First, we present non-equilibrium molecular dynamics (NEMD) results because the corresponding Soret coefficients serve as a benchmark for the subsequent equilibrium molecular dynamics (EMD) simulations. For both approaches, specific issues, pitfalls, and necessary procedures are highlighted to obtain reliable Soret coefficient data. This is followed by a comparison and discussion of the data for all Lennard-Jones models considered in this work, where two lean prediction models are also included. The first model is based on thermodynamic and approximate kinetic data, whereas the second one is a regression model that relies on Lennard-Jones and mass parameters of the force field. 3.1 NEMD: creating a benchmark