  We report the results of first-principles density functional theory
calculations of the Young's modulus and other mechanical properties of
hydrogen-passivated Si <001> nanowires. The nanowires are taken to have
predominantly {100} surfaces, with small {110} facets according to the Wulff
shape. The Young's modulus, the equilibrium length and the constrained residual
stress of a series of prismatic beams of differing sizes are found to have size
dependences that scale like the surface area to volume ratio for all but the
smallest beam. The results are compared with a continuum model and the results
of classical atomistic calculations based on an empirical potential. We
attribute the size dependence to specific physical structures and interactions.
In particular, the hydrogen interactions on the surface and the charge density
variations within the beam are quantified and used both to parameterize the
continuum model and to account for the discrepancies between the two models and
the first-principles results.
