  Coupled-cluster theory with single, double, and perturbative triple
excitations (CCSD(T)) -- often considered the "gold standard" of main-group
quantum chemistry -- is inapplicable to three-dimensional metals due to an
infrared divergence, preventing its application to many important problems in
materials science. We study the full, nonperturbative inclusion of triple
excitations (CCSDT) and propose a new, iterative method, which we call
ring-CCSDT, that resums the essential triple excitations with the same $N^7$
run-time scaling as CCSD(T). CCSDT and ring-CCSDT are used to calculate the
correlation energy of the uniform electron gas at metallic densities and the
structural properties of solid lithium. Inclusion of connected triple
excitations is shown to be essential to achieving high accuracy. We also
investigate semiempirical CC methods based on spin-component scaling and the
distinguishable cluster approximation and find that they enhance the accuracy
of their parent ab initio methods.
