Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments
The theoretical description of electronic resonances is extended beyond calculations of energies and lifetimes. We present the formalism for calculating Dyson orbitals and transition dipole moments within the equation-of-motion coupled-cluster singles and doubles method for electron-attached states augmented by a complex absorbing potential (CAP-EOM-EA-CCSD). The capabilities of the new methodology are illustrated by calculations of Dyson orbitals of various transient anions. We also present calculations of transition dipole moments between transient and stable anionic states as well as between different transient states. Dyson orbitals characterize the differences between the initial neutral and final electron-attached states without invoking the mean-field approximation. By extending the molecular-orbital description to correlated many-electron wave functions, they deliver qualitative insights into the character of resonance states. Dyson orbitals and transition moments are also needed for calculating experimental observables such as spectra and cross sections. The dependence of Dyson orbitals and transition moments on the CAP strength is investigated. We show that physically meaningful results for these quantities are obtained only in the framework of non-Hermitian quantum mechanics, e.g., in the presence of a CAP, when studying resonances. We illustrate how Dyson orbitals help understand the properties of metastable species and how they are affected by replacing the usual scalar product by the so-called c-product.