Semiclassical Wigner approach to quantum effects in vibrational spectroscopy

激光装置和测量技术的迅速发展使振动光谱学成为研究复杂多体系统动力学的普遍工具。测量的光谱可以产生一个非常准确的动力学信息的原子水平上，如果辅以理论模拟，揭示了潜在的微观机制。因此，需要有理论方法，可以科普解释这样的光谱，从而解开复杂的现象，在凝聚相变得明显。维格纳函数构成了量子力学密度算符的一对一表示，包括相干性。基于线性半经典初始值表示的最新方法很容易再现初始状态中已经存在的静态量子效应，而在非线性势存在下在时间演化过程中出现的真正动态量子效应仍然无法实现。如果传播不是基于单一的而是基于成对的经典轨迹，那么即使是量子相干也可以忠实地时间演化，这一认识可以取得重大进展。这使得人们可以构造一个真正的半经典维格纳传播子在封闭的形式，包括量子校正的相位高达四阶项的潜力。它已被证明是一个强大的工具，已经在分析经典混沌系统的量子谱的时间相关的相空间结构，并已成功地应用于数值传播任务和线性时间相关函数的框架内的网格为基础的方法。在这里，我们试图通过重铸成功的基于网格的配方，这是非常适合于低维问题，到一个无网格的表示，所有相关的动力学量直接评估为平均轨迹合奏向前迈出了重要的一步。这就需要相应地改变形式主义，这在初步工作阶段已经基本实现。因此，该项目的主要目标是实现所提出的方法应用于现实的分子系统与许多自由度的概念验证。我们建议从模型低维系统的线性光谱开始，并逐渐增加其复杂性，系统地解决所有新出现的方法问题。最后，这个概念将在化学相关分子上进行测试。的非线性光谱以及扩展的从头算分子动力学框架治疗周围无论是通过QM/MM或现实的系统浴分区预见。

Rapid progress of the laser facilities and measuring techniques has made the vibrational spectroscopy an ubiquitous tool to probe dynamics of complex many-body systems. The measured spectra can yield an extremely accurate dynamical information on the atomistic level if supplemented by a theoretical simulation, that reveals the underlying microscopic mechanisms. Thus the demand to have theoretical methods that can cope with explaining such spectra and thus unravelling intricate phenomena in condensed phase becomes apparent. The Wigner function constitutes a one-to-one representation of the quantum mechanical density operator, including coherences. The state-of-the-art methods based on linear semiclassical initial value representation readily reproduce static quantum effects already present in the initial state, whereas truly dynamical quantum effects that arise during the time evolution in the presence of nonlinear potentials remain outside reach. Major progress could be achieved through the insight that even quantum coherences can be time-evolved faithfully if the propagation is not based on single but on pairs of classical trajectories. This allows one to construct a truly semiclassical Wigner propagator in closed form that includes quantum corrections of the phase up to fourth-order terms in the potential. It has proven itself as a powerful tool already in analyzing quantum spectra of classically chaotic systems in terms of time-dependent phase-space structures and has been applied successfully to numerical propagation tasks and linear time-correlation functions in the framework of a grid-based methodology. Here, we attempt to make an important step ahead by recasting the successful grid-based formulation, which is well-suited for low-dimensional problems, into a grid-free representation where all relevant dynamical quantities are evaluated directly as averages over trajectory ensembles. This requires to recast the formalism accordingly, which has been mostly achieved during the preliminary work stage. The main goal of this project is thus to achieve the proof-of-concept for the proposed methodology applied to realistic molecular systems with many degrees of freedom. We propose to start from linear spectroscopy of model low-dimensional systems and to gradually increase their complexity, systematically solving all emerging methodological problems. Finally, the concept will be tested on chemically relevant molecules. The non-linear spectroscopy as well as the extension for the ab initio molecular dynamics framework treating the surrounding either by means of a QM/MM or realistic system-bath partitioning is foreseen.