Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities.

Long-range correlation energies are calculated using an approximation of the single-particle density-density response function of the system that leads to an expression requiring only occupied orbitals and eigenvalues. Dipole-dipole polarisabilities and isotropic leading-order dispersion coefficients obtained from this approximation are shown to be in a reasonable agreement with corresponding values from the experiment or dipole oscillator strength distributions. The localised polarisabilities were used to calculate a long-range correlation correction to a hybrid-generalised gradient approximation functional using a proper damping function at short ranges. It was found that the hybrid density-functional theory+dispersion method obtained in this way has a comparable accuracy than high-level ab initio wave function methods at a much lower computational cost. This has been analysed for a number of systems from the GMTKN30 database including subsets for noncovalently bound complexes, relative energies for sugar conformers and reaction energies and barrier heights of pericyclic reactions of some medium sized organic molecules.