Theoretical studies of nonlinear optical properties of fluorescent proteins by novel low-cost quantum chemistry methods

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The high computational cost limits the use of ab initio electronic structure calculations for large molecules, e.g., biochemical systems. Particularly, the investigation of nonlinear optical properties is currently restrained to molecules sizing up to a few hundred atoms, making them impractical for systems such as fluorescent proteins. Though, the design of new bright fluorescent proteins for nonlinear optical imaging microscopy as genetically-encoded bio-tags requires the theoretical understanding of phenomena such as second-harmonic generation (SHG) or two-photon absorption (2PA). This project aims at investigating nonlinear optical properties of “novel” (non-GFP) fluorescent proteins by low-cost quantum chemistry methods. In the application part of the proposal, mainly the recently discovered bilirubin fluorescent proteins such as UnaG and its derivatives are considered. The main goal is to provide new insights on how to improve their nonlinear optical properties, e.g., by fine-tuning of the chromophore cavity inside the protein. This is an important prospect because lower intensity laser light sources can reduce phototoxicity problems. A systematic theoretical procedure is proposed to obtain design principles, which are then tested experimentally by a network of collaborators. In this context, our well established simplified time-dependent density functional theory (sTD-DFT) framework will be used and accordingly extended. More specifically, it is not yet possible to compute accurate two-photon transitions with sTD-DFT. Method developments will be carried out to remedy this and to improve the accuracy for the calculation of 2PA cross-sections. The existing monopole approximation for the two-electron integrals will be replaced by a multipole expansion including all second-order terms in a computationally efficient manner. We will investigate the possible re-introduction of the exchange correlation kernel into the linear response equations that may be needed for accurate 2PA cross-sections. The re-instatement of orbital relaxation effects into the quadratic response function will be also investigated. For large fluorescent proteins, the extended Tight-Binding version sTD-DFT-xTB will be used initially. In addition to this minimal atomic orbital basis set xTB version, a more general, non-self-consistent mean-field electronic structure theory for large systems (gTB, general (basis set) Tight-Binding) will be developed for an improved accuracy in particular for 2PA transitions whose accurate prediction may require extended basis sets.