Entropy effects in hydrocarbon conversion reactions: free-energy integrations and transition-path sampling

The standard approach to ab initio simulations of activated chemical processes is based on the harmonic-oscillator/rigid-rotor approximation to transition state theory. However, there is increasing evidence that these approximations fail for reactions involving loosely bound reactant and/or transitions states where entropy makes a significant contribution to the free-energy reaction barrier. Examples are provided by the conversion (proton exchange, dehydrogenation, monomolecular cracking) of short alkanes over acidic zeolites. For proton exchange and monomolecular cracking the reaction path may be described reasonably well by simple vectorial reaction coordinates and the free energy of activation may be derived by free-energy integration schemes such as the Blue-Moon ensemble technique in combination with constrained ab initio molecular dynamics simulations. For alkane dehydrogenation, however, several reaction scenarios are in competition and techniques such as transition-path sampling must be used to determine the dominant reaction mechanism. In our paper we describe the fundamental aspects of these techniques and discuss their application to compute free-energy barriers for proton exchange between isobutane and acidic chabazite and for monomolecular cracking of propane. Dehydrogenation of propane has been studied using transition-path sampling. In this case the static approach based on harmonic transition state theory not only fails in producing accurate reaction barriers but even leads to incorrect predictions of reaction intermediates and products.