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A simple method for computing accurate density-dependent dispersion coefficients is presented. The dispersion coefficients are modeled by a generalized gradient-type approximation to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a molecule, gives mean absolute errors in the C 6 coefficients for 90 complexes below 10%. The inclusion of the missing long-range van der Waals interactions in density functionals using the derived coefficients in a pair wise correction leads to highly accurate typical noncovalent interaction energies.