Advancement and Application of TDDFT-based Non-Adiabatic Molecular Dynamics Methods for Triplet States

非绝热分子动力学（NAMD）模拟是研究飞秒时间尺度上超快光诱导过程的重要理论工具。以前的研究主要集中在电子跃迁不涉及电子自旋变化的过程（单重态激发和内转换）。涉及自旋反转的过程（三重激发和系间穿越，ISC）通常在更长的时间尺度上进行。然而，越来越多地发现这一规则的重要例外，例如过渡金属络合物中的超快ISC过程，这与染料敏化太阳能电池或OLED的开发有关。然而，在NAMD模拟中考虑三重态也带来了各种问题，其中一些问题将在本项目中解决。对于较大的系统，含时密度泛函理论（TDDFT）是计算NAMD模拟所需量子化学量的流行方法，因为它提供了有吸引力的性价比。然而，传统的密度泛函表现出较大的误差三重态激发能，这可能会导致不正确的结果NAMD模拟。另一方面，相对较新的一类局域杂化泛函在描述三重态方面具有显著的优势，因此第一个目标是为这些泛函开发非绝热耦合矩阵元，使其可用于NAMD模拟。为了效率和简单，这通常使用微扰方法来完成。然而，对于强耦合，例如在与重元素的配合物中预期的那些，这些方法可能失败。本文的第二个目标是在NAMD模拟中，采用对强耦合更为可靠的变分双分量TDDFT方法来确定SOC矩阵元。在NAMD模拟中，为了计算控制原子核运动的力，需要计算激发态的核梯度。然而，当代NAMD方法忽略了SOC项的梯度，因为它们还无法通过任何量子化学程序进行分析计算。该项目的第三个目标是在双组分TDDFT的框架下推导和实现这些梯度。新方法将用于探索在太阳能收集背景下高度相关的分子中的ISC过程，但到目前为止只使用更简单的方法进行了研究或根本没有。在这方面，还将比较不同方法的准确性。

Non-adiabatic molecular dynamics (NAMD) simulations are an important theoretical tool to study ultrafast light-induced processes occurring on a femtosecond time scale. Previous research has been predominantly focused on processes in which the electronic transitions involve no change in electron spin (singlet excitations and internal conversion). Processes involving spin reversal (triplet excitations and intersystem crossing, ISC) typically proceed on a much longer time scale. However, important exceptions to this rule are increasingly found, such as ultrafast ISC processes in transition-metal complexes, which are relevant for the development of dye-sensitized solar cells or OLEDs. However, the consideration of triplet states in NAMD simulations also introduces various problems, some of which will be addressed in this project.For larger systems, time-dependent density functional theory (TDDFT) is a popular method for calculating the quantum chemical quantities needed for NAMD simulations, as it offers an attractive cost-performance ratio. However, conventional density functionals exhibit large errors for triplet excitation energies, which can lead to incorrect results in NAMD simulations. The relatively recent class of local hybrid functionals, on the other hand, offers significant advantages in describing triplet states, so a first goal is to develop non-adiabatic coupling matrix elements for these functionals to make them available for NAMD simulations.To describe ISC in NAMD simulations, the underlying spin-orbit coupling (SOC) effect must be described. For efficiency and simplicity, this is usually done using perturbative approaches. However, for strong couplings, such as those expected in complexes with heavy elements, these approaches may fail. The second goal of this project is to instead use variational, two-component TDDFT methods that are more reliable for strong couplings to determine SOC matrix elements in NAMD simulations.For the calculation of the forces governing the motion of atomic nuclei in NAMD simulations, the nuclear gradients of the excited states are needed. However, contemporary NAMD methods neglect the gradients of the SOC terms because they are not yet analytically computable by any quantum chemical program. The third goal of this project is to derive and implement these gradients in the framework of two-component TDDFT.The new methods will be used to explore ISC processes in molecules that are highly relevant in the context of solar energy harvesting but have so far only been studied using simpler approaches or not at all. The accuracy of the different methods will also be compared in this context.