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.