Research presented in this dissertation aims at enabling (correlated) fragmentation methods to explore biochemistry and catalysis effects of macrosystems at high levels of accuracy using exascale computing resources. The target is the second-order MollerPlesset perturbation theory (MP2), and MP2 in the FMO framework (FMO/MP2). First, the 2-electron integral bottleneck is addressed by using the resolution-of-the-identity (RI) approximation to reduce the memory storage and the computational cost of the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis. The RI approximation is also combined with the singular value decomposition (SVD) to introduce a flexible compression factor that fully controls the accuracy of the integral compression. The RIMP2 energy and analytic energy gradient are implemented in the GAMESS electronic structure program and are parallelized with an efficient hybrid distributed/shared memory model with the support of the MPI and OpenMP APIs. Both the RI-MP2 energy and gradient are interfaced to the FMO framework for large system calculations.