Abstract The ab initio calculation of molecular electron affinities (EA) is a difficult task because the energy of interest is a very small fraction of the total electronic energy of the parent neutral. That is, EAs typically lie in the 0.01–10 eV range, but the total electronic energy of even a small molecule is usually several orders of magnitude larger. Moreover, because the EA is an intensive quantity but the total energy is an extensive quantity, the difficulty in evaluating EAs to within a fixed specified (e.g., ±0.1 eV) accuracy becomes more and more difficult as the size and number of electrons in the molecule grows. The situation becomes especially problematic when studying extended systems such as solids, polymers, or surfaces for which the EA is an infinitesimal fraction of the total energy. The equations of motion (EOM) methods offer a route to calculating the intensive EAs directly as eigenvalues of a set of working equations. A history of the development of the EOM theories as applied to EAs, their numerous practical implementations, and their relations to Green's function or propagator theories are covered in this contribution. EOM methods based upon Møller–Plesset, multiconfiguration self‐consistent field, and coupled‐cluster reference wave functions are included in the discussion as is the application of EOM methods to metastable resonance states of anions.

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