School of Chemistry - Theses
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ItemDevelopment and Assessment of new Time-Dependent Long-Range Corrected Double-Hybrid Density Functionals for Excited States( 2021)This thesis presents the implementation, assessment, and applicability of the currently most accurate density functional approximations (DFAs) for the calculation of vertical excitation energies by means of linear-response time-dependent density functional theory (TD-DFT). Firstly, we demonstrate how the inclusion of a single parameter, which controls the interplay between interlectronic short- and long-regimes, improves global double-hybrid density functional approximations (DHDFAs) when it comes to long-range excitations; such as Rydberg states and charge-transfer (CT) transitions, without much loss of accuracy for local-valence ones. In this context, we define the two first long-range corrected (LC) DHDFAs optimised for excitation energies, namely, wB2PLYP and wB2GP-PLYP, being the best TD-DFT methods until then. Furthermore, we include an additional analysis of the CT problem after noticing some misconceptions by some in the developer community regarding the application of global DHDFAs as an alternative to the LC ones. In the second part, we investigate the performance of the best DHDFAs for singlet-singlet transitions in the Tamm-Dancoff Approximation (TDA) but, more importantly, we revive the applicability of DHDFAs for singlet-triplet excitations after 12 years of slumber. Herein, we demonstrate once again that our LC-DHDFAs are the best-performing methods not only for singlet but also for triplet excitations, being the most accurate and robust methods until then. Finally, inspired by the precursory work done by Schwabe and Goerigk in 2017, we extend our two previous studies by combining our methods with the Spin-Component Scaling (SCS) and Spin-Opposite Scaling (SOS) techniques, with the main difference being the inclusion of LC-DHDFAs and singlet-triplet excitations in the context of DHDFAs. We also defined the currently two best LC-DHDFAs optimised for excitation energies on the market, namely, wB88PP86 and wPBEPP86. We particularly note that the SCS and SOS variants our new functionals delivered the best TD(A)-DHDFA results to date for 1La and 1Lb transitions in Policyclic Aromatic Hydrocarbons (PAHs). Finally, SCS/SOS-wB88PP86 and SCS/SOS-wPBEPP86 have been demonstrated to be the most accurate and robust approximations for the calculation of singlet and triplet excitations regardless of the type of transition, i.e., they describe local-valence, Rydberg states, and CT transitions with the same excellent accuracy, and we highly recommend them for future applications. Note that during the peer-review of this work, new SCS/-SOS methods were also published in the very same journal. Therefore, we also included them after some minor comments from the reviewers. Nevertheless, our newly proposed methods are still the best-performing SCS/SOS-DHDFAs for the calculation of excitation energies. All the methods presented in this thesis are implemented into the ORCA5 quantum package, which is free for academics.