Simplified quantum chemistry methods to evaluate non-linear optical properties of large systems

This review presents the theoretical background concerning simplified quantum chemistry (sQC) methods to compute non-linear optical (NLO) properties and their applications to large systems. To evaluate any NLO responses such as hyperpolarizabilities or two-photon absorption (2PA), one should evidently perform first a ground state calculation and compute its response. Because of this, methods used to compute ground states of large systems are outlined, especially the xTB (extended tight-binding) scheme. An overview on approaches to compute excited state and response properties is given, emphasizing the simplified time-dependent density functional theory (sTD-DFT). The formalism of the eXact integral sTD-DFT (XsTD-DFT) method is also introduced. For the first hyperpolarizability, 2PA, excited state absorption, and second hyperpolarizability, a brief historical review is given on early-stage semi-empirical method applications to systems that were considered large at the time. Then, we showcase recent applications with sQC methods, especially the sTD-DFT scheme to large challenging systems such as fluorescent proteins or fluorescent organic nanoparticles as well as dynamic structural effects on flexible tryptophan-rich peptides and gramicidin A. Thanks to the sTD-DFT-xTB scheme, all-atom quantum chemistry methodologies are now possible for the computation of the first hyperpolarizability and 2PA of systems up to 5000 atoms. This review concludes by summing-up current and future method developments in the sQC framework as well as forthcoming applications on large systems.

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