  Within the framework of time-dependent density-functional theory (TDDFT), we
derive the dynamical linear response of LDA+U functional and benchmark it on
NiO, a prototypical Mott insulator. Formulated using real-space Wannier
functions, our computationally inexpensive framework gives detailed insights
into the formation of tightly bound Frenkel excitons with reasonable accuracy.
Specifically, a strong hybridization of multiple excitons is found to
significantly modify the exciton properties. Furthermore, our study exposes a
significant generic limitation of adiabatic approximation in TDDFT with hybrid
functionals and in existing Bethe-Salpeter-equation approaches, advocating the
necessity of strongly energy-dependent kernels in future development.
