Covariant Jacobi-Legendre expansion for total energy calculations within the projector-augmented-wave formalism

TL;DR

This paper introduces a covariant Jacobi-Legendre model for predicting local charge densities in DFT calculations, enabling efficient phase transition energy barrier predictions with minimal training, and providing insights into electronic structure evolution.

Contribution

The paper develops a covariant Jacobi-Legendre model that accurately predicts augmentation charges in PAW-DFT, improving efficiency and enabling electronic structure analysis during phase transitions.

Findings

Model predicts energy barriers with accuracy comparable to full DFT.

Enables non-self-consistent calculations with minimal training data.

Provides charge density evolution across phase transition.

Abstract

Machine-learning models can be trained to predict the converged electron charge density of a density functional theory (DFT) calculation. In general, the value of the density at a given point in space is invariant under global translations and rotations having that point as a centre. Hence, one can construct locally invariant machine-learning density predictors. However, the widely used projector augmented wave (PAW) implementation of DFT requires the evaluation of the one-center augmentation contributions, that are not rotationally invariant. Building on our recently proposed Jacobi-Legendre charge-density scheme, we construct a covariant Jacobi-Legendre model capable of predicting the local occupancies needed to compose the augmentation charge density. Our formalism is then applied to the prediction of the energy barrier for the 1H-to-1T phase transition of two-dimensional MoS$_2$. With extremely modest training, the model is capable of performing a non-self-consistent nudged elastic band calculation at virtually the same accuracy as a fully DFT-converged one, thus saving thousands of self-consistent DFT steps. Furthermore, at variance with machine-learning force fields, the charge density is here available for any nudged elastic band image, so that we can trace the evolution of the electronic structure across the phase transition.