Accurate stress calculations based on numerical atomic orbital bases: Implementation and benchmarks

Abstract

We present the detailed formalism for stress calculations within the framework of numerical atomic orbital (NAO) bases, as implemented in the first-principles electronic code package ABACUS. The validity and numerical precision of our implementation are benchmarked against reference results obtained using the finite difference method as well as those calculated using plane wave (PW) bases. The equation of state for α-quartz calculated using our NAO-based implementation is in excellent agreement with the experimental data. We further show that the stresses calculated in terms of NAO bases converge much faster with respect to the energy cutoff than those calculated using PW bases. This enables accurate stress calculations at relatively low cost. An analysis is provided to elucidate the origin of this behavior.