The possibilities of obtaining accurate total energies from GW calculations
at Various levels of self-consistency are investigated. In the conserving
approximation known as the fully self-consistent GW approach there is no am
biguity in calculating the total energy, and the results for the electron a
s compare well with those of accurate Monte Carlo calculations. We demonstr
ate how to obtain chemical potentials and total energies of similar accurac
y from partially self-consistent (GW(0)) calculations.