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Benchmark calculations on noncovalent interactions typically excludecorrelation effects beyond valence CCSD(T) owing to their steep computationalcost scaling. In this work, we consider their importance for water clusters,specifically, eight isomers of (H$_2$O)$_6$ and four Wales-Hodges isomers of(H$_2$O)$_{20}$. Higher order connected triples, $T_3$--(T), reducedissociation energies of the latter by about 0.4 kcal/mol, but this is morethan compensated by an increase of up to 0.85 kcal/mol due to connectedquadruple excitations. In general, higher-order correlation effects favor morecompact isomers over more `spread-out' ones. We also consider additional smalleffects for balance: scalar relativistics reduce binding in (H$_2$O)$_{20}$ byca. --0.4 kcal/mol, which fortuitously is compensated by the ca. 0.55 kcal/moldiagonal Born-Oppenheimer correction. Core-valence correlation has the greatestimpact, at ca. 1.3 kcal/mol for the icosamer.

Is valence CCSD(T) enough for the binding of water clusters? The isomers of (H$_2$O)$_6$ and (H$_2$O)$_{20}$ as a case study