。另外,兩相熱力學模型在預測具有複雜構型的分子上尚有發展空間。於本次研究的第一部分中,我們參照Desjarlais博士在類氣體狀態密度上的修正模型,提出能簡單應於於電腦計算上的分離類氣體及類固體部分的方法。在利用此新方法 (於類氣體狀態密度的決定上使用高斯函數) 以及原來的方法 (於類氣體狀態密度的決定上使用狄拉克函數) 於Lennard-Jones流體、水以及一些常見的有機物質上發現,由新方法算出的熵值總是低於原方法。在Lennard-Jones流體的實測上,新方法能較原方法在液相及超臨界流體的熵值計算上高出1%的準確度,然而在其他相態上新方法卻沒有比原方法來的好。此外在水及有機物的熵值計算,兩種方法所得之結果相當接近,只有1%左右的偏差。 於第二部分中,我們探討關於分子內兩面角轉矩運動上所體現出的非簡諧震動。由於兩相熱力學模型在計算分子內震動的狀態密度是建構於直角坐標系統上,所以非簡諧震動的影響會被忽略。於本研究上,將分子內震動的狀態密度建構於內部坐標系上,並將其狀態密度拆解成類氣體及類固體部分,套用合適的統計力學模型即可計算出熱力學性質。於本論文中,我們藉由與Pitzer and Gwinn以及McClurg等人所提出之理論模型,在大範圍的溫度條件下,與兩相熱力學模型所得之分子內震動的能量以及熵值作比較發現,兩相熱力學模型相較於其他方法較能考慮更多的非簡諧震動所貢獻於熱力學性質的影響。

並列摘要


The two-phase thermodynamic (2PT) method is a method which extracts the atomic data (position and velocity) and systematic data (density and classical energy) from molecular dynamic (MD) simulation to determine thermodynamic properties rapidly and accurately, especially absolute entropy and free energy. In 2PT method, it assumes that atoms in a system are all in vibrational motion and the vibrational density of state (DOS) is determined by the Fourier transform of the velocity autocorrelation (VAC) function. With another assumption, considering the vibrational motion is harmonic, the quantum statistic can be applied to calculate the entropy and free energy. According to the fact that low frequency vibration is usually anharmonic, the DOS is decomposed to a gas-like (non-harmonic) and a solid-like (harmonic) component by a fluidicity parameter in 2PT method. The partition function applied to the gas-like component is hard sphere/rigid rotor statistics so that the 2PT method can be extended to gas and liquid system from a short (within 20 ps) MD simulation. The thermodynamics properties calculated by 2PT method always give high accuracy for pure fluids, as well as mixtures. Despite of its success, recently Desjarlais noted that 2PT method always overestimate the entropy of liquid metals. That is to say, predicting the thermodynamic properties of conformational complex molecules by 2PT method still has a development space. In the first part in this research, a further work following the suggestion proposed by Desjarlais in gas-like DOS, we propose a new approach to determine the fluidicity which can be easily implemented in a computer code. The application of this new approach to Lennard-Jones fluids, water and common organic fluids provides an information that the entropy determined from using the Gaussian memory function for the gas-like component (denoted as 2PT-GMF) is always lower than that determined from that using delta memory function (denoted as 2PT-δMF). In Lennard-Jones cases the 2PT-GMF method (with an absolute average relative error of 1 % compared to the results from MBWR EOS) is usually more accurate 2PT-δMF (AARD = 2 %) in the liquid and supercritical regions; whereas, in other phases, the 2PT-GMF method does not provide better approach than 2PT-δMF. Moreover, in water and common organic fluids cases, we find the results from 2PT-GMF method are similar to those from 2PT-δMF (within 1% relative difference). In the second part, considering the conformation of molecules, the anharmonic effects from torsions play an important role in vibrational mode. In 2PT method, the atomic velocity in Cartesian coordinates is used to construct the vibrational DOS so that the anharmonic effects may be ignored. In this work, we will develop the 2PT method taking torsions into account. After constructing the DOS based on internal coordinates, the 2PT method decomposes the DOS into a gas-like (free rotation) and a solid-like (harmonic vibration) component. The thermodynamic properties associated with each component of DOS can be obtained by a suitable quantum statistics. In this part of thesis, we examine the vibrational energy and entropy of ethane over a wide range of temperatures (200 K to 1000 K) and compare our results to the theoretical model proposed by Pitzer and Gwinn and the revised form proposed by McClurg et al. We find that the 2PT method gives higher value of energy and entropy at high temperature region, which means the 2PT model can include more anharmonic effects.

參考文獻


[32] H.J.C. Berendsen, D. van der Spoel, R. van Drunen, Computer Physics Communications 91 (1995) 43.
[40] W.L. Jorgensen, J. Tirado-Rives, Journal of the American Chemical Society 110 (1988) 1657.
[36] T. Darden, D. York, L. Pedersen, The Journal of Chemical Physics 98 (1993) 10089.
[42] J.K. Johnson, J.A. Zollweg, K.E. Gubbins, Mol Phys 78 (1993) 591.
[4] P.K. Lai, C.M. Hsieh, S.T. Lin, Phys Chem Chem Phys 14 (2012) 15206.

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