Does Basis Set Superposition Error Significantly Affect Post‐<scp>CCSD</scp>(<i>T</i>) Corrections?

We have investigated the title question for both a subset of the W4-11 total atomization energies benchmark, and for the A24x8 noncovalent interactions benchmark. Overall, counterpoise corrections to post-CCSD(T) contributions are about two orders of magnitude less important than those to the CCSD(T) interaction energy. Counterpoise corrections for connected quadruple substitutions (Q) are negligible, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mfenced><mml:mi>Q</mml:mi></mml:mfenced> <mml:mi>Λ</mml:mi></mml:msub> <mml:mo>-</mml:mo> <mml:mfenced><mml:mi>Q</mml:mi></mml:mfenced> </mml:mrow> <mml:annotation>$$ {(Q)}_{\Lambda}-(Q) $$</mml:annotation></mml:semantics> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>4</mml:mn></mml:msub> <mml:mo>-</mml:mo> <mml:mfenced><mml:mi>Q</mml:mi></mml:mfenced> </mml:mrow> <mml:annotation>$$ {T}_4-(Q) $$</mml:annotation></mml:semantics> </mml:math> especially so. In contrast, for atomization energies, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>3</mml:mn></mml:msub> <mml:mo>-</mml:mo> <mml:mfenced><mml:mi>T</mml:mi></mml:mfenced> </mml:mrow> <mml:annotation>$$ {T}_3-(T) $$</mml:annotation></mml:semantics> </mml:math> counterpoise correction can reach about 0.05 kcal/mol for small basis sets like cc-pVDZ, thought it rapidly tapers off with cc-pVTZ and especially aug-cc-pVTZ basis sets. It is reduced to insignificance by the extrapolation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>3</mml:mn></mml:msub> <mml:mo>-</mml:mo> <mml:mfenced><mml:mi>T</mml:mi></mml:mfenced> </mml:mrow> <mml:annotation>$$ {T}_3-(T) $$</mml:annotation></mml:semantics> </mml:math> applied in both W4 and HEAT thermochemistry protocols. In noncovalent dimers, the differential BSSE on post-CCSD(T) correlation contributions is negligible even in basis sets as small as the unpolarized split-valence cc-pVDZ(no d).