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研究生:張郁
研究生(外文):YU CHANG
論文名稱:非馬可夫性的測量及使用CMRT 模擬能量傳遞的動力學表現
論文名稱(外文):Non-Markovianity Measurement and Coherent Modified RedfieldTheory in Simulating Dynamics of Excitation Energy Transfer
指導教授:鄭原忠
指導教授(外文):Yuan-Chung Cheng
口試委員:金必耀陳益佳
口試委員(外文):Bih-Yaw JinI-Chia Chen
口試日期:2015-06-16
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:化學研究所
學門:自然科學學門
學類:化學學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:111
中文關鍵詞:非馬可夫性能量傳遞動力學
外文關鍵詞:Non-MarkovianityCoherent Modified Redfield TheoryExcitation Energy Transfer
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激發態能量傳遞廣泛存在於自然及人造體系中。能量透過激發態間弱耦合的傳遞是一種Förster 共振能量傳遞;而能量傳遞受控於系統鬆弛的過程則是一種Redfield 的形式,處理系統與環境間的耦合為此理論中的關鍵。因此,一個能成功描述能量傳遞的理論必須考慮系統中不同耦合值間的平衡關係。

在這篇論文中,我們首先檢驗了馬可夫假設的適用性。在大多數初始條件下,Markovian Redfield equation 無法遵守約化密度矩陣中的population 恆正,尤其在強的電子聲子耦合和高溫下。其揭示了初始動力學的重要,因而需要建立一個測量系統非馬可夫性的指標。除此之外,藉由適當地切割哈密頓算符,CMRT 不僅可得到更小的微擾量,同時還可考慮多次的聲子鬆弛過程,提高CMRT 的適用範圍。Secular approximation 則可保留系統主要的耗散過程,減少計算的繁瑣,同時模擬具相干性的動力學表現。而在與QUAPI 的比較中,CMRT 由於高估了相干性效應,導致其可能忽略dynamical localization 的現象。

最後,我們以CMRT 模擬高分子中的能量傳遞,解釋了傳統Förster無法解釋的動力學表現。我們模擬了與實驗相符的光譜,利用得到的參數計算高分子中的能量傳遞,動力學的結果顯示多種狀態存在於分子中,由於寬廣的能階的分布造成部份系統擁有較大的相干性,繼而提高部份系統能量傳遞的速率。總而言之,我們在此篇中估算了馬可夫假設的適用性,並且使用CMRT 模擬分子中能量傳遞的動力學表現。


Excitation energy transfer (EET) is a crucial process in many natural and artificial light-harvesting systems. Such process may occur when the energies of two weakly coupled electronic excitations are matched, which is widely recognized as a Förster resonance energy transfer. However, EET can also occur through a relaxation process especially for the cases, where the interaction between the interested system and its external environment is weak. This process is called a Redfield energy transfer. A successful theoretical method to simulate EET dynamics strongly depends on how to solve the balance between the two limits.

In this study, we first investigate the shortcoming of the Markovian Redfield theory, which is widely used in simulating energy relaxation in molecular systems. We show that for general initial conditions, Markovian Redfield theory almost always yields dynamics that violates the positivity requirement for density matrices particularly on strong electron-phonon coupling and high temperature, making the theory inadequate for simulating EET in molecular systems. It is evident that the non-Markovian effects cannot be ignored in most situations. We then adopt the positivity violation to establish a non-Markovianity measure to quantify non-Markovian effects. To remedy the Redfield approach, a coherent modified Redfield theory was recently developed. Compared to traditional Förster and Redfield theory, the CMRT has a wider range of applicability resulting from the smaller perturbation and inclusion of multiphonon relaxation. In addition, by using a secular approximation to retain the major pathways in dissipation process, the secular CMRT can not only reduce the computational cost, but also capture the important coherent dynamics. In this work, the accuracy of CMRT is comprehensively investigated in the comparisons with numerically exact path-integral method. The results reveal an important role of “dynamical localization” when the coherence effect is overestimated.

Finally, we apply the CMRT to study non-Förster EET dynamics in a silylene-spaced copolymer system. We reproduce the absorption and fluorescence spectra of the systems and derive parameters from spectral fitting. The parameters are subsequently used to calculate the EET dynamics, which allows us to describe both Förster and non-Förster dynamics in the system. We also investigated the effects of static energetic disorder on EET dynamics, which shows several dynamical groups with different EET rates. The energetic disorder causes a distribution of delocalization lengths, where the longer delocalization lengths characterized by strongly coherent systems is accounted for the fast dynamics. In summary, we examine the applicability of Markovian Redfield theory and simulate the EET dynamics with newly developed CMRT.


Contents
口試委員會審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Condensed Phase Quantum Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Reduced Density Matrix Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Markovian Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Applicability of Markovian Approximation . . . . . . . . . . . . . . . . . . . . . . 14
3.1 Positivity Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Electron-Phonon Coupling Strength . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Energy Gap Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Temperature Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Non-Markovianity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Excitation Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1 Frenkel-Exciton Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Förster Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Redfield Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Modified Redfield Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5 Coherent Modified Redfield Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Accuracy of Coherent Modified Redfield Theory . . . . . . . . . . . . . . . . . . 56
5.1 Comparisons with the Quasi Adiabatic Path Integral Method . . . . . . . . 56
5.2 Accuracy Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Comparisons with the Small Polaron Quantum Master Equation . . . . . 66
6 Application of the Coherent Modified Redfield Theory to Silylene-Spaced Copolymer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1 Silylene-Spaced Copolymer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Spectral Fitting of Monomer D, Monomer A and D3 . . . . . . . . . . . . . . 72
6.3 Simulation of Energy Transfer Dynamics in D3 System . . . . . . . . . . . 80
A Full Set of Comparisons between CMRT and QUAPI . . . . . . . . . . . . . . 89
B Electronic Coupling Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102


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