  We recently proposed a novel approach to converging electronic energies
equivalent to high-level coupled-cluster (CC) computations by combining the
deterministic CC($P$;$Q$) formalism with the stochastic configuration
interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article
extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev.
Lett. 119, 223003 (2017)], which focused on recovering the energies obtained
with the CC method with singles, doubles, and triples (CCSDT) using the
information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches
truncated at triples and quadruples. It also reports our first semi-stochastic
CC($P$;$Q$) calculations aimed at converging the energies that correspond to
the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The
ability of the semi-stochastic CC($P$;$Q$) formalism to recover the CCSDT and
CCSDTQ energies, even when electronic quasi-degeneracies and triply and
quadruply excited clusters become substantial, is illustrated by a few
numerical examples, including the F-F bond breaking in ${\rm F}_{2}$, the
automerization of cyclobutadiene, and the double dissociation of the water
molecule.
