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. In this work, we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep-learning functional model. We build the essential nonlocality 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 in training, which unleashes the appealing scaling 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）是一种量子化学计算方法，相较于主流的Kohn-Sham DFT具有更低的计算复杂度，这使其在当前分子研究中日益受到青睐。然而，其精度受限于动能密度泛函，而该泛函对非周期性分子系统的近似极为困难。本文提出M-OFDFT，一种利用深度学习泛函模型求解分子系统的OFDFT方法。我们将必要的非局域性融入模型，并通过将密度简洁表示为原子基组下的展开系数，从而使得该模型计算可行。通过解决其中非传统的学习挑战，M-OFDFT在以前OFDFT无法触及的多种分子上达到与Kohn-Sham DFT相当的精度。更具吸引力的是，M-OFDFT能够良好地外推至远大于训练集的分子，从而释放出该方法的可扩展性优势，适用于包括蛋白质在内的大分子研究，标志着量子化学中精度-效率权衡前沿的进步。