New and Efficient Implementation of CC3.

Alexander C Paul,Rolf H Myhre,Henrik Koch

doi:10.1021/acs.jctc.0c00686

Abstract

We present a new and efficient implementation of the closed shell coupled cluster singles and doubles with perturbative triples method (CC3) in the electronic structure program eT. Asymptotically, a ground state calculation has an iterative cost of 4nV4nO3 floating point operations (FLOP), where nV and nO are the number of virtual and occupied orbitals, respectively. The Jacobian and transpose Jacobian transformations, required to iteratively solve for excitation energies and transition moments, both require 8nV4nO3 FLOP. We have also implemented equation of motion (EOM) transition moments for CC3. The EOM transition densities require recalculation of triples amplitudes, as nV3nO3 tensors are not stored in memory. This results in a noniterative computational cost of 10nV4nO3 FLOP for the ground state density and 26nV4nO3 FLOP per state for the transition densities. The code is compared to the CC3 implementations in CFOUR, DALTON, and PSI4. We demonstrate the capabilities of our implementation by calculating valence and core excited states of l-proline.

Highlights

X-ray spectroscopies such as near-edge X-ray absorption fine structure (NEXAFS) can provide detailed insight into the electronic structure of molecules and their local environment.[1,2] With the new facilities at the European XFEL and LCLS2 at SLAC, the number of high-resolution spectroscopic experiments is increasing
Coupled cluster theory is the preferred model when calculating spectroscopic properties for molecules, combining high accuracy and correct scaling with system size in the coupled cluster response theory (CCRT) formulation.[7−9] Coupled cluster singles and doubles (CCSD) is the most widely used variant of coupled cluster because of its high accuracy and relatively feasible computational scaling of 6(nV4nO2), where nV is the number of virtual and nO is the number of occupied orbitals
We present an implementation of CC3 ground and excited states, as well as equation of motion (EOM)[36] transition moments

Summary

■ INTRODUCTION

X-ray spectroscopies such as near-edge X-ray absorption fine structure (NEXAFS) can provide detailed insight into the electronic structure of molecules and their local environment.[1,2] With the new facilities at the European XFEL and LCLS2 at SLAC, the number of high-resolution spectroscopic experiments is increasing. The closed shell CC3 ground state, singlet excitation energies, and EOM transition moments have been implemented in the eT program.[49] The core part of the algorithms is a triple loop over the occupied indices i ≥ j ≥ k, as proposed for CCSD(T) by Rendell et al.,[50] and has been used in several other implementations.[27,51,52] Within the triple loop, we first construct the triples amplitudes for a given set of {i, j, k} and contract them with integrals to obtain the contribution to the resulting vector. The CVS approximation reduces the computational cost of the Jacobian transformations from 8nV4 nO3 to 8nV4 nO2 FLOP.[35,67] one iteration is 6 times faster than a ground state iteration These savings are achieved by cycling the triple loop over the occupied indices when none of the indices correspond to the core orbitals of interest. This is reflected in a reduction of the oscillator strength from 0.181 to 0.168

■ CONCLUSIONS

■ ACKNOWLEDGMENTS

Findings

■ REFERENCES