Critical evaluation of some computational approaches to the problem of basis set superposition error

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Abstract
The basis set extension (BSE) effects such as primary and secondary basis set superposition errors (BSSE) are discussed on the formal and numerical ground. The symmetry-adapted perturbation theory of intermolecular forces offers an independent reference point to determine efficacy of some computational approaches aiming at elimination of BSSE. The formal and numerical results support the credibility of the function counterpoise method which dictates that the dimer energy calculated within a supermolecular approach decomposes into monomer energies reproduced with the dimer centered basis set and the interaction energy term which also takes advantage of the full dimer basis. Another consistent approach was found to be Cullen's ''strictly monomer molecular orbital'' SCF method [J. M. Cullen, Int. J. Quantum Chem. Symp. 25, 193 (1991)] in which all BSE effects are a priori eliminated. This approach misses, however, the charge transfer component of the interaction energy. The SCF and MP2 results obtained within the ''chemical Hamiltonian approach'' [J. Noga and A. Vibok, Chem. Phys. Lett. 180, 114 (1991)] were found to be inconsistent with the interaction energies resulting from the symmetry-adapted perturbation theory. The constraint equations of Sadlej's ''constrained dimer function'' approach [A. J. Sadlej, J. Chem. Phys. 95, 6707 (1991)] were shown to degrade the quality of dimer orbitals in comparison with the quality of monomer orbitals obtained with their monomer centered basis sets.