How accurate are EOM-CC4 vertical excitation energies?

TL;DR

This study evaluates the accuracy of the EOM-CC4 method for vertical excitation energies, demonstrating it achieves near CCSDTQ accuracy for single excitation states in small molecules, offering a computationally efficient alternative.

Contribution

First assessment of EOM-CC4's performance for excitation energies, showing its high accuracy for single excitation states compared to more expensive methods.

Findings

EOM-CC4 achieves sub-kJ/mol accuracy for single excitation states.

EOM-CC4 closely matches CCSDTQ results, outperforming CC3 and CCSDT.

Less accurate for states dominated by double excitations.

Abstract

We report the first investigation of the performance of EOM-CC4 -- an approximate equation-of-motion coupled-cluster model which includes iterative quadruple excitations -- for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CCSDTQP and FCI reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ~mol$^{-1}$ accuracy (i.e., error below $0.01$ eV), in very close agreement with its more expensive CCSDTQ parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CCSDT. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions with a dominant contribution from the double excitations.