  To follow up on the unexpectedly-good performance of several coupled-cluster
models with approximate inclusion of 3-body clusters [J. Chem. Phys. 151,
064102 (2019)] we performed a more complete assessment of the 3CC method [J.
Chem. Phys. 125, 204105 (2006)] for accurate computational thermochemistry in
the standard HEAT framework. New spin-integrated implementation of the 3CC
method applicable to closed- and open-shell systems utilizes a new automated
toolchain for derivation, optimization, and evaluation of operator algebra in
many-body electronic structure. We found that with a double-zeta basis set the
3CC correlation energies and their atomization energy contributions are almost
always more accurate (with respect to the CCSDTQ reference) than the CCSDT
model as well as the standard CCSD(T) model. The mean absolute errors in
cc-pVDZ {3CC, CCSDT, and CCSD(T)} electronic (per valence electron) and
atomization energies relative to the CCSDTQ reference for the HEAT dataset [J.
Chem. Phys. 121, 11599 (2004)], were {24, 70, 122} $\mu E_h/e$ and {0.46, 2.00,
2.58} kJ/mol, respectively. The mean absolute errors in the complete-basis-set
limit {3CC, CCSDT, and CCSD(T)} atomization energies relative to the HEAT model
reference, were {0.52, 2.00, and 1.07} kJ/mol, The significant and systematic
reduction of the error by the 3CC method and its lower cost than CCSDT suggests
it as a viable candidate for post-CCSD(T) thermochemistry applications, as well
as the preferred alternative to CCSDT in general.
