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 ⁵) 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 C₆₀@C₆₀H₂₈ (144 atoms, 1820 atomic orbitals (AOs) for def2‐SVP basis set, and 3888 AOs for def2‐TZVP), nanographene dimer (C₉₆H₂₄)₂ (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.