Can coupled-cluster theory treat conical intersections?

Conical intersections between electronic states are of great importance for the understanding of radiationless ultrafast relaxation processes. In particular, accidental degeneracies of hypersurfaces, i.e., between states of the same symmetry, become increasingly relevant for larger molecular systems. Coupled-cluster theory, including both single and multireference based schemes, offers a size-extensive description of the electronic wave function, but it sacrifices the Hermitian character of the theory. In this contribution, we examine the consequences of anti-Hermitian contributions to the coupling matrix element between near-degenerate states such as linear dependent eigenvectors and complex eigenvalues. Numerical examples are given for conical intersections between two excited states calculated at the equation-of-motion coupled-cluster level which indeed show the predicted artifacts. A simple method is suggested which allows physically meaningful potential energy surfaces to be extracted from the otherwise ill-behaved results. This provides a perspective for obtaining potential energy surfaces near conical intersections at the coupled-cluster level.