Cluster perturbation theory. XII. Parallel implementation of variational excitation energy series for the coupled cluster singles and doubles model

Abstract

An efficient implementation of the variational cluster perturbation excitation energy series through fifth order is described. The series has the coupled cluster singles excitation energies as zeroth order and targets the coupled cluster singles and doubles (CCSD) excitation energies. The implementation utilizes the resolution of the identity approximation for the two-electron integrals. The perturbation series uses the 2n + 1/2n + 2 rules to eliminate all parameters higher than second order. The computational efficiency is illustrated by performing excitation energy calculations on a single node for systems with up to 1000 basis functions and comparing with CCSD calculations. Using the hybrid parallel open multiprocessing/message-passing interface implementation with graphics processing unit offloading, fifth-order cluster perturbation excitation energies for systems with 1750 basis functions can be calculated in 8 h using 20 nodes on the Frontier supercomputer at the Oak Ridge National Laboratory. A benchmark of 131 excitation energies for a diverse set of molecules is presented. For the fourth and fifth order models, a few prominent outliers are present. We demonstrate how these cases may be identified using a simple diagnostic, with the remaining values being indistinguishable from CCSD excitation energies in practice.