Development of the FMO/RI-MP2 Fully Analytic Gradient Using a Hybrid-Distributed/Shared Memory Programming Model

Abstract

The fully analytic gradient of the second-order Møller–Plesset perturbation theory (MP2) with the resolution-of-the-identity (RI) approximation in the fragment molecular orbital (FMO) framework is derived and implemented using a hybrid multilevel parallel programming model, a combination of the general distributed data interface (GDDI) and the OpenMP API. The FMO/MP2 analytic gradient contains three parts, i.e., the internal fragment component, the electrostatic potential (ESP) component, and the response terms. The RI approximation is applied to the internal fragment MP2 gradient term, whose MP2 densities and monomer MP2 Lagrangians are shared with the ESP and the response terms. The FMO/RI-MP2 analytic gradient implementation is validated against the numerical gradient (with errors ∼10–6–10–5 Hartree/Bohr) and the energy conservation in molecular dynamics (MD) simulations using NVE ensembles. The RI approximation introduces an error of ∼10–5 Hartree/Bohr with a speedup of 4.0–8.0× compared with the currently available GDDI FMO/MP2 gradient. The node linear scaling of the fragmentation framework due to multilevel parallelism is well-preserved and is demonstrated in single-point gradient calculations of large water clusters (e.g., 1120 and 2165 molecules) using 300–800 KNL compute nodes with a parallel efficiency of more than 90%.

PDG: A Composite Method Based on the Resolution of the Identity

“…Bottlenecks in the RI-G3 method, including the HF/6-31G­(d) gradient, RI-MP2/6-31G­(d) gradient, RI-CCSD­(T)/6-31G­(d), and RI-MP2/G3L single point energy calculations have been parallelized using the hybrid distributed/shared memory models based on MPI and OpenMP API. In practice, one MPI rank is created on each compute node or socket, which then spawns a team of threads for the actual computation.…”

“…12−15 In the RI approximation one employs an auxiliary basis set to reduce time-consuming and memory-demanding 4index 2-electron integrals to 3-index 2-electron integrals. Recently, the authors have derived and implemented in GAMESS 16 computationally efficient second-order perturbation theory (MP2) energies 17 and gradients 18 and coupled cluster with singles, doubles, and noniterative triples [CCSD-(T)] energies 19 within the RI ansatz. In this work, the RI-MP2 and RI-CCSD(T) methods in GAMESS are used in a reformulation of the Gaussian-3 (G3) method.…”

“…One approach to reduce the computational effort as well as the memory footprint of correlated electronic structure methods is to apply the resolution of the identity (RI) approximation. − In the RI approximation one employs an auxiliary basis set to reduce time-consuming and memory-demanding 4-index 2-electron integrals to 3-index 2-electron integrals. Recently, the authors have derived and implemented in GAMESS computationally efficient second-order perturbation theory (MP2) energies and gradients and coupled cluster with singles, doubles, and noniterative triples [CCSD­(T)] energies within the RI ansatz . In this work, the RI-MP2 and RI-CCSD­(T) methods in GAMESS are used in a reformulation of the Gaussian-3 (G3) method. − The accuracy of this new RI-G3 method, also called the PDG method, is essentially the same as that of the original method, while the computational efficiency and memory footprint are greatly improved.…”

“…Recently, the MPI/OpenMP hybrid distributed/shared memory parallel programming model has been applied to the RI-MP2 energy and gradient and RI-CCSD­(T) energy and implemented in the GAMESS suite of electronic structure programs. These new algorithms have been demonstrated to significantly increase the performance and the applicability domain of these electron correlation methods.…”

Third-order many-body expansion of OSV-MP2 wavefunction for low-order scaling analytical gradient computation

“…In recent years, successful applications have been highlighted in a number of ab-initio problems involving electric-field derivatives for electric moments, 67,68 polarizabilities 69,70 and vibrational spectra, [71][72][73] and nuclear gradients for geometry optimizations 55, [74][75][76][77] and molecular dynamics (MD) simulations. [78][79][80][81][82][83][84][85] A tremendous variety of these MBE methods for both energies and properties features the fragmentation schemes in which the subsystems are formed by properly and explicitly cutting macromolecule into overlapping or non-overlapping atomic fragments 86,87 prior to post-HF.…”