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We present an algorithm and implementation of integral-direct, density-fittedHartree-Fock (HF) and second-order M{\o}ller-Plesset perturbation theory (MP2)for periodic systems. The new code eliminates the formerly prohibitive storagerequirements and allows us to study systems one order of magnitude larger thanbefore at the periodic MP2 level. We demonstrate the significance of thedevelopment by studying the benzene crystal in both the thermodynamic limit andthe 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 allpreviously reported MP2 calculations. Compared to the best theoretical estimatefrom literature, several modified MP2 models approach chemical accuracy in thepredicted cohesive energy of the benzene crystal and hence may be promisingcost-effective choices for future applications on molecular crystals.

Integral-direct Hartree-Fock and M{\o}ller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal