Dispersion from Polarizabilities of Atoms in Molecule: DPAIM

Abstract

A new atom–atom dispersion function DPAIM (dispersion from polarizabilities of atoms in molecules) has been developed. The dynamic polarizabilities, both dipole–dipole and quadrupole–quadrupole, of a set of reference molecules obtained from the time-dependent density functional theory (TD-DFT) are first spherically averaged and then split into AIM contributions using the generalized effective atomic sizes based on Hirshfeld’s partitioning of DFT molecular density. The polarizability of an atom in a target molecule is determined by scaling a weighted average of AIM polarizabilities of reference molecules with the closest generalized effective atomic sizes. The scaling uses an expansion in powers of the ratio of the atom’s generalized effective size in the target molecule to that in the reference molecule. Three adjustable parameters of this expansion were fitted to ab initio computed dispersion energies for a set of molecular dimers at large intermolecular separations. The dispersion coefficients are then obtained on the fly from the Casimir–Polder formula. DPAIM is the first dispersion function that uses the quadrupole–quadrupole polarizabilities in this way. The resulting asymptotic expansion is damped, with four damping parameters fitted to ab initio computed two-body dispersion plus exchange-dispersion energies at the second order with respect to the intermolecular perturbation operator for a set of molecular dimers. Benchmarking against an extensive and chemically diverse data set demonstrates that DPAIM represents true dispersion energies comparably to or better than published dispersion functions. Notably, this method exhibits accurate long-range and asymptotic behavior and performs consistently across interaction types, including dispersion-bound, hydrogen-bonded, and π-stacked systems. The DPAIM function was also combined with standard DFT methods by adjusting its damping parameters to fit a set of accurate total interaction energies. The resulting DFT+D approach demonstrates the performance comparable to or better than the published dispersion functions applied to the same functionals. In particular, the mean unsigned error on the benchmark test set of the ωB97M-V functional is reduced from 0.20 to 0.15 kcal/mol when the V dispersion functional is replaced by the DPAIM dispersion functions. Both the performance on the dispersion energies and in the DFT+D approach indicate that the DPAIM model captures dispersion interactions as accurately as the best published methods, while it may be considered the most physically appealing of such models.