Extension of the D3 dispersion coefficient model

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities $α$(i$ω$⁠). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.