Development of a Hierarchy of Theoretical Methods towards In Silico Photochemistry

分子吸收光的过程的计算研究多年来一直引起人们极大的兴趣。为了深入了解分子在激发时的时间演化，已经开发了几种方法。通常对于这些方法来说，提高精度是以增加计算量为代价的，这使得精确的动力学变得不可行。该项目将围绕三个主要挑战展开：测试一种仍然提供正确描述退相干效应的有效方法，扩展非绝热动力学的框架，也考虑通过光子自发发射的衰变，并最终进一步引入时间相关势能面（PES）的理论概念，作为替代通常使用的时间相关波函数在时间无关的PES上的演化概念。一种广泛应用于非绝热动力学模拟的方法是混合量子/经典方法。在这些方法的低端，发现了表面跳变，即使对于更大的高维系统，这在计算上也是可行的，但有一个已知的问题：在这种框架中，退相干现象不会自然产生，导致“过相干”。这一障碍只有通过引入不同的特别修正才得以规避。相反，从头算多重衍生（AIMS）提供了一种正确预测非绝热过程退相干效应的方法。在AIMS中，经典轨迹被耦合高斯轨迹基函数（TBF）所取代，从而能够准确地描述量子效应。然而，准确性的提高是以计算效率为代价的。最近提出了一种方法来缓解这一计算瓶颈，该方法基于随机选择过程，即随机选择- (SS-) AIMS，检测耦合tbf的不耦合组并将其减少为一组。在项目的第一部分，几个分子的表面跳跃动力学将研究使用和不使用退相干校正。相比之下，将使用AIMS和SS-AIMS来研究相同分子的动力学，以深入了解SS-AIMS与表面跳跃和AIMS相比的性能。尽管AIMS模拟的精度很高，但仍有一些过程无法用该方法描述，例如，目前还不存在能够考虑受激原子自发发射的AIMS框架。当发射光子时，描述从激发态到基态的自发跃迁，需要量子化电磁场的存在。然而，Schrödinger方程的框架只考虑电子能级的量子化。因此，它必须扩展到量子场论，其中电磁场是量子化的，并且哈密顿量包括原子以及场和它们之间的耦合。该项目的下一部分包括开发和实施AIMS到量子电动力学的扩展，目标是考虑自发发射。上述描述非绝热动力学的方法都是基于所谓的Born-Huang ansatz，其中分子波函数表示为电子本征态的基础。精确因子分解提供了波函数的替代表示，其中分子波函数表示为核波函数和电子因子的单个乘积。由此产生的随时间变化的PES概念可以作为一个起点，用于开发更简单的方法来模拟非绝热过程。该项目的最后一部分将致力于基于波函数精确分解的进一步理论方法。

Computational investigation of the processes occurring in molecules upon absorption of light has been of great interest throughout the years. Several methods have been developed with the goal to provide insight into the time evolution of molecules upon excitation. Usually for these methods increased accuracy comes at the cost of increased computational effort, which renders exact dynamics unfeasible. This project will be centered around three main challenges: testing an efficient method that still provides the proper description of decoherence effects, expanding the framework of nonadiabatic dynamics to also account for the decay through spontaneous emission of photons, and finally furthering the theoretical concept of introducing a time-dependent potential energy surface (PES) as an alternative to the usually used concept of the evolution of a time-dependent wavefunction on time-independent PES.One widely used approach for the simulation of nonadiabatic dynamics consists of mixed quantum/classical methods. At the lower end of these methods surface hopping is found, which is computationally feasible even for larger, high-dimensional systems, but comes with a known problem: The phenomenon of decoherence does not arise naturally in this framework leading to "overcoherence". This obstacle has only been circumvented by introducing different ad hoc corrections.In contrast, ab-initio multiple spawning (AIMS) presents a method that correctly predicts decoherence effects during nonadiabatic processes. In AIMS the classical trajectories are substituted by coupled gaussian trajectory basis functions (TBF), which enables an accurate description of quantum effects. However, the increase in accuracy comes at the cost of computational efficiency. An approach has recently been proposed to alleviate this computational bottleneck, where uncoupled groups of coupled TBFs are detected and reduced to only one group, based on a stochastic selection process, the stochastic selection- (SS-) AIMS.In the first part of the project, the surface hopping dynamics of several molecules will be investigated with and without using decoherence corrections. In comparison, the dynamics of the same molecules will be studied employing AIMS as well as SS-AIMS, to get insight into the performance of SS-AIMS, as compared to surface hopping and AIMS.Despite the high accuracy of AIMS simulations, there are still processes that cannot be described by the method, e.g., there does not yet exist a framework of AIMS that would be able to take spontaneous emission of an excited atom into account. The description of spontaneous transitions from an excited state to the ground state while emitting a photon, necessitates the presence of a quantized electromagnetic field. However, the framework of the Schrödinger equation only accounts for the quantisation of electronic energy levels. Hence, it has to be extended to a quantum field theory where the electromagnetic field is quantised, and the Hamiltonian includes the atoms as well as the field and the coupling between them. The next part of the project consists of the development and implementation of an extension of AIMS to quantum electrodynamics with the goal to enable the consideration of spontaneous emission.The above-stated methods for describing nonadiabatic dynamics are all based on the so-called Born-Huang ansatz, where the molecular wavefunction is expressed into a basis of electronic eigenstates. An alternative to this representation of the wavefunction is provided by the exact factorisation, where the molecular wavefunction is expressed as a single product of a nuclear wavefunction and an electronic factor. The resulting concept of a time-dependent PES can be used as a starting point for the development of simpler ways to simulate nonadiabatic processes. The final part of the project would be dedicated to further theoretical approaches based on the exact factorisation of the wavefunction.