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

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.