Valence and core excitons in solids from velocity-gauge real-time TDDFT with range-separated hybrid functionals: An LCAO approach

An atomic-orbital basis set framework is presented for carrying out velocity-gauge real-time time-dependent density functional theory (TDDFT) simulations in periodic systems employing range-separated hybrid functionals. Linear optical response obtained from real-time propagation of the time-dependent Kohn-Sham equations including nonlocal exchange is considered in prototypical solid-state materials such as bulk Si, LiF and monolayer hexagonal-BN. Additionally core excitations in monolayer hexagonal-BN at the B and N K-edges are investigated and the role of long-range and short-range nonlocal exchange in capturing valence and core excitonic effects is discussed. Results obtained using this time-domain atomic orbital basis set framework are shown to be consistent with equivalent frequency-domain planewave results in the literature. The developments discussed lead to a time-domain generalized Kohn-Sham TDDFT implementation for the treatment of core and valence electron dynamics and light-matter interaction in periodic solid-state systems.