Smooth dispersion is physically appropriate: Assessing and amending the D4 dispersion model

The addition of dispersion corrections to density functionals is essential for accurate energy and geometry predictions. Among them, the D4 scheme is popular due to low computational cost and high accuracy. However, due to its design, the D4 correction can occasionally lead to anomalies, such as un-physical curvature and bumps in the potential energy surface. We find these anomalies are common in the D4 model, although observable consequences are rarer than in the D3 model for reasons we explain. Nevertheless we uncover instances of unphysical local minima and stationary points with the D4 scheme, and propose two solutions that yield smoother dispersion energy as a function of nuclear position. One is trivial to implement, based on a smoother re-parametrization of gaussian weighting (D4S) to find the effective coordination number. The other replaces gaussian weighting with soft linear interpolation (D4SL). These new approaches usually remove artificial extremum points, while maintaining accuracy.