The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, where the specific form of the GLE depends on the choice of projection formalism. We compare parameters derived from different GLE formulations using molecular dynamics (MD) simulations of the dihedral angle dynamics of butane in water. Our analysis reveals non-negligible non-Gaussian contributions of the orthogonal force in all GLEs, being most significant for the Mori-GLE, where all non-linearities are relegated to the orthogonal force. By using the orthogonal-force trajectory extracted from MD simulations to perform simulations of the GLE, we show that the non-Gaussianity and higher-than-two-point autocorrelations of the orthogonal force are relevant for accurately reproducing the dihedral-angle distribution and dynamics. We find that the accuracy of GLE simulations depends significantly on the chosen GLE formalism. Surprisingly, the Mori-GLE offers the most accurate framework for capturing the dihedral angle dynamics as judged by comparing barrier-crossing times calculated from different GLE formulations, provided an accurate non-Gaussian orthogonal-force trajectory with the correct higher-than-two-point autocorrelations is used.
