  Excitonic and vibronic spectra of Frenkel excitons (FEs) in a two-dimensional
(2D) lattice with one molecule per unit cell have been studied and their
manifestation in the linear absorption is simulated. We use the Green function
formalism, the vibronic approach (see Lalov and Zhelyazkov [Phys. Rev. B
\textbf{75}, 245435 (2007)]), and the nearest-neighbor approximation to find
expressions of the linear absorption lineshape in closed form (in terms of the
elliptic integrals) for the following 2D models: (a) vibronic spectra of
polyacenes (naphthalene, anthracene, tetracene); (b) vibronic spectra of a
simple hexagonal lattice. The two 2D models include both linear and quadratic
FE--phonon coupling. Our simulations concern the excitonic density of state
(DOS), and also the position and lineshape of vibronic spectra (FE plus one
phonon, FE plus two phonons). The positions of many-particle (MP-unbound)
FE--phonon states, as well as the impact of the Van Hove singularities on the
linear absorption have been established by using typical values of the
excitonic and vibrational parameters. In the case of a simple hexagonal lattice
the following types of FEs have been considered: (i) non-degenerate FEs whose
transition dipole moment is perpendicular to the plane of the lattice, and (ii)
degenerate FEs with transition dipole moments parallel to the layer. We found a
cumulative impact of the linear and quadratic FE--phonon coupling on the
positions of vibronic maxima in the case (ii), and a compensating impact in the
case (i).
