Ab initio and density functional study of the activation barrier for ethane cracking in cluster models of zeolite H-ZSM-5

Protolytic cracking of ethane in zeolites has been investigated using quant um-chemical techniques and a cluster model of the zeolite acid site. An alu minosilicate cluster model containing five tetrahedral (Si, Al) atoms (5T) was used to locate all of the stationary points along a reaction path fur e thane cracking at the HF/6-31G(d), B3LYP/6-31 G(d), and MP2(FC)/6-31 G(d) l evels of theory. The cracking reaction occurs via a protonated structure th at is a carbonium-like ion and is a transition state on the potential energ y surface. The activation barrier for cracking calculated at each level of theory was refined by including (i) vibrational energies at the experimenta l reaction temperature of 773 K, (ii) electron correlation and/or all exten ded basis set at the B3LYP/6-311+G(3df,2p) or MP2(FC)/6-311+G(3df,2p) level s, and (iii) the influence of the surrounding zeolite lattice from a 58T cl uster model of the zeolite H-ZSM-5. The barrier is especially sensitive to the long-range electrostatic effect of the lattice, which reduces it by 14. 5 kcal/mol from the value obtained with the 5T cluster. The final calculate d barrier of 54.1 kcal/mol at the MP2(FC)/6-311+G(3df,2p)//MP2(FC)/6-31G(d) level, including corrections, is significantly smaller than values obtaine d by previous theoretical studies and is in reasonable agreement with typic al experimental values for short alkanes. The other levels of theory give s imilar values for the barrier.