Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic-diagrammatic construction schemes

Employing an intermediate state representation (ISR) approach, Hermitian second-order methods for the calculation of electronic excitation energies are presented and compared in detail. These comprise the algebraic-diagrammatic construction scheme for the polarization propagator, a hybrid second-order ISR scheme based on traditional coupled-cluster theory as well as two similar approaches based on a unitary coupled-cluster (UCC) ansatz. Although in a strict perturbation-theoretical framework all prove to be identical, differences emerge when the corresponding converged cluster amplitudes are used and depending on how the similarity-transformed UCC Hamiltonian is evaluated. The resulting excitation energies, however, do not significantly differ for systems well described by means of perturbation theory.