應用量子薛丁格朗之萬方程式的研究在費米共振系統上之二維紅外光譜

Abstract

紅外二維光譜為近二十年成為研究凝態中振動模資訊及微觀環境的化學工具。在模擬方法方面，目前仰賴分子動力學模擬，來得到無細節波包資訊之二維光譜。本研究之主題為得到精確的振動波包動態的情況下，模擬二維紅外光譜。吾人的方法是結合量子朗之萬方程式（quantum Langevin equation）、微擾理論（perturbation theory）和得到的非簡諧振動態的第一原理計算。並在以獨立震盪體（independent oscillators）模型描述系統環境耦合的物理模型為基礎，再搭配高斯波包近似法（Gaussian wavepacket approximation）後，得到量子薛丁格朗之萬方程式。而吾人將此模擬技術應用在有費米共振（Fermi resonance）現象的系統上。費米共振現象是在紅外光譜上具有特徵的現象，主要源自於振動模之間非簡諧耦合。在關於費米共振系統在紅外二維光譜之研究中，討論費米共振之光譜特徵的研究是較於缺乏的。故在這份研究中，吾人將會使用此二維紅外光譜模擬技術，來研究在二維光譜上費米共振的光譜特徵。在水合氫離子系統中，吾人發現方形四重譜線（square quartet）和量子拍（quantum beating）是費米共振的光譜特徵。除此之外，氣相二維紅外光譜在偵測近紅外光區能態的能力也被仔細討論。接下來在甲基銨離子的研究中，吾人發現費米共振可作為偵測有機－無機混合型鈣鈦礦中甲基銨離子所感受到的微觀環境，像是甲基銨離子和鉛與鹵素晶格間的相互作用力。最後，吾人研究如何將馬可夫假設的模擬技術推展到非馬可夫假設的情況，使模擬方法更接近現實中的物理現象。

Two-dimensional infrared (2DIR) spectroscopy has become a powerful tool for probing micoscopic dynamics in the condensed phase over the past two decades. Theoretically, the modern method to simulate 2DIR spectra combines moleclular dynamics simulation and response function calculation. However, this approach often depends on empirical parameters and Newton model mechanism. Thus, the exact treatment of coherent and dissipative dynamics is lacking. In this work, we introduce a dynamical method for the simulation of 2DIR spectra including full coherent quantum dynamics of a molecular system and dissipation involved by the surrounding environment, and then demonstrate the effectiveness of the method by simulating 2DIR spectra of solvated hydronium systems and sol- vated methylaommonium systems. The dynamical method combines quantum Langevin equation (QLE) and a perturbation scheme that extract phase-matching signals by propagating auxiliary wavefunctions. We present the derivation of the QLE using a linear system-bath coupling model, and show that the quantum Schrödinger-Langevin equation (QSLE) can be written as a Schrödinger equation with the addition of a friction operator by adopting a Gaussian wavepacket picture. This approach explicitly treat the wavepacket dynamics, including coherent and dissipative dynamics, evolving on the complex potential energy surface. Subsequently, we demonstrate the effectiveness of our method by simulating 2DIR spectra of molecular systems with Fermi resonance phenomenon. We first demonstrate the QSLE simulation of 2DIR spectra on Ar- and N2-tagged hydronium system, which exhibits Fermi resonance, and we are interested in revealing 2DIR spectral signatures of Fermi resonance on these systems. The Fermi resonance is a unique feature on infrared spectra that stems from the anharmonic coupling between vibrational modes. However, the discussion of spectral signiture on 2DIR spectra of the Fermi resonance remains under developed. Our simulation reveals that square quartets and the beatings of 2DIR peaks can provide decisive evidence for Fermi resonance in the Ar-tagged system. Moreover, the potential of gas-phase 2DIR spectroscopy is disclosed in probing the states in the near-IR region. Secondly, we apply the QSLE method to the simulation of 2DIR spectra of hydrogen bromide- and chloride- tagged methylammonium (MA), which mimic the micro-environment within the organic-inorganic perovskite (MAPbX3, X is halogen). The simulation indicates a physical insight in which the Fermi resonance occurs in N-H stretching region is sensitive to the intermolecular interactions. Finally, we conduct the examination of our theoretical method with the non-Markovian friction operator. To validate the new approach, we simulate the dissipative dynamics, infrared and 2DIR spectra of a vibrational mode in an independent oscillator model. The results show that the dissipative dynamics induced by explicit system-bath coupling are manifested in our approach. Therefore, this study demonstrate the effectiveness of QSLE in 2DIR spectroscopic simulation, which is useful for assigning complex 2DIR spectra and provide physical insights.