  For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading
free energy is given by F_{1}(S)=\pm{1/4}\frac{\del F_{0}(S)}{\del S}.
Motivated by the fact that this relationship does not hold for Chern-Simons
theory on S^{3}, we calculate the sub-leading free energy in the matrix model
for this theory, which is a Gaussian matrix model with Haar measure on the
group SO/Sp. We derive a quantum loop equation for this matrix model and then
find that F_{1} is an integral of the leading order resolvent over the spectral
curve. We explicitly calculate this integral for quadratic potential and find
agreement with previous studies of SO/Sp Chern-Simons theory.
