  We perform the first-principles many-body GW and Bethe-Salpeter equation
(BSE) calculations on the two-dimensional hexagonal boron nitride (2D-hBN) to
explore the effects of opposite atoms on the electronic structure and linear
one-photon absorption (OPA). Five AA- and AB-stacked bilayer and eight
AAB-stacked trilayer structures are considered. The AAB-stacked trilayer hBN
(TL-BN) structures are constructed by mixing the AA- and AB-stacked bilayer hBN
(BL-BN). We show that the GW approximation gives rise to different types (i.e.,
indirect or direct) of fundamental band gaps from the independent particle
approximation for all structures except those dominated by the B-B opposite.
The stacking modes dominated by the B-B opposite have a direct fundamental band
gap in both approximations. The OPA spectra are calculated by solving the
Bethe-Salpeter equation combined with the GW quasi-particle correction. Strong
absorption peaks are found for most structures in the deep-ultraviolet region.
The binding energy and Davydov splitting of excitons of TL-BN strongly depend
on the opposite atoms and are related to the role of the stacking BL-BN
substructure. Finally, taking the six-layer and below AB-stacked structures as
examples, we show that the B-B opposite unit is helpful in constructing the
turbostratic-phase-like stacking structures with a direct fundamental band gap
which are more suitable for optoelectronic applications.
