A new and efficient implementation of CC3

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.