  Solving the Bethe-Salpeter equation (BSE) for the optical polarization
functions is a first principles means to model optical properties of materials
including excitonic effects. One almost ubiquitously used approximation
neglects the frequency dependence of the screened electron-hole interaction.
This is commonly justified by the large difference in magnitude of electronic
plasma frequency and exciton binding energy. We incorporated dynamical effects
into the screening of the electron-hole interaction in the BSE using two
different approximations as well as exact diagonalization of the exciton
Hamiltonian. We compare these approaches for a naphthalene organic crystal, for
which the difference between exciton binding energy and plasma frequency is
only about a factor of ten. Our results show that in this case, corrections due
to dynamical screening are about 15\,\% of the exciton binding energy. We
analyze the effect of screening dynamics on optical absorption across the
visible spectral range and use our data to establish an \emph{effective}
screening model as a computationally efficient approach to approximate
dynamical effects in complex materials in the future.
