Unitary coupled-cluster theory for the electron propagator: electron attachment and physical properties <i>via</i> the intermediate state representation

A scheme for the calculation of electron-attachment (EA) processes within the framework of unitary coupled-cluster (UCC) theory is presented. Analogous to the description of electron-detachment, the intermediate state representation (ISR) approach is used for the formulation and its relation to the algebraic-diagrammatic construction scheme is pointed out. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions, but need to be approximated. Explicit working equations for two computational schemes referred to as EA-UCC2 and EA-UCC3 are given, providing electron-attachment energies and spectroscopic amplitudes of electron-attached states dominated by one-particle excitations correct through second and third order in perturbation theory, respectively. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is employed. In a benchmark against full configuration interaction (FCI) results including 50 states of 21 different species, both neutral and charged, closed- and open-shell, the novel methods are characterized by mean absolute errors of 0.15 eV (EA-UCC2) and 0.10 eV (EA-UCC3). Furthermore, an approach for the computation of physical properties of electron-attached as well as electron-detached states within the UCC framework is presented. It also builds upon the ISR approach, featuring an expectation value-like formulation similar to that of the equation-of-motion coupled-cluster (EOM-CC) method or the ISR approach of the algebraic-diagrammatic construction (ADC) method. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory are given and shown to be equivalent to those of the second-order ADC/ISR procedure.