  At zero temperature coupled cluster theory is widely used to predict total
energies, ground state expectation values and even excited states for molecules
and extended systems. Generalizations to finite temperature exist, however,
they are in practice several orders of magnitude more demanding compared to the
zero temperature case since the amplitudes must be computed and stored for many
Matsubara frequencies to yield sufficiently accurate results.
  Instead of using Matsubara frequencies one can also work directly in the
imaginary time domain on the compact interval [0, beta]. The arising imaginary
time dependent coupled cluster amplitude integral equations are solved
numerically on a non-uniform grid. About a dozen grid points provide sufficient
accuracy if the Hamiltonian is repartitioned to include particle/hole
interactions in the non-perturbative part. In this framework the transition
from finite to zero temperature is uniform and comes at no extra costs,
allowing, for instance, to benchmark fractional occupancy formulations of
coupled cluster theories. Finite temperature direct ring coupled cluster
doubles free energies are calculated for various temperatures for solid
lithium, a metallic system, and for solid silicon, a semiconductor.
