Complex ground-state and excitation energies in coupled-cluster theory

Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these can principle take on complex values. In this paper we discuss the appearance energy values CC calculations from mathematical perspective. We analyze behaviour Hermitian matrices that perturbed (in manner) by real parameter. Based results show for with real-valued Hamiltonian generally takes value. Furthermore, case only occur context conical intersections. such case, unphysical consequences encountered as wrong dimension intersection seam, large numerical deviations full configuration-interaction (FCI) results, square-root-like potential surfaces near intersection. complex-valued matrix elements, it turns out to be expected ground excited states when no symmetry is present. confirm occurrence sample using six-state model H2O molecule strong magnetic field. furthermore prevent Lastly, demonstrate most cases part provides very good approximation FCI energy.