A Parallel Computing Method for the Coupled-Cluster Singles and Doubles

TL;DR

This paper introduces a parallel computing approach for the CCSD method in periodic systems, significantly reducing computational cost and memory requirements by distributing calculations across processes based on electron momentum indices.

Contribution

The paper presents a novel parallelization strategy for CCSD in periodic systems that efficiently distributes calculations using momentum indices, reducing computational complexity.

Findings

Reduces computational cost by a factor of N_k^2.

Decreases memory requirements compared to sequential methods.

Maintains efficient communication in parallel implementation.

Abstract

In this paper, we present a parallel computing method for the coupled-cluster singles and doubles (CCSD) in periodic systems. The CCSD in periodic systems solves simultaneous equations for single-excitation and double-excitation amplitudes. In the simultaneous equations for double-excitation amplitudes, each equations are characterized by four spin orbitals and three independent momentums of electrons. One of key ideas of our method is to use process numbers in parallel computing to identify two indices which represent momentum of an electron. When momentum of an electron takes $N_{\bm{k}}$ values, $N_{\bm{k}}^2$ processes are prepared in our method. Such parallel distribution processing and way of distribution of known quantities in the simultaneous equations reduces orders of computational cost and required memory scales by $N_{\bm{k}}^2$ compared with a sequential method. In implementation of out method, communication between processes in parallel computing appears in the outmost loop in a nested loop but does not appear inner nested loop.