We present a scalable cross-platform hybrid MPI / OpenMP / OpenACC implementation of the Divide-Expand-Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide-Expand-Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI+X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the "resolution of the identity second-order Møller-Plesset perturbation theory" (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24440 basis functions and 91280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. The new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature is also retained for the DEC-RIMP2-F12 method. In this paper we present the working equations for the DEC-RIMP2-F12 method and proof of concept numerical results for a set of test molecules.

We augment the recently introduced same number of optimized parameters (SNOOP) scheme [K. Kristensen et al., J. Chem. Phys. 142, 114116 (2015)] for calculating interaction energies of molecular dimers with an F12 correction and generalize the method to enable the determination of interaction energies of general molecular clusters. The SNOOP, uncorrected (UC), and counterpoise (CP) schemes with/without an F12 correction are compared for the S22 test set of Jurečka et al. [Phys. Chem. Chem. Phys. 8, 1985(2006]-which consists of 22 molecular dimers of biological importance-and for water and methane molecular clusters. The calculations have been performed using the Resolution of the Identity second-order Møller-Plesset perturbation theory method. We conclude from the results that the SNOOP scheme generally yields interaction energies closer to the complete basis set limit value than the UC and CP approaches, regardless of whether the F12 correction is applied or not. Specifically, using the SNOOP scheme with an F12 correction yields the computationally most efficient way of achieving accurate results at low basis set levels. These conclusions hold both for molecular dimers and more general molecular clusters. Published by AIP Publishing. [http://dx