Unified Inter- and Intramolecular Dispersion Correction Formula for Generalized Gradient Approximation Density Functional Theory

Abstract

Density functionals fail to provide a consistent description of weak intra- (i.e., short-range) and inter- (i.e., long-range) molecular interactions arising from nonoverlapping electron densities. An efficient way to correct the long-range errors is to add an empirical atom pair wise interaction-correction, inspired by the Lennard-Jones potential (R⁻⁶ dependence). We show that the universal damping function of Tang and Toennies (TT) that includes higher-order correction terms (R⁻⁸ and R⁻¹⁰ dependent) reduces the intramolecular errors more efficiently, without altering the long-range correction. For general applicability, the TT damping function is augmented by a Fermi damping to prevent corrections at covalent distances. The performance of the new dD10 correction was tested in combination with three nonempirical GGAs (PBE, PBEsol, RGE2) on 64 illustrative reaction energies featuring both intra- and intermolecular interactions. With only two empirical parameters, PBE-dD10 outperforms the computationally more demanding and most recent functionals such as M06-2X or B2PLYP-D (MAD = 3.78 and 1.95 kcal mol⁻¹, respectively). At the cc-pVTZ level, PBE-dD10 (MAD = 1.24 kcal mol⁻¹) considerably reduces common DFT errors successfully balancing intra- (short-range) and inter- (long-range) molecular interactions. While REG2-dD10 performs closely to PBE-dD10 (MAD = 1.48 kcal mol⁻¹), the overall MAD of PBEsol-dD10 is again slightly higher (MAD = 1.76 kcal mol⁻¹).