标题： 利用量子化学中的偏差-方差权衡进行准确单重-三重能隙预测：双杂化DFT的一个案例 显示英文标题

标题： Leveraging the Bias-Variance Tradeoff in Quantum Chemistry for Accurate Negative Singlet-Triplet Gap Predictions: A Case for Double-Hybrid DFT

摘要： 违反 Hund 规则的分子很少见，这类分子具有第一激发单重态（S$_1$）的能量低于三重态（T$_1$）。然而，它们有望成为高效的发光材料。它们的大规模识别需要极其精确的激发态建模，以尽量减少定性错误预测。我们评估了十二个 S$_1$-T$_1$能量间隙，发现 ADC(2) 和 CC2 激发态方法的局域相关版本在筛选中型分子时提供了出色的准确性和速度。值得注意的是，尽管双杂化泛函（如 B2GP-PLYP 和 PBE-QIDH）的标准偏差非常低（$\approx10$meV），但它们的平均绝对误差却很高（$>100$meV）。探索其参数空间显示，一种包含 75% 交换和 55% 相关性的配置可将平均绝对误差降低到 5 meV以下，但方差有所增加。使用这种低偏倚参数化作为内部参考，我们在保持低方差的同时纠正了系统误差，有效地结合了低偏倚和低方差密度泛函参数化的优点，从而提高了整体准确性。我们的研究结果表明，由于高偏倚而经常被忽视的低方差密度泛函方法可以作为第一性原理分子设计中可靠的预测建模工具。偏差校正数据拟合程序可以应用于任何已预先确定两种方法（一种具有低偏倚，另一种具有低方差）的一般问题。 显示英文摘要

摘要： Molecules that have been suggested to violate the Hund's rule, having a first excited singlet state (S$_1$) energetically below the triplet state (T$_1$), are rare. Yet, they hold the promise to be efficient light emitters. Their high-throughput identification demands exceptionally accurate excited-state modeling to minimize qualitatively wrong predictions. We benchmark twelve S$_1$-T$_1$ energy gaps to find that the local-correlated versions of ADC(2) and CC2 excited state methods deliver excellent accuracy and speed for screening medium-sized molecules. Notably, we find that double-hybrid DFT approximations (e.g., B2GP-PLYP and PBE-QIDH) exhibit high mean absolute errors ($>100$ meV) despite very low standard deviations ($\approx10$ meV). Exploring their parameter space reveals that a configuration with 75% exchange and 55% correlation, which reduces the mean absolute error to below 5 meV, but with an increased variance. Using this low-bias parameterization as an internal reference, we correct the systematic error while maintaining low variance, effectively combining the strengths of both low-bias and low-variance DFT parameterizations to enhance overall accuracy. Our findings suggest that low-variance DFT methods, often overlooked due to their high bias, can serve as reliable tools for predictive modeling in first-principles molecular design. The bias-correction data-fitting procedure can be applied to any general problem where two flavors of a method, one with low bias and another with low variance, have been identified a priori.