A new and efficient implementation of CC3

TL;DR

This paper introduces a new, efficient implementation of the CC3 method for electronic structure calculations, optimizing computational costs and enabling accurate excited state analyses in molecules like L-proline.

Contribution

The authors present a novel implementation of CC3 with reduced computational costs and added capabilities for EOM transition moments, improving efficiency over previous software.

Findings

Achieved a computational cost of 4nV^4 nO^3 FLOP for ground state calculations.

Implemented EOM transition moments with a noniterative cost of 10nV^4 nO^3 FLOP per state.

Successfully calculated valence and core excited states of L-proline.

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 $e^T$. Asymptotically, a ground state calculation has an iterative cost of $4n_{\text{V}}^{4}n_{\text{O}}^{3}$ floating point operations (FLOP), where $n_{\text{V}}$ and $n_{\text{O}}$ 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 $8n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP. We have also implemented equation of motion (EOM) transition moments for CC3. The EOM transition densities require recalculation of triples amplitudes, as $n_{\text{V}}^{3}n_{\text{O}}^{3}$ tensors are not stored in memory. This results in a noniterative computational cost of $10n_{\text{V}}^{4}n_{\text{O}}^{3}$ FLOP for the ground state density and $26n_{\text{V}}^{4}n_{\text{O}}^{3}$ 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.