通过将基态电子能量作为基于原子的电子布居的函数来逼近，将电子信息转化为机器学习势能面
Incorporating electronic information into Machine Learning potential energy surfaces via approaching the ground-state electronic energy as a function of atom-based electronic populations
摘要：
密度泛函理论（DFT）势能面（PES）的机器学习（ML）近似在降低精确分子模拟的计算成本方面显示出巨大的前景，但目前它们不适用于变化的电子状态，特别是，它们不太适合于局部电子结构对中远程电子环境敏感的分子系统。这个问题作为焦点，我们提出了一种新的机器学习方法称为bpopNN获得有效的近似DFT PES。该方法是基于接近真实的DFT能量作为原子上的电子布居的函数，这可以在实践中实现与约束DFT（CDFT）。新方法通过深度神经网络创建了该函数的近似值。因此，这些近似将电子信息自然地结合到ML方法中，并且相对于种群优化模型能量允许电子项自洽地适应环境，如DFT中那样。我们证实了这种方法的有效性与各种计算的锂$_n$ H $_n$集群。
英文摘要：
Machine Learning (ML) approximations to Density Functional Theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present they are not applicable to varying electronic states, and in particular, they are not well suited for molecular systems in which the local electronic structure is sensitive to the medium to long-range electronic environment. With this issue as the focal point, we present a new Machine Learning approach called bpopNN for obtaining efficient approximations to DFT PESs. The methodology is based on approaching the true DFT energy as a function of electron populations on atoms, which may be realized in practice with constrained DFT (CDFT). The new approach creates approximations to this function with deep neural networks. These approximations thereby incorporate electronic information naturally into a ML approach, and optimizing the model energy with respect to populations allows the electronic terms to self-consistently adapt to the environment, as in DFT. We confirm the effectiveness of this approach with a variety of calculations on Li$_n$H$_n$ clusters.
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