Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks
This work addresses the computational bottleneck in quantum chemistry simulations for researchers, offering a more efficient method, though it builds incrementally on prior neural network approaches.
The authors tackled the problem of representing electron density in Kohn-Sham density functional theory by developing Deep Density, a neural network that bypasses traditional equations, achieving excellent performance with a small number of training snapshots for various systems including 1D insulators/metals and 3D molecules up to 512 water molecules and 256 aluminum atoms.
The recently developed Deep Potential [Phys. Rev. Lett. 120, 143001, 2018] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to $512$ molecules) and aluminum (up to $256$ atoms).