Highly Accurate Real-space Electron Densities with Neural Networks

TL;DR

This paper introduces a neural network-based method to accurately extract electron densities from wave functions obtained via variational quantum Monte Carlo, enabling precise calculation of various density-dependent properties.

Contribution

The novel approach combines neural networks with score matching to derive accurate electron densities from wave functions, improving upon traditional methods.

Findings

Achieved highly accurate electron densities free of basis set errors.

Successfully calculated properties like dipole moments and nuclear forces.

Demonstrated the method's effectiveness with variational quantum Monte Carlo data.

Abstract

Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy, but in practice this extraction is often technically difficult and computationally impractical. Here, we consider the electron density as a central observable in quantum chemistry and introduce a novel method to obtain accurate densities from real-space many-electron wave functions by representing the density with a neural network that captures known asymptotic properties and is trained from the wave function by score matching and noise-contrastive estimation. We use variational quantum Monte Carlo with deep-learning ans\"atze (deep QMC) to obtain highly accurate wave functions free of basis set errors, and from them, using our novel method, correspondingly accurate electron densities, which we demonstrate by calculating dipole moments, nuclear forces, contact densities, and other density-based properties.