Ab initio electronic structure calculations based on numerical atomic orbitals: Basic fomalisms and recent progresses

The numerical atomic orbital (NAO) basis sets offer a computationally efficient option for electronic structure calculations, as they require fewer basis functions compared with other types of basis sets. Moreover, their strict localization allows for easy combination with current linear scaling methods, enabling efficient calculation of large physical systems. In recent years, NAO bases have become increasingly popular in modern electronic structure codes. This article provides a review of the ab initio electronic structure calculations using NAO bases. We begin by introducing basic formalisms of the NAO-based electronic structure method, including NAO base set generation, self-consistent calculations, force, and stress calculations. We will then discuss some recent advances in the methods based on the NAO bases, such as real-time dependent density functional theory (rt-TDDFT), efficient implementation of hybrid functionals, and other advanced electronic structure methods. Finally, we introduce the ab initio tight-binding model, which can be generated directly after the self-consistent calculations. The model allows for efficient calculation of electronic structures, and the associated topological, and optical properties of the systems.

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