Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. Here we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep learning functional model. We build the essential non-locality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those seen in training, which unleashes the appealing scaling of OFDFT for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

翻译：无轨道密度泛函理论（OFDFT）是一种量子化学方法，其计算成本标度低于主流的Kohn-Sham DFT，因此在当代分子研究中愈发受到青睐。然而，其精度受限于动能密度泛函，后者在非周期性分子系统中极难近似。本文提出 M-OFDFT，一种能够通过深度学习泛函模型求解分子系统的 OFDFT 方法。我们将关键的非局域性引入模型，并通过将密度简洁表示为原子基组下的展开系数，使该模型在计算上可行。针对其中非传统学习挑战所采用的技术，使得 M-OFDFT 在大量此前 OFDFT 未触及的分子上达到了与 Kohn-Sham DFT 相当的精度。更引人注目的是，M-OFDFT 能够良好地外推至远大于训练集的分子，从而释放了 OFDFT 在蛋白质等大分子研究中诱人的标度优势，代表了量子化学中精度-效率权衡前沿的进步。