  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.
