  We present an algorithm and implementation of integral-direct, density-fitted
Hartree-Fock (HF) and second-order M{\o}ller-Plesset perturbation theory (MP2)
for periodic systems. The new code eliminates the formerly prohibitive storage
requirements and allows us to study systems one order of magnitude larger than
before at the periodic MP2 level. We demonstrate the significance of the
development by studying the benzene crystal in both the thermodynamic limit and
the complete basis set limit, for which we predict an MP2 cohesive energy of
$-72.8$ kJ/mol, which is about $10$--$15$ kJ/mol larger in magnitude than all
previously reported MP2 calculations. Compared to the best theoretical estimate
from literature, several modified MP2 models approach chemical accuracy in the
predicted cohesive energy of the benzene crystal and hence may be promising
cost-effective choices for future applications on molecular crystals.
