  We implemented various DFT+U schemes, including the ACBN0 self-consistent
density-functional version of the DFT+U method [Phys. Rev. X 5, 011006 (2015)]
within the massively parallel real-space time-dependent density functional
theory (TDDFT) code Octopus. We further extended the method to the case of the
calculation of response functions with real-time TDDFT+U and to the description
of non-collinear spin systems. The implementation is tested by investigating
the ground-state and optical properties of various transition metal oxides,
bulk topological insulators, and molecules. Our results are found to be in good
agreement with previously published results for both the electronic band
structure and structural properties. The self consistent calculated values of U
and J are also in good agreement with the values commonly used in the
literature. We found that the time-dependent extension of the self-consistent
DFT+U method yields improved optical properties when compared to the empirical
TDDFT+U scheme. This work thus opens a different theoretical framework to
address the non equilibrium properties of correlated systems.
