Correlation Energy Divergences in Metallic Systems

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.