I thought that BSSE referred to the error induced by the
*incompleteness in the basis set*, that is, the lack of a sufficient
number of basis functions, but I feel that what people are talking about
here is the error in the *overlap between wavefunctions* (or orbitals)
The name says it itself Basis Set SUPERPOSITION Error.
The description of the atom can be improved by using the basis of
another atom (in a different place).
When you remove the second atom you noticeably affect the completeness
of the basis, so the counterpoise correction (ghost atoms) is often used
as a remedy for BSSE.
It does not however mean that with the second atom's basis your basis
for atom1 became complete. No. It became better but still far from
complete.
The idea of BSSE (for calculation of binding energies) is at least NOT
TO CHANGE the basis between two calculations, so that the error due to
incompletness of the basis would cancel out.
