熱庫時間自相關函數的量子修正—於激發能轉移動力學上的應用

Abstract

以含有古典力學之分子動力學結果計算量子動力學時,量子修正實 為必要。量子修正過去已廣泛應用在紅外線等光譜計算上,但應用於 激發能轉移動力學上的研究則較少。本研究之目的在於測試並比較前 人提出的標準法與簡諧法、我們提出的擬合法與 Prony 法等量子修正 方法在激發能轉移應用上的效果。希望能對量子修正在激發能轉移上 的應用提出有用之建議。為此,本論文利用線性地耦合了簡諧熱庫的 雙階系統以釐清量子修正在不同參數條件的表現。我們的計算結果說 明了以分子動力學研究激發能轉移時使用量子修正的必要性;並發現 在前述模型中,簡諧法表現最佳,擬合法與標準法表現接近、並都在 高溫時表現較佳、或在由相干性主導弛豫時表現較佳,且 Prony 法有 嚴重缺陷。

Quantum correction is necessary when calculating dissipative quantum dynamics based on results from classical molecular dynamics simulation in which quantum effects are ignored. Quantum correction has been used in many fields to make use of classical trajectories in quantum simulations, such as calculation of infrared spectra. However, in the context of excitation energy transfer in molecular system, the need of applications of quantum corrections is less discussed. In this study, we examine four quantum correction methods, including the Harmonic method and the Standard method proposed by other groups previously, and the Fitting method and the Prony method proposed by us. We aim to elucidate the performance of the correction by the four correc- tion methods in order to properly apply them to simulating excitation energy transfer dynamics. We focus on a model that describes a two-level system linearly coupled to a harmonic bath to explore the applicability of quantum correction methods in various parameter conditions. Our results reveal the necessity of applying quantum correction when studying excitation energy transfer dynamics based on results of classical molecular dynamics simula- tion. Our calculations also conclude that the Harmonic method performs the best among the four approaches and that the Prony method has serious draw- backs. The Fitting method provides similar results as the Standard method, and both methods perform well at a higher temperature or in the condition where relaxation is driven by coherent evolution.