This data set contains example input and output files from density functional theory calculations of rare earth systems, using the Vienna Ab initio Simulation Package (VASP), The data set it split into two parts. The first data set contains the input and output files of molecular dynamics simulations of MCl3 in solution, where (M = Nd, Gd and Er) at ambient conditions, which was modelled at 341 K using the optB88 exchange-correlation functional. The calculations were run in order to investigate speciation in rare earth chloride solutions, including trends across the row, using a light (Nd), medium (Gd) and heavy (Er) rare earth. These particular calculations were used to validate classical interatomic potentials that were used to perform more complex simulation on larger systems and longer timescales. Only the first 2 ps of the trajectories are deposited here, since the complete trajectories are large. The second data set contains example input and output files for lattice dynamics calculations of the thermodynamics properties (heat capacity and entropy) of Nd-monazite and Nd-xenotime at ambient conditions up to 1200 K. In addition, it includes scripts for processing and plots of final results. These are useful for thermodynamical modelling of rare earth systems. Only the input and output files for Nd are deposited here, since the files are large and input files for Gd and Er are identical, save for the change in element.