半导体和金属泛函衍生物的机器学习的有序- $N$轨道自由密度泛函计算
Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
摘要：
无轨道密度泛函理论（OFDFT）提供了一种具有挑战性的电子结构计算方法，可按$\mathcal{O}(N)$计算系统尺寸$N$。在这里，我们开发了一个计划的OFDFT计算的基础上，准确和transferable动能密度泛函（KEDF），这是创建在一个前所未有的方式使用适当构造的神经网络（NN）。我们表明，我们的OFDFT方案再现了在最先进的DFT计算中获得的电子密度，然后提供了24个不同的系统，从原子，分子，金属，半导体和离子材料的准确的结构特性。我们的KEDF的准确性和可转移性是通过我们的NN训练系统来实现的，在该系统中，使用了每个实空间网格点处的动能泛函导数（KEFD）。选择KEFD作为一组训练数据本质上是重要的，因为首先它直接出现在应该求解的欧拉方程中，其次，它的学习有助于再现表示为总能量的一阶导数的物理量。更一般地说，目前$T[ρ]$的开发是通过逐步增加$\ell_1$，在功能衍生物$δ^{\ell_1} T/δρ^{\ell_1}$方面进行系统扩展。目前在数字上的成功证明了这一方法的有效性。本OFDFT方案的计算成本确实示出了$\mathcal{O}(N)$缩放，如通过电力电子中使用的半导体SiC的计算所证明的。
英文摘要：
Orbital-free density functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the accurate and transferrable kinetic-energy density functional (KEDF) which is created in an unprecedented way using appropriately constructed neural network (NN). We show that our OFDFT scheme reproduces the electron density obtained in the state-of-the-art DFT calculations and then provides accurate structural properties of 24 different systems, ranging from atoms, molecules, metals, semiconductors and an ionic material. The accuracy and the transferability of our KEDF is achieved by our NN training system in which the kinetic-energy functional derivative (KEFD) at each real-space grid point is used. The choice of the KEFD as a set of training data is essentially important, because first it appears directly in the Euler equation which one should solve and second, its learning assists in reproducing the physical quantity expressed as the first derivative of the total energy. More generally, the present development of KEDF $T[ρ]$ is in the line of systematic expansion in terms of the functional derivatives $δ^{\ell_1} T/δρ^{\ell_1}$ through progressive increase of $\ell_1$. The present numerical success demonstrates the validity of this approach. The computational cost of the present OFDFT scheme indeed shows the $\mathcal{O}(N)$ scaling, as is evidenced by the computations of the semiconductor SiC used in power electronics.
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