Recent developments in nonlinear imaging microscopy show the need to implement new theoretical tools, which are able to characterize nonlinear optical properties in an efficient way. For second-harmonic imaging microscopy (SHIM), quantum chemistry could play an important role to design new exogenous dyes with enhanced first hyperpolarizabilities or to characterize the response origin in large endogenous biological systems. Such methods should be able to screen a large number of compounds while reproducing their trends and to treat large systems in reasonable computation times. To fulfill these requirements, we present a new simplified time-dependent density functional theory (sTD-DFT) implementation to evaluate the first hyperpolarizability where the Coulomb and exchange integrals are approximated by short-range damped Coulomb interactions of transition density monopoles. For an ultra-fast computation of the first hyperpolarizability, a tight-binding version (sTD-DFT-xTB) is also proposed. In our implementation, a sTD-DFT calculation is more than 600 time faster with respect to a regular TD-DFT treatment, while the xTB version speeds up the entire calculation further by at least two orders of magnitude. We challenge our implementation on three test cases: typical push-pull π-conjugated compounds, fluorescent proteins, and a collagen model, which were selected to model requirements for SHIM applications.

中文翻译：

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简化的时变密度泛函理论（sTD-DFT）框架中的非线性响应特性：第一个超极化性的评估

非线性成像显微镜的最新发展表明需要实施新的理论工具，这些工具能够以有效的方式表征非线性光学特性。对于二次谐波成像显微镜（SHIM），量子化学可能在设计具有增强的第一超极化能力的新外源染料或表征大型内源生物系统的响应起源方面起重要作用。这样的方法应该能够在重现其趋势的同时筛选出大量化合物，并在合理的计算时间内处理大型系统。为了满足这些要求，我们提出了一种新的简化的时变密度泛函理论（sTD-DFT）实现，以评估第一个超极化率，其中库仑和交换积分通过过渡密度单极子的短程阻尼库仑相互作用来近似。为了对第一超极化率进行超快速计算，还提出了紧密绑定版本（sTD-DFT-xTB）。在我们的实现中，相对于常规TD-DFT处理，sTD-DFT计算快600倍以上，而xTB版本将整个计算速度进一步提高至少两个数量级。我们在以下三个测试用例上挑战实现：典型的推挽式 与常规的TD-DFT处理相比，sTD-DFT的计算速度快600倍以上，而xTB版本则使整个计算速度至少提高了两个数量级。我们在以下三个测试用例上挑战实现：典型的推挽式 与常规的TD-DFT处理相比，sTD-DFT的计算速度快600倍以上，而xTB版本则使整个计算速度至少提高了两个数量级。我们在以下三个测试用例上挑战实现：典型的推挽式选择了π共轭化合物，荧光蛋白和胶原蛋白模型来模拟SHIM应用的需求。