Meshfree implementation for the real-space electronic-structure calculation of crystalline solids

A meshfree formulation of the Schrödinger equation having periodic potential is presented. The conventional meshfree shape function is modified to express properly the periodicity of Bravais lattice. Then, it is applied to the electronic-structure calculation of crystalline solids in real space. Numerical examples are the Kronig–Penney model potential and the empirical pseudopotentials of diamond and zinc-blende semiconductors. Results prove that the meshfree method is a promising one to be used as a real-space technique for the calculations of electronic structures