Ab initio electronic structure methods such as Moller-Plesset (MP) theory can be used to compute electron affinities (EAs) of molecules or clusters of molecules to reasonable accuracy (a few tenths of an electron volt) For systems in which an electron is bound to a closed-shell neutral in a manner that primarily localizes the excess electron exterior to most of the electron density of the neutral, we investigate how a given level of ab initio description can be accurately described by a one-electron potential governing the excess electron's interaction with the neutral We show what ingredients such a potential must possess not only to reproduce the ab initio EA but also to have long-range electrostatic, polarization, and other contributions identical to the ab initio potential In particular, we show that using Hartree-Fock level electrostatic moments and polarizability can produce a one-electron potential consistent with MP2 theory To be consistent with MP3 theory, MP2-level electrostatics and polarizabilities must be used. The long-range components of the ab initio potential are shown to embody both orbital relaxation induced by the excess electron and the dispersion interactions between the excess electron and the other electrons of the neutral. Even though these individual contributions do not necessarily scale as r(-4), they are shown to combine into a total potential that can be represented in the familiar polarization form -1/2 alpha r(-4) These findings suggest that electrostatic potentials combined with polarization potentials scaling as r(-4) can indeed describe the relaxation (induction) and dispersion energies of an excess electron Finally, how these observations might assist in constructing new electron-molecule potentials is also discussed.