Predicting Quantum Monte Carlo Charge Densities using Graph Neural Networks*

The electronic charge density is a fundamental quantity in accurately predicting the properties of 

quantum materials. Although density functional approximations have been improving in energetics,

the progress in charge densities has been stagnant. We use quantum Monte Carlo (QMC) to calculate

charge densities as well as total and kinetic energies of over 1700 QM9 dataset molecules with

closed-shell singlet and open-shell triplet configurations. A message-passing graph neural network

designed for grid-based data was trained to predict the charge densities. We explore the viability

of reaching accurate predictions using a small QMC dataset, which we make publicly available for

future machine-learning models.