We determine the stability, the geometry, the electronic, and magnetic structure of hydrogen-terminated graphene-nanoribbon edges as a function of the hydrogen content of the environment by means of density functional theory. Antiferromagnetic zigzag ribbons are stable only at extremely low ultravacuum pressures. Under more standard conditions, the most stable structures are the mono- and dihydrogenated armchair edges and a zigzag edge reconstruction with one di- and two monohydrogenated sites. At high hydrogen concentration "bulk" graphene is not stable and spontaneously breaks to form ribbons, in analogy to the spontaneous breaking of graphene into small-width nanoribbons observed experimentally in solution. The stability and the existence of exotic edge electronic states and/or magnetism is rationalized in terms of simple concepts from organic chemistry (Clar's rule).

The high pressure behavior of optical phonons in wurtzite zinc oxide (w-ZnO) has been studied using room temperature Raman spectroscopy and ab-initio calculations based on a plane wave pseudopotential method within the density functional theory. The pressure dependence of the zonecenter phonons (E2, A1 and E1) was measured for the wurtzite structure up to the hexagonal→cubic transition near 9 GPa. Above this pressure no active mode was observed. The only negative Grüneisen parameter is that of the E low 2 mode. E1(LO) and (TO) frequencies increase with increasing pressure. The corresponding perpendicular tensor component of the Born's transverse dynamic charge e * T is experimentally found to increase under compression like e * T (P) = 2.02 + 6.4 • 10 −3 .P whereas calculations give e * T (P) = 2.09−2.5•10 −3 .P (in units of the elementary charge e, P in GPa). In both cases, the pressure variation is small, indicating a weak dependence of the bond ionicity with pressure. The pressure dependence of the optical mode energies is also compared with the prediction of a model that treats the wurtzite-to-rocksalt transition as an homogeneous shear strain. There is no evidence of anomaly in the E2 and A1 modes behavior before the phase transition.

Many experiments have been done to determine the relative strengths of different knots, and these show that the break in a knotted rope almost invariably occurs at the point just outside the 'entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or 'overhand' knot is likely to be present in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use ab initio computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.