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

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches