  Basis set convergence of correlation effects on molecular atomization
energies beyond the CCSD (coupled cluster with singles and doubles)
approximation has been studied near the one-particle basis set limit.
Quasiperturbative connected triple excitations, (T), converge more rapidly than
$L^{-3}$ (where $L$ is the highest angular momentum represented in the basis
set), while higher-order connected triples, $T_3-(T)$, converge more slowly --
empirically, $\propto L^{-5/2}$. Quasiperturbative connected quadruple
excitations, (Q), converge smoothly as $\propto L^{-3}$ starting with the
cc-pVTZ basis set, while the cc-pVDZ basis set causes overshooting of the
contribution in highly polar systems. Higher-order connected quadruples display
only weak, but somewhat erratic, basis set dependence. Connected quintuple
excitations converge very rapidly with the basis set, to the point where even
an unpolarized double-zeta basis set yields useful numbers. In cases where
fully iterative CCSDTQ5 (coupled cluster up to connected quintuples)
calculations are not an option, CCSDTQ(5) (i.e., coupled cluster up to
connected quadruples plus a quasiperturbative connected quintuples correction)
cannot be relied upon in the presence of significant nondynamical correlation,
whereas CCSDTQ(5)$_\Lambda$ represents a viable alternative. Connected
quadruples corrections to the core-valence contribution are thermochemically
significant in some systems. [...] We conclude that ``$3\sigma\leq 1$ kJ/mol''
thermochemistry is feasible with current technology, but that the more
ambitious goal of $\pm$10 cm$^{-1}$ accuracy is illusory, at least for
atomization energies.
