臺灣博碩士論文加值系統

在此論文，運用分子動力學(MD)模擬液態水SPC/E模型，我嘗試將液態水的定向自相關函數(OCF)修正至第四階累積量。由瞬間正則模(INM)理論或角速度自相關函數(AVAF)所得到的功率頻譜，我們可以預估OCF在不同時間尺度下的行為，並且使用特定漸進函數估算OCF的時間尺度。此外，藉由Voronoi多面體(VP)分析，我們研究氫鍵所產生的局部結構對定向自相關函數的影響。
　在短時間尺度下，定向自相關函數是一高斯衰減，而在長時間尺度下定向自相關函數的行為應該是一個單一指數函數衰減。藉由AVAF所得到的功率頻譜，長時間尺度下的行為可以被修正至第二階累積量OCF預測。若將OCF修正至第四階累積量，INM理論所得到的功率頻譜可以很好的預測MD模擬的結果。

In this thesis, with the SPC/E model of liquid water, I extent the calculations for the orientational correlation function (OCF) up to the fourth cumulant expansion. By the instantaneous normal mode (INM) theory or the power spectra of the angular velocity autocorrelation function (AVAF), we predict the behavior of the OCFs in the short and long time regimes and estimate the time scales for different regimes by using the asymptotic functions of the cumulant expansion. Besides, by Voronoi polyhedra (VP) analysis for liquids generated with classical MD simulations, we study the local-structure effects on the OCFs of this water model.
In the short-time regime, the OCFs is a Gaussian decay, no matter what kind of rotational spectrum is used for calculation. In the long-time regime, the behavior of the OCFs predicted by the second cumulant expansion is a single exponential decay calculated with the AVAF spectrum and a logarithmic divergence calculated with the stable-INM spectrum. Up to the fourth cumulant expansion, the long-rime behavior of the OCFs calculated with the stable-INM spectrum agrees well with the results of MD simulation.

摘要……………………………………………………………………………………i
Abstract………………………………………………………………………………ii
誌謝………………………………………………………………………………..…iii
Contents…………………………………………………………………………...…iv
List of tables………………………………………………………………………….v
List of figures………………………………………………………………………..vi

Chapter 1 Introduction……………………………………………………………1
Chapter 2 Orientational correlation function……………………………………4
2.1 Orientational Motion……………………………………………………………4
2.2 Orientational Correlation Function………………………………..……………6
2.3 Cumulant approximation…………………………………………..……………8
2.4 Angular velocity autocorrelation function……………………….……………14
2.5 Instantaneous normal mode……………………………………..……………19
2.6 Asymptotic of the second cumulant……………………………..……………22
2.6.1 Case I: Ohmic spectral DOS………………………………..…….………24
2.6.1 Case II ……………………………..………………………………….…25
Chapter 3 Model, Simulation and Local Structure………………………………29
3.1 SPC/E model…………………………..……………………..………………29
3.2 MD simulation…………………………………………………………………29
3.3 Local structure: Voronoi group………………………………………………30
Chapter 4 Results and Discussions…………………….………………………..33
4.1 Rotational stable-INM spectrum………….………………………….……..33
4.2 Power spectrum of AVAF………………….…………………………………..34
4.4 Short-time behavior of the OCF…………….………………………………….35
4.4 Long-time behavior of the OCF…………….………………………………….36
4.4.1 Second cumulant prediction………….………………………………….36
4.4.2 Fourth cumulant………….……………………………………………….38
Chapter 5 Conclusions………………….….….………………………………… 41
Tables………………………………………………………………………………..44
Figures……………………………………………………………………………….47
Appendix A Asymptotic functions and Parameters………………………………75
Appendix B Discussion of I1423-contribution integration…………….…………77
References…………………………………………………………………………...80

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