Machine-learning models can be trained to predict the converged electron charge density of a density functional theory (DFT) calculation. In general, the value of the density at a given point in space is invariant under global translations and rotations having that point as a center. Hence, one can construct locally invariant machine-learning density predictors. However, the widely used projector augmented wave (PAW) implementation of DFT requires the evaluation of the one-center augmentation contributions that are not rotationally invariant. Building on our recently proposed Jacobi-Legendre charge-density scheme, we construct a covariant Jacobi-Legendre model capable of predicting the local occupancies needed to compose the augmentation charge density. Our formalism is then applied to the prediction of the energy barrier for the 1H-to-1T phase transition of two-dimensional MoS2. With extremely modest training, the model is capable of performing a non-self-consistent nudged elastic band calculation at virtually the same accuracy as a fully DFT-converged one, thus saving thousands of self-consistent DFT steps. Furthermore, at variance with machine-learning force fields, the charge density is here available for any nudged elastic band image, so that we can trace the evolution of the electronic structure across the phase transition.

中文翻译：

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协变 Jacobi-Legendre 展开，用于投影机增强波形式内的总能量计算


可以训练机器学习模型来预测密度泛函论 （DFT） 计算的收敛电子电荷密度。通常，在以该点为中心的全局平移和旋转下，空间中给定点的密度值是不变的。因此，我们可以构建局部不变的机器学习密度预测器。然而，DFT 的广泛使用的投影仪增强波 （PAW） 实现需要评估非旋转不变的单中心增强贡献。在我们最近提出的 Jacobi-Legendre 电荷密度方案的基础上，我们构建了一个协变 Jacobi-Legendre 模型，该模型能够预测组成增强电荷密度所需的局部占用。然后将我们的形式应用于二维 MoS2 的 1H 到 1T 相变的能垒预测。通过极其适度的训练，该模型能够以与完全 DFT 收敛的模型几乎相同的精度执行非自洽轻推松紧带计算，从而节省了数千个自洽 DFT 步骤。此外，与机器学习力场不同，电荷密度可用于任何微动的松紧带图像，因此我们可以追踪电子结构在整个相变过程中的演变。