Eight β-scission modes involving C 6 and C 8 olefin isomers are investigated using dispersion-corrected density functional theory (i.e., PBE-D) calculations. Potential energy surfaces are evaluated within an acidic H-ZSM-5 supercell containing a single, isolated active site. Minimum energy pathways are localized using the nudged elastic band method. The relative enthalpic barriers of β-scission steps can be described by the substitution order of the carbocationic carbon atom present in the reactant and transition states. Specifically, the total charge on the hydrocarbon fragment containing the β C atom increases going from the physi-or chemisorbed reactant state to the β-scission transition state; the magnitude of this change (+0.37e−0.97e) is found to correlate nearly monotonically with the activation energy (89−233 kJ mol −1 ). A comparison of 1°to 3°(E 1 ) and 3°to 1°(E 2 ) β-scission modes as well as 2°to 3°(B 1 ) and 3°to 2°(B 2 ) β-scission modes reveals that the barrier heights depend on the substitution order of the β C, indicating that a subcategorization of βscission modes is required based on the substitution order of the β C atom. Isomerization reactions, which are fast with respect to β-scission, enable reactant hydrocarbons to explore and find low-barrier β-scission pathways. Selectivities predicted on the basis of the relative barrier heights of β-scission modes accessible to C 6 and C 8 species indicate agreement with experimental observations.

The role of zeolite topology in the stepwise methylation of ethene by surface methoxides was investigated. Density functional theory was employed in the determination of reaction mechanisms and energy barriers. Elementary steps were studied across multiple frameworks (i.e., BEA, CHA, FER, MFI, and MOR) constituting a wide variety of confinement environments. Surface methoxides were found to react with ethene through a transition state containing planar CH 3 species, which was best stabilized at the intersection of the 10-membered ring channels of MFI. A cyclopropane reaction intermediate was found in all cases; its decomposition necessitated a transition state containing a primary carbocation, which was best stabilized within the 8-membered ring side pockets of MOR. The activation energies corresponding to each transition state geometry depend upon different aspects of the local pore topology, implying that confinement effects can not be simply correlated to pore size.

The full catalytic cycle for the self-metathesis of ethane was studied by density functional theory (DFT). The active site was a Tadihydride grafted on a Brønsted acid site [(tAlO) 2 Ta(H 2 )] of the internal pore surface of the FER zeolite. The transition state geometries and activation energies were determined through the nudged elastic band (NEB) method for each elementary step, and the complete cycle was found to be thermodynamically consistent. Investigated elementary steps include ethane CÀH σ-bond activation, ethylene desorption through R and β hydrogen elimination mechanisms, Ta-ethylcarbene formation, olefin metathesis, and hydrogenation of olefin metathesis products. For the activation of ethane, as compared to catalytic systems involving zeolitesupported Ga and Zn, a low barrier (∼64 kJ mol À1 ) was observed. In the olefin metathesis step, where Ta-ethylcarbene reacts with ethylene, it was found that the Ta-metallacyclobutane has a relatively high stability (∼143 kJ mol À1 ) as compared to similar metallacyclobutane species and that the forward decomposition of the Ta-metallacyclobutane is the most energetically demanding step.