Abstract: Plane wave and Wannier function are two commonly-used basis sets in electronic structure of solid. The transformation between different basis sets and coordinate systems is helpful for understanding electronic structure. Taking 2D single-layer ferromagnetic semiconductor CrI3 as an illustration example, the present work performs a basis set transformation from plane-wave and Wannier function in localized coordinate system. And then, crystal field splitting of single-layer CrI3 is discussed in localized coordinate system. Moreover, the underlying mechanism of electronic structure and magnetism are also discussed clearly. Our work not only lets student understand the difference between two basis sets, but also increases the ability to solve physical problems.

Key words: plane wave, maximally localized Wannier functions, crystal field, electronic structure, plane wave, maximally localized Wannier functions, crystal field