MPI/OpenMP hybrid parallel algorithm for resolution of identity second-order Møller-Plesset perturbation calculation of analytical energy gradient for massively parallel multicore supercomputers.

A massively parallel algorithm of the analytical energy gradient calculations based the resolution of identity Møller-Plesset perturbation (RI-MP2) method from the restricted Hartree-Fock reference is presented for geometry optimization calculations and one-electron property calculations of large molecules. This algorithm is designed for massively parallel computation on multicore supercomputers applying the Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) hybrid parallel programming model. In this algorithm, the two-dimensional hierarchical MP2 parallelization scheme is applied using a huge number of MPI processes (more than 1000 MPI processes) for acceleration of the computationally demanding O(N ) step such as calculations of occupied-occupied and virtual-virtual blocks of MP2 one-particle density matrix and MP2 two-particle density matrices. The new parallel algorithm performance is assessed using test calculations of several large molecules such as buckycatcher C @C H (144 atoms, 1820 atomic orbitals (AOs) for def2-SVP basis set, and 3888 AOs for def2-TZVP), nanographene dimer (C H ) (240 atoms, 2928 AOs for def2-SVP, and 6432 AOs for cc-pVTZ), and trp-cage protein 1L2Y (304 atoms and 2906 AOs for def2-SVP) using up to 32,768 nodes and 262,144 central processing unit (CPU) cores of the K computer. The results of geometry optimization calculations of trp-cage protein 1L2Y at the RI-MP2/def2-SVP level using the 3072 nodes and 24,576 cores of the K computer are presented and discussed to assess the efficiency of the proposed algorithm. © 2017 Wiley Periodicals, Inc.