Fast electron correlation methods for molecular clusters without basis set superposition errors

Two critical extensions to our fast, accurate, and easy-to-implement binary or ternary interaction method for weakly interacting molecular clusters [S. Hirata et al., Mol. Phys. 103, 2255 (2005)] have been proposed, implemented, and applied to water hexamers, hydrogen fluoride chains and rings, and neutral and zwitterionic glycine-water clusters with an excellent initial performance assessment result. Our original method included up to two- or three-body Coulomb, exchange, and correlation energies exactly and higher-order Coulomb energies in the dipole-dipole interaction approximation. In this work, the dipole moments are replaced by atom-centered point charges determined so that they reproduce the electrostatic potentials of the cluster subunits accurately and also self-consistently with one another in the cluster environment. They have been shown to lead to a dramatic improvement in the description of short-range electrostatic potentials not only of large, charge-separated subunits such as zwitterionic glycine but also of small subunits. Furthermore, basis set superposition errors (BSSEs) have been eliminated by combining the Valiron-Mayer function counterpoise (VMFC) correction with our binary or ternary interaction method. A new BSSE-correction scheme has been proposed on this basis, wherein three-body and all higher-order Coulomb effects on BSSE are also estimated. The BSSE-corrected ternary interaction method with atom-centered point charges reproduces the VMFC-corrected results within 0.1 kcal/mol. The proposed method is not only more efficient but also significantly more accurate than conventional correlation methods uncorrected of BSSE.