臺灣博碩士論文加值系統

在此論文中，我使用SPC/E模型並應用分子動力學(MD simulation)模擬液態水分子氫氧鍵結的定向相干函數(OCF)。由模擬所得到的定向相干函數可以運用不同的擬合函數來描述水分子在不同時間尺度下的轉動。我們也使用Voronoi多面體(VP)與水分子氫鍵分佈分析來研究局部區域結構對水分子轉動的影響。
在短時間尺度下( t < 0.2 ps )，定向相干函數是一個高斯函數，此高斯函數可以用瞬間正則模(INM)理論或角速度自相干函數(AVAF)的頻譜來驗證。在長時間尺度下( t > 2 ps)，定向相干函數如Debye理論所預期是指數函數衰減。在中間時間尺度(0.2 ps < t < 2 ps )，扣除掉在長時間尺度下的指數函數衰減，所剩餘的OCFs可以由一擬合函數完全描述，而此一擬合函數是由一個幕次函數乘上一個高斯函數。在中間時間尺度下，VP分析中特別的局部區域結構，水分子氫氧鍵結的OCF仍然可以發現到有震盪的現象。

In this thesis, I apply molecular dynamics (MD) simulate with the SPC/E model to study the orientational correlation function of the OH-bond of water molecule in liquid phase. The simulated OCFs in different time scales are described by various fitting functions. We also use the Voronoi polyhedral (VP) analysis and H-bond configuration analysis to study the influences of the H-bonds attaching to a water molecule on the relaxation of the OCF.
In the short-time regime (t < 0.2 ps), the OCF is described by a Gaussian decay, which can be verified by the instantaneous-normal-mode(INM) theory or the power spectra of the angular velocity autocorrelation functions(AVAFs). In the long-time regime (t > 2 ps), the OCF of the OH bond decays exponentially as the prediction by the Debye theory and the dynamics of the OH bond can be described as a diffusion behavior on a spherical surface. In the intermediate regime (0.2 ps < t < 2 ps), by subtracting out the exponential decay in the long-time regime, the residual OCFs can be well fit by a surmised function, which is a multiplication of a power-law function and a Gaussian function. For molecules with some special local structures in the VP analysis, the OCF of the OH bond still oscillates in the intermediate regime.

Chapter 1 Introduction…………………………………………………...1
Chapter 2 Orientational correlation function…………………………..3
2.1 Orientational motion of a OH-bond of a rigid water molecule……………3
2.2 Orientational correlation function(OCF) of liquid water………………….7
2.3 Short-time behavior of and ……………………………….7
2.3.1 Orientational motion of a rigid water molecule………………….8
2.3.1.1 Angular Velocity Autocorrelation function (AVAF)……….9
2.3.1.2 Power spectrum and effective spectrum………………….11
2.3.1.3 Short-time approximation of and ………..12
2.3.2 Instantaneous normal mode (INM) theorem……………………13
2.3.2.1 The contributions of INM DOS associated
with the OH and axes………………………………16
2.4 Long-time behaviors of and …………………………19
Chapter 3 Model, MD Simulation and Local Structures………………..22
3.1 SPC/E model………………………………………………………………..22
3.2 MD simulations…………………………………………………………….22
3.3 Local structures…………………………………………………………….23
3.3.1 Voronoi polyhedral analysis…………………………………….23
3.3.2 Analysis by H-bond configurations……………………………..27
Chapter 4 Results and Discussions……………………………………….29
4.1 Instantaneous normal mode of density of state (DOS)…………………….29
4.2 Angular velocity autocorrelation function (AVAF) and Power spectrum…30
4.3 Short-time behavior of and ……………………………….33
4.4 Long-time behavior of and ……………………………….34
4.5 Intermediate-time behavior of and ………………….37
Chapter 5 Conclusions……………………………………………………41

[1] S. Woutersen, U. Emmerichs, and H. J. Bakker, Science, 278, 658 (1997)
[2] Rebecca A. Nicodemus, S. A. Corcelli, J. L. Skinner, and Andrei Tokmakoff, J. Chem. Phys. 115, 5604 (2011)
[3] Yu-ling Yeh and Chung-Yuan Mou, J. Phys. Chem. B, 103, 3699 (1999)
[4] S. L. Chang, Ten-Ming Wu, and Chung-Yuan Mou, J. Chem. Phys. 121, 8 (2004)
[5] Wei-Ren You, Orientational correlation function of liquid water : SPC/E model, NCTU, thesis (2011).
[6] Herbert Goldstein, Charles Poole and John Safko, Classical mechanics, third edition, Addison Wesley (2002)
[7] Michael Buchner, Branka M. Ladanyi, and Richard M. Stratt, J. Chem. Phys. 97, 8522 (1992)
[8] Minhaeng Cho, Graham R. Fleming, Shinji Saito and lwao Ohmine, and Richard M. Stratt, J. Chem. Phys. 100, 6672 (1994)
[9] A. Carrington and A. D. McLachlan, Introduction to magnetic resonance, Joanna Cotler Books (1976)
[10] H. J. C. Berendsen, J. R. Griera, and T. P. Straatsma, J. Phys. Chem. 91, 6269(1987)
[11] M. P . Allen and D. J. Tildesley, Computer Simulation of Liquids, first edition, Oxford Univerisity Press (1987)
[12] G. Ruocca, M. Sampoli, and R. Vallauri, J. Chem. Phys. 96, 6167 (1992)
[13] Damien Laage and James T. Hynes. Science, 311, 832 (2006) ;
Damien Laage and James T. hynes. J. Phys. Chem. B. 112, 14230 (2008)
[14] Hu Cang, V. N. Novikov, and M. D. Fayer. Phys. Rev. Lett. 90, 197401 (2003)
[15] J. P. Hansen and I. R. McDonald, Theory of simple liquid, second edition, ACADEMIC PRESS (1990).