Dehydrogenation of propane over Zn-MOR. Static and dynamic reaction energy diagram

The dehydrogenation of propane over Zn2+-exchanged mordenite has been studied theoretically using ab initio density-functional calculations at different levels of theory. We compare (i) total-energy calculations based on semilocal exchange-correlation functionals with those adding semi-empirical corrections for dispersion forces, (ii) calculations based on a large periodic model of the zeolite with calculations based on small and large finite cluster models, and (iii) calculations of the free energies of activation and of the reaction rates based on harmonic transition state theory (hTST) with those based on thermodynamic integration over free-energy gradients determined by constrained ab initio molecular dynamics. Dehydrogenation proceeds in four steps: (i) adsorption of propane on the Zn2+ cation, (ii) dissociation of a hydrogen atom leading to the formation of a Zn-propyl complex and a Bronsted acid site, (iii) reaction of the acid proton and a beta-H atom of propyl, resulting in the elimination of a hydrogen molecule, and (iv) desorption of propene from the Zn2+ cation. The periodic calculations demonstrate that the dispersion corrections increase the adsorption/desorption energies from 70 to 107 kJ/mol for propane and from 177 to 233 kJ/mol for propene and decrease the activation energy for H-dissociation from 73 to 61 kJ/mol, while the activation energy for the heterolytic dehydrogenation is almost unaffected with 132 kJ/mol. Hence, dispersion corrections are of foremost importance for lowering the activation energy for H-dissociation below the desorption energy of propane. While according to the periodic calculations the highest activation energies are predicted for the heterolytic dehydrogenation and the desorption of propene, cluster calculations predict a higher activation energy for H-dissociation than for H-2 elimination. Both hTST and thermodynamic integrations show that both activation processes lead to a loss of entropy because the transition state configurations admit for a lower degree of disorder than the initial and intermediate states. hTST consistently underestimates the loss of entropy, the anharmonic corrections are most important for the H-dissociation step. (C) 2010 Elsevier Inc. All rights reserved.