Rank-Reduced Equation-of-Motion\nCoupled Cluster Triples:\nan Accurate and Affordable Way of Calculating Electronic Excitation\nEnergies

In the present work, we report an implementation of the\nrank-reduced\nequation-of-motion coupled cluster method with approximate triple\nexcitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition\ntechniques in order to alleviate the high cost of computing and manipulating\nthe triply excited amplitudes. In the RR-EOM-CC3 method, both ground-state\nand excited-state triple-excitation amplitudes are compressed according\nto the Tucker-3 format. This enables factorization of the working\nequations such that the formal scaling of the method is reduced to <i>N</i><sup>6</sup>, where <i>N</i> is the system size.\nAn additional advantage of our method is the fact that the accuracy\ncan be strictly controlled by proper choice of two parameters defining\nsizes of triple-excitation subspaces in the Tucker decomposition for\nthe ground and excited states. Optimal strategies of selecting these\nparameters are discussed. The developed method has been tested in\na series of calculations of electronic excitation energies and compared\nto its canonical EOM-CC3 counterpart. Errors several times smaller\nthan the inherent error of the canonical EOM-CC3 method (in comparison\nto FCI) are straightforward to achieve. This conclusion holds both\nfor valence states dominated by single excitations and for states\nwith pronounced doubly excited character. Taking advantage of the\ndecreased scaling, we demonstrate substantial computational costs\nreductions (in comparison with the canonical EOM-CC3) in the case\nof two large molecules – l-proline and heptazine.\nThis illustrates the usefulness of the RR-EOM-CC3 method for accurate\ndetermination of excitation energies of large molecules.