  While the title question is a clear 'yes' from purely theoretical arguments,
the case is less clear for practical calculations with finite (one-particle)
basis sets. To shed further light on this issue, the basis set limits of CCSD
(coupled cluster theory with all single and double excitations) and of
different approximate implementations of CCSD-F12 (explicitly correlated CCSD)
have been investigated on detail for the W4-17 thermochemical benchmark. Near
the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to
within their respective uncertainties (about \pm0.04 kcal/mol) due to residual
basis set incompleteness error, but a nontrivial difference remains between
CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static
correlation. The observed basis set convergence behavior results from the
superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b
difference (consisting mostly of third-order terms), and a more slowly
converging, repulsive, fourth-order difference between CCSD(F12*) and
CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b
if at all possible. There are some indications that the nZaPa family of basis
sets exhibits somewhat smoother convergence than the correlation consistent
family.
