  Coupled-cluster theory with single and double excitations (CCSD) is a
promising ab initio method for the electronic structure of three-dimensional
metals, for which second-order perturbation theory (MP2) diverges in the
thermodynamic limit. However, due to the high cost and poor convergence of CCSD
with respect to basis size, applying CCSD to periodic systems often leads to
large basis set errors. In a common "composite" method, MP2 is used to recover
the missing dynamical correlation energy through a focal-point correction, but
the inadequacy of MP2 for metals raises questions about this approach. Here we
describe how high-energy excitations treated by MP2 can be "downfolded" into a
low-energy active space to be treated by CCSD. Comparing how the composite and
downfolding approaches perform for the uniform electron gas, we find that the
latter converges more quickly with respect to the basis set size. Nonetheless,
the composite approach is surprisingly accurate because it removes the
problematic MP2 treatment of double excitations near the Fermi surface. Using
the method to estimate the CCSD correlation energy in the combined complete
basis set and thermodynamic limits, we find CCSD recovers over 90% of the exact
correlation energy at $r_s=4$. We also test the composite and downfolding
approaches with the random-phase approximation used in place of MP2, yielding a
method that is more effective but more expensive.
