  We construct multiple families of solitary standing waves of the discrete
cubically nonlinear Schr\"{o}dinger equation (DNLS) in dimensions $d=1,2$ and
$3$. These states are obtained via a bifurcation analysis about the continuum
(NLS) limit. One family consists {\it on-site symmetric} (vertex-centered)
states; these are spatially localized solitary standing waves which are
symmetric about any fixed lattice site. The other spatially localized states
are {\it off-site symmetric}. Depending on the spatial dimension, these may be
bond-centered, cell-centered, or face-centered. Finally, we show that the
energy difference among distinct states of the same frequency is exponentially
small with respect to a natural parameter. This provides a rigorous bound for
the so-called {\it Peierls-Nabarro} energy barrier.
