  We present a formulation of spin-conserving and spin-flip, hybrid
time-dependent density functional theory (TDDFT), including the calculation of
analytical forces, which allows for efficient calculations of excited state
properties of solid-state systems with hundreds to thousands of atoms. We
discuss an implementation on both GPU and CPU based architectures, along with
several acceleration techniques. We then apply our formulation to the study of
several point defects in semiconductors and insulators, specifically the
negatively charged nitrogen-vacancy and neutral silicon-vacancy centers in
diamond, the neutral divacancy center in 4H silicon carbide, and the neutral
oxygen-vacancy center in magnesium oxide. Our results highlight the importance
of taking into account structural relaxations in excited states, in order to
interpret and predict optical absorption and emission mechanisms in
spin-defects.
