  In this study we present a theoretical investigation of structural,
electronic and mechanical properties of pentagonal monolayers of carbon
(p-graphene), boron nitride (p-B$_{2}$N$_{4}$ and p-B$_{4}$N$_{2}$) and silver
azide (p-AgN$_{3}$) by performing state-of-the-art first principles
calculations. Our total energy calculations suggest feasible formation of
monolayer crystal structures composed entirely of pentagons. In addition,
electronic band dispersion calculations indicate that while p-graphene and
p-AgN$_{3}$ are semiconductors with indirect bandgaps, p-BN structures display
metallic behavior. We also investigate the mechanical properties (in-plane
stiffness and the Poisson's ratio) of four different pentagonal structures
under uniaxial strain. p-graphene is found to have the highest stiffness value
and the corresponding Poisson's ratio is found to be negative. Similarly,
p-B$_{2}$N$_{4}$ and p-B$_{4}$N$_{2}$ have negative Poisson's ratio values. On
the other hand, the p-AgN$_{3}$ has a large and positive Poisson's ratio. In
dynamical stability tests based on calculated phonon spectra of these
pentagonal monolayers, we find that only p-graphene and p-B$_{2}$N$_{4}$ are
stable, but p-AgN$_{3}$ and p-B$_{4}$N$_{2}$ are vulnerable against vibrational
excitations.
