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 Poissons ratio) of four different pentagonal structures under uniaxial strain. p-graphene is found to have the highest stiffness value and the corresponding Poissons ratio is found to be negative. Similarly, p-B$_{2}$N$_{4}$ and p-B$_{4}$N$_{2}$ have negative Poissons ratio values. On the other hand, the p-AgN$_{3}$ has a large and positive Poissons 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.
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