  Nonuniversal effects due to leading effective-range corrections are computed
for the ground-state energy of the weakly-coupled repulsive Bose gas in two
spatial dimensions. Using an effective field theory of contact interactions,
these corrections are computed first by considering fluctuations around the
mean-field free energy of a system of interacting bosons. This result is then
confirmed by an exact calculation in which the energy of a finite number of
bosons interacting in a square with period boundary conditions is computed and
the thermodynamic limit is explicitly taken.
