The second-order, two-electron Dyson propagator is derived using superoperator theory with a spin-adapted formulation. To include certain ladder diagrams to all orders, the shifted-denominator (SD2) approximation is made. Formal and computational comparisons with other approximations illustrate the advantages of the SD2 procedure. Vertical double ionization potentials (DIPs) for a set of closed-shell molecules are evaluated with the second-order propagator and the SD2 method. The results of the SD2 approximation are in good agreement with experiment. To systematically examine the quality of the results, we compared SD2 and equation-of-motion, coupled-cluster predictions. The average absolute discrepancy is for 36 doubly ionized states.
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