Basis Set Superposition Errors and the Counterpoise Correction

The reason that the MP2/aug-cc-pVXZ results approach the MP2/CBS limit from below is that weakly bound complexes feature large basis set superposition errors (BSSEs). A tutorial on BSSEs, in theory and in practice, was presented earlier in this book series. Qualitatively, each molecule in the complex desires more basis functions to describe electron correlation effects more accurately. Each molecule can gain access to more basis functions, and can thus be stabilized, by moving closer to another molecule. This creates an artificial stabilization that lowers the energy when the molecules come closer together—simply because the electrons aroimd each molecule can be stabilized 

It is helpful to look at some simple equations to see exactly how the CP correction is applied. We may write the interaction energy of a bimolecular complex consisting of molecules A and B as 

If one then subtracts the total CP error, E from the equation for 

Although we are concerned primarily with computations of bimolecular complexes in this review, it is worth mentioning how the CP correction scheme can be extended to trimers or larger clusters. For a trimeric system, the CP-corrected interaction energy may be written as 

The total interaction energy is then written as a sum of these two-body interaction energies plus a three-body interaction energy  

---