Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals.

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

DeePKS + ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials.

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different levels of QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training an ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), an ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model and then use the DeePKS model to label a much larger amount of configurations to train an ML potential. This scheme for periodic systems is implemented in a DFT package ABACUS, which is open source and ready for use in various applications.

Calculation of Berry curvature using non-orthogonal atomic orbitals.

We present a derivation of the full formula to calculate the Berry curvature on non-orthogonal numerical atomic orbital (NAO) bases. Because usually, the number of NAOs is larger than that of the Wannier bases, we use a orbital contraction method to reduce the basis sizes, which can greatly improve the calculation efficiency without significantly reducing the calculation accuracy. We benchmark the formula by calculating the Berry curvature of ferroelectric BaTiO3and bcc Fe, as well as the anomalous Hall conductivity for Fe. The results are in excellent agreement with the finite-difference and previous results in the literature. We find that there are corrections terms to the Kubo formula of the Berry curvature. For the full NAO base, the differences between the two methods are negligibly small, but for the reduced bases sets, the correction terms become larger, which may not be neglected in some cases. The formula developed in this work can readily be applied to the non-orthogonal generalized Wannier functions.

First-principles molecular dynamics study of deuterium diffusion in liquid tin.

Understanding the retention of hydrogen isotopes in liquid metals, such as lithium and tin, is of great importance in designing a liquid plasma-facing component in fusion reactors. However, experimental diffusivity data of hydrogen isotopes in liquid metals are still limited or controversial. We employ first-principles molecular dynamics simulations to predict diffusion coefficients of deuterium in liquid tin at temperatures ranging from 573 to 1673 K. Our simulations indicate faster diffusion of deuterium in liquid tin than the self-diffusivity of tin. In addition, we find that the structural and dynamic properties of tin are insensitive to the inserted deuterium at temperatures and concentrations considered. We also observe that tin and deuterium do not form stable solid compounds. These predicted results from simulations enable us to have a better understanding of the retention of hydrogen isotopes in liquid tin.