  We report an extensive study of the properties of carbyne using
first-principles calculations. We investigate carbyne's mechanical response to
tension, bending, and torsion deformations. Under tension, carbyne is about
twice as stiff as the stiffest known materials and has an unrivaled specific
strength of up to 7.5*10^7 Nm/kg, requiring a force of ~10 nN to break a single
atomic chain. Carbyne has a fairly large room-temperature persistence length of
about 14 nm. Surprisingly, the torsional stiffness of carbyne can be zero but
can be 'switched on' by appropriate functional groups at the ends. Further,
under appropriate termination, carbyne can be switched into a
magnetic-semiconductor state by mechanical twisting. We reconstruct the
equivalent continuum-elasticity representation, providing the full set of
elastic moduli for carbyne, showing its extreme mechanical performance (e.g. a
nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of
0.772 A). We also find an interesting coupling between strain and band gap of
carbyne, which is strongly increased under tension, from 3.2 to 4.4 eV under a
10% strain. Finally, we study the performance of carbyne as a nanoscale
electrical cable, and estimate its chemical stability against self-aggregation,
finding an activation barrier of 0.6 eV for the carbyne-carbyne cross-linking
reaction and an equilibrium cross-link density for two parallel carbyne chains
of 1 cross-link per 17 C atoms (2.2 nm).
