Some observations on counterpoise corrections for explicitly correlated calculations on noncovalent interactions

The basis set convergence of explicitly correlated ab initio 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. J. Chem. Theory Comput. 2014, 10, 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 uncorrected 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.