Rank-Reduced Equation-of-Motion Coupled Cluster Triples: an Accurate and Affordable Way of Calculating Electronic Excitation Energies

In the present work, we report an implementation of the rank-reduced equation-of-motion coupled cluster method with approximate triple excitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition techniques in order to alleviate the high cost of computing and manipulating the triply excited amplitudes. In the RR-EOM-CC3 method, both ground-state and excited-state triple-excitation amplitudes are compressed according to the Tucker-3 format. This enables factorization of the working equations such that the formal scaling of the method is reduced to <i>N</i>⁶, where <i>N</i> is the system size. An additional advantage of our method is the fact that the accuracy can be strictly controlled by proper choice of two parameters defining sizes of triple-excitation subspaces in the Tucker decomposition for the ground and excited states. Optimal strategies of selecting these parameters are discussed. The developed method has been tested in a series of calculations of electronic excitation energies and compared to its canonical EOM-CC3 counterpart. Errors several times smaller than the inherent error of the canonical EOM-CC3 method (in comparison to FCI) are straightforward to achieve. This conclusion holds both for valence states dominated by single excitations and for states with pronounced doubly excited character. Taking advantage of the decreased scaling, we demonstrate substantial computational costs reductions (in comparison with the canonical EOM-CC3) in the case of two large molecules - l-proline and heptazine. This illustrates the usefulness of the RR-EOM-CC3 method for accurate determination of excitation energies of large molecules.