  Time-dependent density functional theory (TDDFT) has been applied to the
calculation of absorption spectra for two-dimensional atomic layer materials.
We reveal that the character of the first bright exciton state of bi-layer
hexagonal boron nitride (h-BN) is dependent on the layer stacking type through
the use of many-body perturbation theory (MBPT) calculations, i.e., the
electron and hole in the AA$'$ stacking are present in the same layer
(intralayer exciton) while the A$'$B stacking exhibits an interlayer exciton.
We demonstrate that the TDDFT approach with the meta-generalized gradient
approximation to the exchange-correlation (XC) potential, and the Bootstrap XC
kernel can capture the absorption peaks that correspond to these excitons
without computationally heavy GW and Bethe-Salpeter equation calculations. We
also show that the TDDFT method provides the absorption spectra for mono-layer
transition metal dichalcogenides, MoS$_2$ and MoSe$_2$. This study confirms the
validity of the TDDFT approach for the first investigation of the optical
properties of complex two-dimensional atomic layer materials to which the MBPT
calculation can not be readily applied.

Materials Science;Chemical Physics;Computational Physics