  We report diffusion quantum Monte Carlo (DMC) calculations of the
quasiparticle and excitonic gaps of hydrogen-terminated oligoynes and polyyne.
The electronic gaps are found to be very sensitive to the atomic structure in
these systems. We have therefore optimised the geometry of polyyne by directly
minimising the DMC energy with respect to the lattice constant and the
Peierls-induced carbon-carbon bond-length alternation. We find the bond-length
alternation of polyyne to be 0.136(2) {\AA} and the excitonic and quasiparticle
gaps to be 3.30(7) and 3.4(1) eV, respectively. The DMC zone-centre
longitudinal optical phonon frequency of polyyne is 2084(5) cm$^{-1}$, which is
consistent with Raman spectroscopic measurements for large oligoynes.
