Development of a Hierarchy of Theoretical Methods towards In Silico Photochemistry

近年来，对分子吸收光的过程的计算研究引起了人们极大的兴趣。已经开发了几种方法，其目标是提供对激发时分子的时间演化的洞察。通常对于这些方法，增加的精度是以增加的计算工作为代价的，这使得精确的动力学不可行。该项目将围绕三个主要挑战展开：测试一种有效的方法，仍然提供适当的描述退相干效应，扩大框架的非绝热动力学也占衰变通过自发发射的光子，最后，进一步的理论概念，引入一个随时间变化的势能面（PES）作为一个替代通常使用的概念的演变的时间-非绝热动力学模拟的一种广泛使用的方法包括混合量子/经典方法。在这些方法的低端发现表面跳跃，这是计算上可行的，即使是更大的，高维系统，但带有一个已知的问题：退相干现象不会自然出现在这个框架中，导致“过相干”。这个障碍只能通过引入不同的特设修正来规避。相反，从头算多重繁殖（AIMS）提出了一种方法，正确预测非绝热过程中的退相干效应。在AIMS中，经典轨迹被耦合高斯轨迹基函数（TBF）所取代，这使得量子效应的精确描述成为可能。然而，精度的提高是以计算效率为代价的。最近提出了一种方法，以减轻这种计算瓶颈，其中未耦合组的耦合TBF检测和减少到只有一个组，基于随机选择过程，随机选择-（SS-）AIMS.In的第一部分的项目，表面跳跃动力学的几个分子将进行调查，并没有使用消相干校正。相比之下，将使用AIMS以及SS-AIMS来研究相同分子的动力学，以了解SS-AIMS与表面跳跃和AIMS相比的性能。尽管AIMS模拟的精度很高，但仍然存在无法通过该方法描述的过程，例如，还不存在能够将受激原子的自发发射考虑在内的AIMS框架。在描述发射光子时从激发态到基态的自发跃迁时，需要量子化电磁场的存在。然而，薛定谔方程的框架只考虑了电子能级的量子化。因此，它必须扩展到量子场论，其中电磁场是量子化的，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扩展到量子电动力学，目标是能够考虑自发辐射。上述描述非绝热动力学的方法都是基于所谓的Born-Huang方法，其中分子波函数表示为电子本征态的基础。波函数的这种表示的另一种选择是由精确因子分解提供的，其中分子波函数被表示为核波函数和电子因子的单一产物。由此产生的概念，随时间变化的PES可以作为一个起点，为发展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进一步的理论方法的基础上精确因式分解的波函数。

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.