  We present a time-dependent formulation of coupled cluster theory. This
theory allows for direct computation of the free energy of quantum systems at
finite temperature by imaginary time integration and is closely related to the
thermal cluster cumulant theory of Mukherjee and co-workers. Our derivation
highlights the connection to perturbation theory and zero-temperature coupled
cluster theory. We show explicitly how the finite-temperature coupled cluster
singles and doubles amplitude equations can be derived in analogy with the
zero-temperature theory and how response properties can be efficiently computed
using a variational Lagrangian. We discuss the implementation for realistic
systems and showcase the potential utility of the method with calculations of
the exchange correlation energy of the uniform electron gas at warm dense
matter conditions.
