  We present a detailed discussion of our novel diagrammatic coupled cluster
Monte Carlo (diagCCMC) [Scott et al. J. Phys. Chem. Lett. 2019, 10, 925]. The
diagCCMC algorithm performs an imaginary-time propagation of the
similarity-transformed coupled cluster Schr\"odinger equation. Imaginary-time
updates are computed by stochastic sampling of the coupled cluster vector
function: each term is evaluated as a randomly realised diagram in the
connected expansion of the similarity-transformed Hamiltonian. We highlight
similarities and differences between deterministic and stochastic linked
coupled cluster theory when the latter is re-expressed as a sampling of the
diagrammatic expansion, and discuss details of our implementation that allow
for a walker-less realisation of the stochastic sampling. Finally, we
demonstrate that in the presence of locality, our algorithm can obtain a fixed
errorbar per electron while only requiring an asymptotic computational effort
that scales quartically with system size, independently of truncation level in
coupled cluster theory. The algorithm only requires an asymptotic memory costs
scaling linearly, as demonstrated previously. These scaling reductions require
no ad hoc modifications to the approach.
