In the present work the intermolecular BSSE, associated to the A-B interaction, is obtained by subtracting the intramolecular BSSE of the fragments from the intramolecular BSSE of the supermolecule, and considering every atom as a fragment in the calculation of each intramolecular BSSE. This atom by atom scheme (CP(aa)) is based on the consideration that the proximity of the fragments may affect the intramolecular BSSE of every involved species, and artificially influences the value of the BSSE associated to the supermolecule formation. It drastically decreases the reported counterpoise overcorrection of the A-B interaction, even though it does not deal with all the overcorrection because it includes all the orbitals, and not only the unoccupied ones. This new approach has been tested on the water dimer, some hydrogen fluoride weakly bonded complexes, the conformational analysis of 1,2-dichloroethane, and the reaction profile of formaldehyde + OH reaction.
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