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.

使用深度学习功能模型的 M-OFDFT 方法，在非周期性分子体系中具有与 Kohn-Sham DFT 相当的精确度，并且能够推广到大规模分子的研究，突破了量子化学中的准确性与效率之间的制约。

M-OFDFT：利用深度学习克服分子系统中无轨道密度泛函理论的障碍

M-OFDFT: Overcoming the Barrier of Orbital-Free Density Functional  Theory for Molecular Systems Using Deep Learning

Orbital-free density functional theory (OF-DFT) holds the promise to compute
ground state molecular properties at minimal cost. However, it has been held
back by our inability to compute the kinetic energy as a functional of the
electron density only. We here set out to learn the kinetic energy functional
from ground truth provided by the more expensive Kohn-Sham density functional
theory. Such learning is confronted with two key challenges: Giving the model
sufficient expressivity and spatial context while limiting the memory footprint
to afford computations on a GPU; and creating a sufficiently broad distribution
of training data to enable iterative density optimization even when starting
from a poor initial guess. In response, we introduce KineticNet, an equivariant
deep neural network architecture based on point convolutions adapted to the
prediction of quantities on molecular quadrature grids. Important contributions
include convolution filters with sufficient spatial resolution in the vicinity
of the nuclear cusp, an atom-centric sparse but expressive architecture that
relays information across multiple bond lengths; and a new strategy to generate
varied training data by finding ground state densities in the face of
perturbations by a random external potential. KineticNet achieves, for the
first time, chemical accuracy of the learned functionals across input densities
and geometries of tiny molecules. For two electron systems, we additionally
demonstrate OF-DFT density optimization with chemical accuracy.

使用 KineticNet 深度神经网络对轨道自由密度泛函理论中的动能能量进行建模，通过分子平面网格预测分子的动能能量函数，以获得具有化学准确性的模型，从而实现轨道自由密度泛函理论的密度优化，以及对小分子的基态分子属性计算。