Conical intersections within linear-response time-dependent density functional theory

我们对化学反应的理解在很大程度上植根于势能面(PESS)的概念。在光化学领域中，关键是正确描述锥形交点，锥形交点对应于两个或更多PES简并的分子几何。线性响应时间相关密度泛函理论(LR-TDDFT)是研究分子PESS的一种方法。尽管LR-TDDFT取得了很大的成功，但它未能描述基态和第一激发电子态之间的锥形交点的适当形状和维度。令人惊讶的是，文献中很少有研究试图完全描述LR-TDDFT在描述锥形交点时的维度问题。仍有许多显而易见的问题在很大程度上仍未得到解答。首先，LR-TDDFT什么时候提供了圆锥交的充分描述，什么时候它失败了？为什么LR-TDDFT在这种情况下失败了，但在其他情况下却给出了锥形交点的充分逼近？一旦对这些问题的答案有了更深入的了解，是否有可能开发出一种诊断工具，用于检测LR-TDDFT在准确描述锥形交点方面的故障？LR-TDDFT中依赖于频率的核可以提供一种可行的方法来改进LR-TDDFT中锥形交点的描述吗？在调查中，我们将使用与复杂的从头计算方法的比较来深入了解LR-TDDFT何时未能准确地再现锥形交点的正确F-2维度，以及何时它提供了足够的描述。有了这种洞察，我们的下一个目标将是定义一种诊断工具，该工具可以用于确定在准确描述锥形交点的过程中LR-TDDFT/LDA何时崩溃。这将沿着与Tozer教授小组之前的工作类似的思路进行，Tozer教授小组专注于开发一种诊断测试来判断密度泛函在预测激发能量时的性能。最后，我们建议在常规的LR-TDDFT计算中引入与频率相关的核的实现，以促进给定分子中第一激发态和基态之间的适当耦合。我们计划使用降维模型来理解描述两个绝热PES之间耦合的核的潜在特征，对于降维模型存在数值精确解。

Our understanding of chemical reactions is heavily rooted in the concept of potential energy surfaces (PESs). The ability to accurately compute, not only ground state, but also excited state PESs is crucial for the study of a vast array of chemical phenomena and technologies - femtosecond spectroscopy, nanoscale devices, atmospheric photochemical reactions and solid state chemistry are just a few examples of these. Of key importance in the field of photochemistry is the correct description of conical intersections, which correspond to molecular geometries at which two or more PESs are degenerate. Conical intersections provide an ultrafast route for nonradiative deactivation of photoexcited molecules by acting as efficient funnels for population transfer from a molecule's excited states to its ground state, a phenomenon that is ubiquitous to non-adiabatic processes i.e. those involving more than one PES. One method of choice for the study the PESs of a molecule is linear-response time-dependent density functional theory (LR-TDDFT). Despite all its successes, LR-TDDFT fails to describe the proper shape and dimensionality of conical intersections between the ground and the first excited electronic state. Surprisingly, little research is present in the literature that attempts to fully characterise LR-TDDFT's dimensionality problem when describing conical intersections. There are still many obvious questions that remain largely unanswered. Firstly, when does LR-TDDFT provide an adequate description of conical intersections and when does it fail? Why does LR-TDDFT fail in such cases, but give a sufficient approximation to conical intersections in others? Once a deeper understanding of the answers to these questions has been found, is it possible to develop a diagnostic tool that can be used to detect LR-TDDFT's failure in accurately describing conical intersections? Could frequency-dependent kernels in LR-TDDFT provide a viable way of improving the description of conical intersections within LR-TDDFT? To address these questions, the proposed PhD project will be split into the following three main parts:Firstly, we propose to study a series of molecules exhibiting different types of conical intersection, including peaked, sloped, single-path and/or bifurcating. Within the investigation, we will use comparisons with sophisticated ab initio methods to gain insight into when exactly LR-TDDFT fails to reproduce the correct F-2 dimensionality of conical intersections, as well as when it provides a sufficient description.With this insight, our next aim will be to define a diagnostic tool that can be used to determine when LR-TDDFT/LDA breaks down in accurately describing conical intersections. This will be along similar lines to previous work by the group of Prof. Tozer, which focused on the development of a diagnostic test to judge the performance of density functionals in their prediction of excitation energies. Incorporation of such a tool in standard electronic structure packages would be vital for the community that use LR-TDDFT in the simulation of excited state dynamics.Finally, we propose to investigate the implementation of a frequency-dependent kernel in regular LR-TDDFT calculations, in the hope to facilitate proper coupling between the first excited and ground states in a given molecule. We plan to use reduced dimensionality models, for which a numerically-exact solution exists, to understand the underlying features of the kernel in describing the coupling between the two adiabatic PESs.