A soft damping function for dispersion corrections with less overfitting
The use of damping functions in empirical dispersion correction schemes is common and widespread. These damping functions contain scaling and damping parameters, and they are usually optimized for the best performance in practical systems. In this study, it is shown that the overfitting problem can be present in current damping functions, which can sometimes yield erroneous results for real applications beyond the nature of training sets. To this end, we present a damping function called linear soft damping (lsd) that suffers less from this overfitting. This linear damping function damps the asymptotic curve more softly than existing damping functions, attempting to minimize the usual overcorrection. The performance of the proposed damping function was tested with benchmark sets for thermochemistry, reaction energies, and intramolecular interactions, as well as intermolecular interactions including nonequilibrium geometries. For noncovalent interactions, all three damping schemes considered in this study (lsd, lg, and BJ) roughly perform comparably (approximately within 1 kcal/mol), but for atomization energies, lsd clearly exhibits a better performance (up to 2-6 kcal/mol) compared to other schemes due to an overfitting in lg and BJ. The number of unphysical parameters resulting from global optimization also supports the overfitting symptoms shown in the latter numerical tests.