The Basis-set Superposition Error Historical Background

In a standard dimer calculation the energy of the supersystem (AB) is calculated with the union of the subsystem one-electron basis sets 

In practice, the monomer basis sets are never complete, an obvious exception being the H2 van der Waals molecule . The extension of the basis set in the dimer then results in a relatively better description of the dimer with respect to the monomers, yielding a correspondingly better energy. If the interaction energy is obtained as the difference of the separately calculated dimer and monomer energies, each with their own basis. 

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