Correction of the basis set superposition error in SCF and MP2 interaction energies. The water dimer

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Abstract
There has been some discussion concerning whether basis set superposition error is more correctly evaluated using the full set of ghost orbitals of the partner molecule or some subset thereof. A formal treatment is presented, arguing that the full set is required at the Mo/ller–Plesset level. Numerical support for this position is provided by calculation of the interaction energy between a pair of water molecules, using a series of moderate sized basis sets ranging from 6-31G** to the [432/21] contraction suggested by Clementi and Habitz. These energies, at both the SCF and MP2 levels, behave erratically with respect to changes in details of the basis set, e.g., H p-function exponent. On the other hand, after counterpoise correction using the full set of partner ghost orbitals, the interaction energies are rather insensitive to basis set and behave in a manner consistent with calculated monomer properties. For long intersystem separations, the contribution of correlation to the interaction is repulsive despite the attractive influence of dispersion. This effect is attributed to partial account of intrasystem correlation and can be approximated at long distances via electrostatic terms linear in MP2-induced changes in the monomer moments.

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