Efficient basis expansion for describing linear and nonlinear electron dynamics in crystalline solids

We propose an efficient basis expansion for electron orbitals to describe real-time electron dynamics in crystalline solids. Although a conventional grid representation in the three-dimensional Cartesian coordinates works robustly, it requires a large amount of computational resources. To reduce computational costs, we consider basis expansion methods employing eigenstates of the ground state Hamiltonian with a truncation. We have found that adding occupied eigenstates of nearby k points to the truncated basis functions composed of eigenstates of the original k point is crucially important. We demonstrate the usefulness of the method for linear and nonlinear electron dynamics calculations in crystalline SiO2.