Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5

Abstract

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

Molecular Dynamics with Chemical Accuracy─Alkane Adsorption in Acidic Zeolites

“…It uses DFT-D as a low-level method for the full periodic structure and second-order Møller–Plesset perturbation theory (MP2) as a high-level method for cluster models to locally describe the molecule–surface interactions. This hybrid MP2:DFT-D approach has been shown to yield MP2 quality adsorption energies for the whole periodic structure. ,, While it reduces the computational effort by 3 orders of magnitude compared to periodic MP2, it is still 2 orders of magnitude more expensive than DFT-D and only affordable for a few selected structures, e.g., the most stable adsorption complexes, but not for sampling the entire PES beyond these minimum-energy structures. Instead of the harmonic approximation around a minimum-energy structure (local approach, sometimes called “static”) ,− molecular dynamics (MD) is used for the global sampling of the PES. ,,,, This is essential to capture global anharmonicity and to properly describe the temperature-dependent spatial distribution of adsorbed molecules. However, MD simulations require easily 100,000 or more energy and force calculations to provide converged adsorption energies.…”

“…Instead of the harmonic approximation around a minimum-energy structure (local approach, sometimes called “static”) ,− molecular dynamics (MD) is used for the global sampling of the PES. ,,,, This is essential to capture global anharmonicity and to properly describe the temperature-dependent spatial distribution of adsorbed molecules. However, MD simulations require easily 100,000 or more energy and force calculations to provide converged adsorption energies.…”

Molecular Views on Mechanisms of Brønsted Acid-Catalyzed Reactions in Zeolites

“…A few very recent achievements have been reported that open the door to more systematic investigation of this question in the near future. 302 At the GGA+dispersion level of theory currently accessible for AIMD of hydrocarbons in zeolites, secondary carbenium ions are not always deep free energy minima and easily lead to spontaneous transfer of the proton to the zeolite framework, yielding the corresponding π-complex. 306,309,310 Notably, most investigations cited so far deal with the stability of carbenium ions in the bulk structure of zeolites, in the vicinity of bridging Si−(OH)−Al groups.…”

“…In ref 361, alkoxides are invoked as intermediates in that respect, but computational results tend to show that neutral π-complexes are expected to play a dominant kinetic role with respect to alkoxides. 302,306,310,363 For cyclic alkenes (in the case of an endocyclic C�C bond), three kinds of skeletal isomerization reactions can take place. 6 Type A isomerization is split in two subcategories (Figure 12c,d).…”

“…Earlier quantum chemistry calculations, in the 1980s and early 1990s, using small cluster models at semiempirical or Hartree–Fock levels, concluded that carbenium ions were transition states along the formation pathway of alkoxides, calculated to be local energy minima. − It was shown afterward, however, that such a conclusion could be impacted by several factors, beside the nature of the carbenium ion itself: primary versus secondary versus tertiary and variation of chain length. − First, the consideration of confinement effect in the model is crucial. Going from small clusters (with only one to three T sites) to much larger ones (encompassing the description of a complete cavity) or to periodic models, as it was undertaken starting from the second half of the 1990s, leads to an enhanced stabilization of charged species such as carbenium ions. ,− It also reveals steric constraints for the formation of alkoxides, depending on the local topology around each T site, preventing in some cases the formation of the C–O bond. ,, Second, the level of theory used in the calculation has a strong impact on the respective energies of alkoxides and carbenium ions. ,,− In the prototypical case of the tert -butyl ion formation starting from isobutene, hybrid QM/QM approaches at the MP2:PBE level demonstrated that the carbenium ion becomes a local energy minimum at this level of theory within ferrierite, whereas it was not the case at the GGA level (Figure a) . Finally, thermal effects were shown to favor carbenium ions with respect to alkoxides.…”