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 scales as $2n^{4}_{\mathrm{V}}n^{3}_{\mathrm{O}}$ where $n_{\mathrm{V}}$ and $n_{\mathrm{O}}$ are the number of virtual and occupied orbitals respectively. The Jacobian and transpose Jacobian transformations, required to compute excitation energies and transition moments, both scale iteratively as $4n^{4}_{\mathrm{V}}n^{3}_{\mathrm{O}}$. We have also implemented equation-of-motion (EOM) transition moments for CC3. The EOM transition densities require recalculation of triples amplitudes, as N$^6$ tensors are not stored in memory. This results in a noniterative computational cost of $5n^{4}_{\mathrm{V}}n^{3}_{\mathrm{O}}$ for the ground state density and $13n^{4}_{\mathrm{V}}n^{3}_{\mathrm{O}}$ per state for the transition densities. We demonstrate the computational efficiency of the implementation by calculating valence and core excited states of L-proline.