We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to rs = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities.
REFERENCES
More formally where M is the number of basis functions in the system.
We have adopted δτ rather than τ as in Ref. 1 so as to be more consistent with the notation of Alavi et al.
The converse, that solutions to the iteration will also be coupled cluster solutions, is not necessarily true, though we have not found any situations where this is the case. Indeed there is no guarantee that this iteration procedure will converge, though with a sensible choice of δτ it appears to be convergent for primarily single-reference systems.
Note that our previous publication used the word excitor for both the operator and the particle.
This makes use of the PELE suite (see https://github.com/pele-python/pele), and we will describe details of this elsewhere.
