  We determine the band structure of graphene under strain using density
functional calculations. The ab-initio band strucure is then used to extract
the best fit to the tight-binding hopping parameters used in a recent
microscopic model of strained graphene. It is found that the hopping parameters
may increase or decrease upon increasing strain, depending on the orientation
of the applied stress. The fitted values are compared with an available
parametrization for the dependence of the orbital overlap on the distance
separating the two carbon atoms. It is also found that strain does not induce a
gap in graphene, at least for deformations up to 10%.
