Development of efficient computational techniques and codes for second-order Møller–Plesset perturbation calculation of extended systems

Electronic structure theory such as ab initio molecular orbital (MO) theory is the powerful tool in elucidating chemical phenomena such as electronic states, molecular structures, properties, and reaction mechanisms. The high-level quantum chemical calculations excellently reproduce the properties for small molecules in the same or better accuracy with the experiments. However, the computational costs drastically increase with respect to the size of molecules when the highlevel quantum chemical calculations are performed. To elucidate chemical phenomena of nano molecules and biological molecules, the development of fast and robust theories and computational techniques of the ab initio quantum chemistry is desired. Especially, non-covalent interactions such as van der Waals forces play important roles in the chemical phenomena of such systems. Those interactions come from the electron correlations. The generally accepted density functional theory (DFT) functionals fail to describe non-covalent interactions because they suffer from self-interaction problems and do not incorporate the long-range correlation effect. Therefore, the electron correlation theory based on the ab initio MO theory is indispensable for the robust reproduction of noncovalent interactions. Among these theories, second-order Møller–Plesset perturbation theory (MP2) [1] is the simplest method to account for the electron correlations at the ab initio level and often used for the practical chemical applications. However, even the computational cost of MP2 calculations scales O(N) with respect to the size of molecules (N), and practical applications are limited to molecules of moderate size. To make the MP2 calculations applicable to the extended systems such as nano molecules and biological molecules, development of efficient computational techniques is desired. In this study, we present an efficient parallel resolution-ofidentity (RI) MP2 (RI-MP2) algorithm and fragmentation based O(N) parallel RI-MP2 methods. These methods are suitable for the massively parallel computations on the supercomputers such as “K computer”.