Smooth Dispersion\nIs Physically Appropriate: Assessing\nand Amending the D4 Dispersion Model

The addition of dispersion corrections to density functionals\nis\nessential for accurate energy and geometry predictions. Among them,\nthe D4 scheme is popular due to its low computational cost and high\naccuracy. However, due to its design, the D4 correction can occasionally\nlead to anomalies, such as unphysical curvature and bumps in the potential\nenergy surface. We find these anomalies are common in the D4 model,\nalthough observable consequences are rarer than in the D3 model for\nreasons we explain. Nevertheless, we uncover instances of unphysical\nlocal minima and stationary points with the D4 scheme and propose\ntwo solutions that yield smoother dispersion energy as a function\nof nuclear position. One is trivial to implement, based on a smoother\nreparametrization of Gaussian weighting (D4S) to find the effective\ncoordination number. The other replaces Gaussian weighting with soft\nlinear interpolation (D4SL). These new approaches usually remove artificial\nextremum points, while maintaining accuracy.