Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.