線性半古典初始值表示法之適用範圍及其應用於吸收光譜之計算和電子轉移理論的探討

在這份論文中,我們利用線性半古典初始值表示法來研究一些凝態中的動態過程及吸收光譜。首先,我們運用這個方法來處理一個弗蘭克爾激子模型,藉著跟數值上精確的準絕熱路徑積分法比較,我們從系統在某個態隨著時間變化的期望值可以了解這個方法的適用範圍。我們的計算結果指出這個方法在所有考慮的參數範圍都給予了正確的振盪頻率但錯誤的平衡位置,此外,我們觀察到當系統的激子態能階差大於環境普密度的截止頻率時,去相干速率可以被精確的描述。這個方法所有的偏差都可以它採用了半古典假設去解釋。我們更進一步的針對平衡位置的偏差提出修正的方法,並且在大部份的參數範圍都得到了非常準確的結果。在第二部分,我們延伸了這個方法到吸收光譜的計算。我們證實了它在單體以及二聚體系統給予了精確的結果。另外,我們更針對了現實生活的複雜系統計算出合理的結果。最後一部份,我們利用這個方法來處理一個朗之萬耗散的系統,藉此我們觀察到馬庫斯定律的適用範圍在時域上確實有個上界以及下界,我們更系統化的去分析對於不同電子予體態以及電子受體態的能階差,這個範圍的變化,此外我們還找出了對於所有能接差都通用的範圍。

關鍵字

線性半古典初始值表示法；吸收光譜；電子轉移理論

並列摘要

In this thesis, we perform theoretical investigations on dynamical processes in condensed phases and spectra by utilizing the linearized semiclassical initial value representation (LSC-IVR) in the Meyer-Miller representation. First, we apply this method to the Frenkel exciton model, determining its applicable regime by comparing the population dynamics with numerically exact quasi adiabatic path integral results. Our calculations suggest that this method gives correct oscillating frequencies but incorrect equilibrium populations. Besides, the decoherence rate are well described as long as the excitonic energy gap is larger compared with the cut-off frequency. We conclude that all the deviations from exact results can be elucidated from the classical approximation in the LSC-IVR method. Moreover, we provide a long time correction, successfully modifying the equilibrium position. Second, we dis- cuss the validity of the LSC-IVR method in simulating the absorption spectra. We demonstrate that it gives excellent results in both monomer and dimer systems. By utilizing the property of less computational expense in this approach, we also successfully reproduce the reasonable absorption lineshape for real complex system. Finally, we consider a dissipative Hamiltonian with a random force and friction yielding a form of Langevin dynamics, where the propagation is based on the LSC-IVR approach, to study the emergence of the Marcus theory. Our results show that there exists an lower and upper bounds in time domain for obtaining Marcus rates. We further find out an universal regime which is suitable for different driving forces.

並列關鍵字

LSC-IVR ； absorption spectra ； Marcus theory

參考文獻

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[4] J. L. Klepeis, K. Lindorff-Larsen, R. O. Dror, and D. E. Shaw, “Long-timescale molecular dynamics simulations of protein structure and function,” Curr. Opin. Struct. Biol, vol. 19, p. 120, 2009.

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線性半古典初始值表示法之適用範圍及其應用於吸收光譜之計算和電子轉移理論的探討

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