In density functional theory, charge density is the core attribute of atomic
systems from which all chemical properties can be derived. Machine learning
methods are promising in significantly accelerating charge density prediction,
yet existing approaches either lack accuracy or scalability. We propose a
recipe that can achieve both. In particular, we identify three key ingredients:
(1) representing the charge density with atomic and virtual orbitals (spherical
fields centered at atom/virtual coordinates); (2) using expressive and
learnable orbital basis sets (basis function for the spherical fields); and (3)
using high-capacity equivariant neural network architecture. Our method
achieves state-of-the-art accuracy while being more than an order of magnitude
faster than existing methods. Furthermore, our method enables flexible
efficiency-accuracy trade-offs by adjusting the model/basis sizes.

在密度泛函理论中，电荷密度是原子系统的核心属性，可以通过它推导出所有的化学性质。机器学习方法在显著加速电荷密度预测方面具有潜力，然而现有方法要么缺乏准确性，要么缺乏可扩展性。我们提出了一个能够同时实现准确性和可扩展性的方案，其核心是使用原子和虚拟轨道来表示电荷密度，使用具有表达能力和可学习性的轨道基组，并使用高容量的等变神经网络架构。我们的方法在准确性上达到了最先进的水平，同时比现有方法快一个数量级以上。此外，我们的方法通过调整模型 / 基组大小实现了灵活的效率 - 准确性平衡。