  Using ab-initio methods, we show that the uniform deformation either leaves
graphene (semi)metallic or opens up a small gap yet only beyond the mechanical
breaking point of the graphene, contrary to claims in the literature based on
tight-binding (TB) calculations. It is possible, however, to open up a global
gap by a sine-like one-dimensional inhomogeneous deformation applied along any
direction but the armchair one, with the largest gap for the corrugation along
the zigzag direction (~0.5 eV) without any electrostatic gating. The gap
opening has a threshold character with very sharp rise when the ratio of the
amplitude A and the period of the sine wave deformation lambda exceeds
(A/lambda)_c ~0.1 and the inversion symmetry is preserved, while it is
threshold-less when the symmetry is broken, in contrast with TB-derived
pseudo-magnetic field models.
