Smoother Semiclassical\nDispersion for Density Functional\nTheory via D3S: Understanding and Addressing Unphysical Minima in\nthe D3 Dispersion Correction Model

One of the most widely used and computationally efficient\nmodels\nthat accounts for London dispersion interactions within density functional\ntheory (DFT) is the D3 dispersion correction model. In this work,\nwe demonstrate that this model can induce the appearance of unphysical\nminima on the potential energy surface (PES) when the coordination\nnumber of atoms changes. Optimizing to these artifactual structures\ncan lead to significant errors in determining the interaction energy\nbetween two molecules and in estimating the thermodynamic properties\nof the system. In several specific examples, such as Kuratowski-type\nH<sub>2</sub>–NiKur and H<sub>2</sub>–PdKur clusters,\nthese local minima exhibited extremely high PES curvature, resulting\nin incorrect estimations of harmonic frequencies and significant overestimations\nof zero-point energy and enthalpy values. Although such erroneous\nbehavior of the D3 model is relatively rare, it can occur across a\nwide range of chemical species, including molecules like the [Li(C<sub>6</sub>H<sub>6</sub>)]<sup>+</sup> complex and the dispiro(acridan)-substituted\npyracene (DSAP) molecule. Our analysis reveals that the root of the\nproblem lies in the definition of the AB atomic-pair dependent C<sub>6</sub><sup>AB</sup> coefficients in the D3 model. To address this\nissue, we propose a reparameterization of the D3 model by introducing\na modified C<sub>6</sub><sup>AB</sup> functional form that now depends\non the specific pair of considered atoms. This new model, termed D3-Smooth\n(or D3S for short), is designed to smooth out the PES associated with\nthe dispersion correction. By doing so, we demonstrate that D3S eliminates\nunphysical local minima while maintaining the quite satisfactory accuracy\nof the parent D3 method in interaction energy benchmark sets. For\nexample, the RMS difference between using the D3(BJ) correction to\nB3LYP and the D3S(BJ) correction across the large MGCDB84 data set\nof nearly 5000 data points is only 0.12 kJ/mol. Similar results are\nobtained for every other D3-corrected functional tested. Consistent\nwith this result, no significant improvement could be obtained for\nthe B3LYP-D3S(0) correction by reoptimizing the damping function.