Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model

Abstract

The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.

The GPU‐enabled divide‐expand‐consolidate RI‐MP2 method (DEC‐RI‐MP2)

“…All recovery numbers are between 99.73% and 99.81%, which is consistent with the earlier results on the test set of small‐ and medium‐sized molecules and are in accordance with the predefined FOT threshold in these calculations. We therefore also expect this to be valid for even bigger systems.…”

“…The error associated with the RI approximation was in Ref. [ ] determined to be significantly smaller than the corresponding DEC error and as the examined systems are too large for a canonical MP2 calculation, we assume that this conclusion is still valid.…”

“…Capital letters refer to the pseudo‐canonical basis (see Ref. ). There are three parallelization levels in the DEC scheme: Coarse‐grained parallelization: Distribution of the independent fragment calculations among groups of MPI nodes Medium‐grained parallelization: Parallelization of the individual fragment calculation across multiple nodes in an MPI group Fine‐grained parallelization: OpenMP/OpenACC parallelization across multiple CPU/GPU cores on each node This article deals with the fine‐grained parallelization.…”

“…The self‐consistent‐field equations were converged using the “Tight” keyword (corresponding to the energy change of 10 −8 Hartree). The fragment optimization threshold (FOT) in the DEC calculations was chosen to target an accuracy of 10 −3 Hartree in the correlation energy (FOT = 10 −4 ) and a recovery of the canonical RI‐MP2 correlation energy of approximately 99.8% …”

Efficient and portable acceleration of quantum chemical many-body methods in mixed floating point precision using OpenACC compiler directives

“…However, while the computational cost is notably reduced in an RI-MP2 calculation with respect to its MP2 counterpart, its formal O(N 5 ) scaling with the size of the system will often still deem it demanding if no fundamental algorithmic changes are made. [51][52][53][54][55] In the closed-shell (canonical) MP2 model, the correlation energy is given by the following expression…”