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

高昂的计算成本限制了从头算电子结构计算大分子（如生化系统）的使用。特别是，非线性光学性质的研究目前仅限于几百个原子大小的分子，这使得它们在荧光蛋白等系统中不切实际。然而，设计用于非线性光学成像显微镜作为遗传编码生物标签的新型明亮荧光蛋白需要对二次谐波产生（SHG）或双光子吸收（2PA）等现象的理论理解。本项目旨在通过低成本量子化学方法研究“新型”（非绿色荧光蛋白）荧光蛋白的非线性光学性质。在提案的应用部分，主要考虑了最近发现的胆红素荧光蛋白如UnaG及其衍生物。主要目标是提供关于如何改善其非线性光学特性的新见解，例如，通过微调蛋白质内部的发色团腔。这是一个重要的前景，因为低强度激光光源可以减少光毒性问题。提出了一个系统的理论程序来获得设计原则，然后由合作者网络进行实验测试。在这种情况下，我们建立的简化时相关密度泛函理论（sTD-DFT）框架将被使用并相应扩展。更具体地说，尚不可能用sTD-DFT计算精确的双光子跃迁。将进行方法开发来补救这一点，并提高2PA截面计算的准确性。现有的双电子积分的单极近似将以计算效率高的方式被包含所有二阶项的多极展开所取代。我们将研究在线性响应方程中重新引入交换相关核的可能性，这可能需要精确的2PA截面。轨道弛豫效应在二次响应函数中的恢复也将被研究。对于大的荧光蛋白，最初将使用扩展的紧密结合版本sTD-DFT-xTB。除了这个最小原子轨道基集xTB版本之外，还将开发一个更通用的，非自洽的大系统平均场电子结构理论（gTB, general（基集）tightbinding），以提高精度，特别是对于精确预测可能需要扩展基集的2PA跃迁。

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.