  Many methods for computing electronic correlation effects at finite
temperature are related to many-body perturbation theory in the grand-canonical
ensemble. In most applications, however, the average number of electrons is
known rather than the chemical potential, requiring that expensive correlation
calculations must be repeated iteratively in search for the chemical potential
that yields the desired average number of electrons. In extended systems with
mobile charges, however, the long-ranged electrostatic interaction should
guarantee that the average ratio of negative and positive charges is one for
any finite chemical potential. All properties per electron are virtually
independent of the chemical potential, as for instance in an electric wire at
different voltage potentials.
  This work shows that the infinite-size limit of the exchange-correlation free
energy agrees with the infinite-size limit of the exchange-correlation grand
potential at a non-interacting chemical potential. The latter requires only one
expensive correlation calculation for each system size. Analogous to classical
simulations of long-range-interacting particles, this work uses a
regularization of the Coulomb interaction such that each electron on average
interacts only with as many electrons as there are electrons in the simulation,
avoiding interactions with periodic images.
  Numerical calculations of the warm uniform electron gas have been conducted
with the Spencer--Alavi regularization employing the finite-temperature Hartree
approximation for the self-consistent field and linearized finite-temperature
direct-ring coupled cluster doubles for treating correlation.
