For periodic problems like molecular torsions, Fourier-based kernels are intrinsically appropriate. In fact, Fourier functions are ultimately used to solve the corresponding Schrödinger Equations. But direct PES modelling using Fourier functions naïvely comes with problems like oscillations and need extra conditions and treatment as explained within our development of TAMkinTools. Such oscillations of the PES function between the computed points are in general unphysical, therefore we do not use Fourier-based kernels in this study. Instead, kernels are preferred that lead to rather smooth gradients without having to manually tune hyperparameters. In this study, we choose to apply the Matérn kernel for the periodic 1DHR PES problem. By replicating the PES shape at the left and right boundaries, we ensure that the fit meets periodic boundary conditions at the end points (0 • and 360 • ).