Protolytic cracking of ethane in zeolites has been investigated using quantum-chemical techniques and a cluster model of the zeolite acid site. An aluminosilicate cluster model containing five tetrahedral (Si, Al) atoms (5T) was used to locate all of the stationary points along a reaction path for ethane cracking at the HF/6-31G(d), B3LYP/6-31G(d), and MP2(FC)/6-31G(d) levels of theory. The cracking reaction occurs via a protonated structure that is a carbonium-like ion and is a transition state on the potential energy surface. The activation barrier for cracking calculated at each level of theory was refined by including (i) vibrational energies at the experimental reaction temperature of 773 K, (ii) electron correlation and/or an extended basis set at the B3LYP/6-311+G(3df,2p) or MP2(FC)/6-311+G(3df,2p) levels, and (iii) the influence of the surrounding zeolite lattice from a 58T cluster 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 calculated 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 obtained by previous theoretical studies and is in reasonable agreement with typical experimental values for short alkanes. The other levels of theory give similar values for the barrier.

A combined experimental and theoretical study of vanadium oxide monomers on a θ-alumina surface under different environments has identified four different structures. Deep UV Raman results suggest that vanadia is attached predominantly to an aluminum site that was an isolated terminal Al−OH group on the θ-alumina surface. The preresonance Raman spectra for vanadium oxide supported on θ-alumina with a very low VO x surface density show three distinct VO bands under dehydrated conditions. The observed frequencies match well with the calculated stretching frequencies from B3LYP density functional theory for tridendate, bidendate, and molecular structures of vanadium oxide monomers on a dehydrated surface. The free energies calculated for these three structures from density functional theory as a function of temperature suggest that all three could exist on the surface with the tridentate structure being the most stable of the three on the dehydrated surface. Different structures and different degrees of vibrational coupling of V−O to V=O modes may cause the appearance of three VO bands in the preresonance Raman spectra. On the hydrated surface, the Raman spectra show a V−O band, in agreement with the calculated frequency for a monodentate structure on this surface. Finally, the calculated free energies of hydrated and dehydrated surfaces indicate a transition from a hydrated to a dehydrated θ-alumina surface occurs at around 600 K at 10−6 atm pressure of H2O.

Ab initio molecular orbital calculations using Hartree−Fock theory and Møller−Plesset perturbation theory have been used to study the interaction of H2O with the Brønsted acid site in the zeolite H-ZSM-5. Aluminosilicate clusters with up to 28 T atoms (T = Si, Al) were used as models for the zeolite framework. Full optimization of a 3 T atom cluster at the MP2/6-31G(d) level indicates that the “ion-pair” structure, Z-···HOH2 +, formed by proton transfer from the acid site of the zeolite (ZH) to the adsorbed H2O molecule, is a transition state, while the “neutral” adsorption structure, ZH···OH2, is a local energy minimum. Partial optimization of a larger 8 T cluster at the HF/6-31G(d) level also gave results suggesting that the ion-pair structure is a transition state. Calculations were carried out to obtain corrections for high levels of theory, zero-point energies, and larger cluster size. The resulting energy difference between the neutral and ion-pair structure is small (less than 5 kcal/mol and possibly close to zero). The interaction energy of ZH···OH2 is 13−14 kcal/mol, in agreement with experiment. We find that addition of a second H2O molecule to Z-···HOH2 + in the 3 T atom cluster stabilizes the ion-pair structure, Z-···H(OH2)2 +, making it a local energy minimum. Finally, calculated vibrational frequencies for a 3 T atom cluster are used to help interpret experimental IR absorption spectra.