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An atomic-orbital basis set framework is presented for carrying out velocity-gauge real-time time-dependent density functional theory (TDDFT) simulations inperiodic systems employing range-separated hybrid functionals. Linear opticalresponse obtained from real-time propagation of the time-dependent Kohn-Shamequations including nonlocal exchange is considered in prototypical solid-statematerials such as bulk Si, LiF and monolayer hexagonal-BN. Additionally coreexcitations in monolayer hexagonal-BN at the B and N K-edges are investigatedand the role of long-range and short-range nonlocal exchange in capturingvalence and core excitonic effects is discussed. Results obtained using thistime-domain atomic orbital basis set framework are shown to be consistent withequivalent frequency-domain planewave results in the literature. Thedevelopments discussed lead to a time-domain generalized Kohn-Sham TDDFTimplementation for the treatment of core and valence electron dynamics andlight-matter interaction in periodic solid-state systems.

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