  We numerically examine divergences of the total energy in metallic systems of
approximate many-body theories using Hartree--Fock as a reference, including
perturbative (M\oller-Plesset, MP), coupled cluster (CC) and configuration
interaction (CI) approaches. Controlling for finite size effects and basis set
incompleteness error by comparison with energies from the random phase
approximation (RPA), we suggest convincingly that non-perturbative coupled
cluster theories are acceptable for modelling electronic interactions in metals
whilst perturbative coupled cluster theories are not. Data are provided from
the RPA with which it is possible to test other approximate finite-basis
methods for divergences with only modest computational cost.
