Some Observations on Counterpoise Corrections for Explicitly Correlated Calculations on Noncovalent Interactions

The basis set convergence of explicitly correlated <i>ab initio</i> methods, when applied to noncovalent interactions, has been considered in the presence (and absence) of Boys–Bernardi counterpoise corrections, as well as using “half-counterpoise” (the average of raw and counterpoise-corrected values) as recently advocated in this journal [Burns, L. A.; Marshall, M. S.; Sherrill, C. D. <i>J. Chem. Theory Comput.</i> <b>2014</b>, <i>10</i>, 49–57]. Reference results were obtained using basis sets so large that BSSE (basis set superposition error) can be shown to be negligible. For the HF+CABS component, full counterpoise unequivocally exhibits the fastest basis set convergence. However, at the MP2-F12 and CCSD­(T*)-F12b levels, surprisingly good <i>uncorrected</i> results can be obtained with small basis sets like cc-pVDZ-F12, owing to error compensation between basis set superposition error (which overbinds) and intrinsic basis set insufficiency (which underbinds). For intermediate sets like cc-pVTZ-F12, “half–half” averages work best, while for large basis sets like cc-pVQZ-F12, full counterpoise may be preferred but BSSE in uncorrected values is tolerably small for most purposes. A composite scheme in which CCSD­(T)–MP2 “high level corrections” obtained at the CCSD­(T*)-F12b/cc-pVDZ-F12 level are combined with “half-counterpoise” MP2-F12/cc-pVTZ-F12 interaction energies yields surprisingly good performance for standard benchmark sets like S22 and S66.