Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations

The Roothaan equations have been modified to compute molecular interactions between weakly bonded systems at the SCF level of theory without the basis set superposition error (BSSE). The increase in complication with respect to the usual SCF algorithm is negligible. Calculation of the SCF energy on large systems, such as nucleic acid pairs, does not pose any computational problem. At the same time, it is shown that a modest change in basis-set quality from 3-21G to 6-31G changes the binding energy by about 50% when computed according to standard SCF “supermolecule” techniques, while remaining practically constant when computed without introducing BSSE. Bader analysis shows that the amount of charge transferred between the interacting units is of the same order of magnitude when performed on standard SCF wave functions and those computed using the new method. The large difference between the corresponding computed energies is thus ascribed to the BSSE. © 1996 John Wiley & Sons, Inc.     

Dressed Second-order Epstein–Nesbet Perturbation Theory and Consequences of Orbital Delocalization for the BSSE Correction in Dimer Systems (in Honor of J.-P. Malrieu)

The dressed diagonal approximation to the self-consistent – size consistent CI, corrected for off-diagonal Fock matrix elements in localized orbitals is developed and applied to the ammoniac dimer system. A quite correct correlation energy can be obtained for this system, with a significantly reduced dependence of the results on the choice of the localization procedure. When calculating an interaction energy, the choice of the monomer orbitals and the application of the Boys–Bernardi counterpoise procedure shows in this case an unusual behavior: the correlation energy does not increase with the size of the atomic basis sets. Nevertheless a reasonable potential curve can be obtained.     

Perturbation calculation of the interaction energy using orthogonalized orbitals

The diagrammatic Rayleigh-Schr?dinger perturbation theory for the interaction of two closed-shell systems is developed up to the third order of pertur-bation using orthogonalized orbitals. The interaction energy is expressed by the Rayleigh-Schr?dinger perturbation expansion. A simple approach for the estimation of basis set superposition error is introduced. The preliminary calculations of the intermolecular interactions for the He dimer within the augmented cc-pVTZ basis set are compared with the supermolecular approach, perturbation calculation in biorthogonal basis sets and symmetry adapted perturbation theory results. Received: 17 December 1996 / Accepted: 5 November 1997     

On the non-additivity of the basis set superposition error and how to prevent its appearance

An analytical consideration is made for the simplest possible model in which the BSSE problem may appear. The results demonstrate that BSSE cannot be corrected in any consistent manner by readjusting the monomer energies to the enlarged basis, because the energy effects caused by BSSE and by the true interactions are not additive. The way out is to correct BSSE, or prevent its appearance by an appropriate analysis and special treatment at the supermolecule level, permitting to keep the supermolecule problem consistent with the monomer calculations, as provided by the chemical Hamiltonian approach recently introduced.     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001