Comparison of Free Energy Surfaces Calculations from Ab Initio Molecular Dynamic Simulations at the Example of Two Transition Metal Catalyzed Reactions

Abstract

We carried out ab initio molecular dynamic simulations in order to determine the free energy surfaces of two selected reactions including solvents, namely a rearrangement of a ruthenium oxoester in water and a carbon dioxide addition to a palladium complex in carbon dioxide. For the latter reaction we also investigated the gas phase reaction in order to take solvent effects into account. We used two techniques to reconstruct the free energy surfaces: thermodynamic integration and metadynamics. Furthermore, we gave a reasonable error estimation of the computed free energy surface. We calculated a reaction barrier of ΔF = 59.5 ± 8.5 kJ mol−1 for the rearrangement of a ruthenium oxoester in water from thermodynamic integration. For the carbon dioxide addition to the palladium complex in carbon dioxide we found a ΔF = 44.9 ± 3.3 kJ mol−1 from metadynamics simulations with one collective variable. The investigation of the same reactions in the gas phase resulted in ΔF = 24.9 ± 6.7 kJ mol−1 from thermodynamic integration, in ΔF = 26.7 ± 2.3 kJ mol−1 from metadynamics simulations with one collective variable, and in ΔF = 27.1 ± 5.9 kJ mol−1 from metadynamics simulations with two collective variables.