Unequivocal relations between properties of solid Brønsted acids and their catalytic function must be developed further to provide guidance for their design and application. Structure-function relations for solid Brønsted acid catalysis are developed here on Keggin polyoxometalate (POM) clusters and proton forms of zeolites because their well-defined structures permit reliable calculations of their deprotonation energies (DPE) by theory as measures of acid strength. Keggin POM clusters with W-metal atoms, but different central atoms (P, Si, Al, Co), have a wide range of acid strengths and reactivities without concomitant structural changes. Zeolites also have known structures and DPE values that are accessible to theory, however, their acid sites are located within voids of molecular dimensions, which stabilize confined reactants and transition states via van der Waals interactions. CH3OH dehydration and isomerization of C6 alkanes with different backbone structures served as probes of reactivity on these solid acids and provided illustrative examples of how reactions sense the strength and the confining environments of solid acids through the stabilities of intermediates and transition states that mediate them. Rate constants of kinetically-relevant steps in these reactions were obtained from mechanism-based interpretations of rates that were normalized as turnovers by counting the number of accessible protons with 2,6-di-tertbutyl pyridine titrations during catalysis. These rate constants were correlated with the catalyst DPE values in structure-function relations to determine how reactions "sense" the strength and the solvating environments of solid acids.
Rate constants decrease exponentially with increasing DPE values on POM clusters for all probe reactions; these trends reflect predominantly higher activation energies on weaker acids because ion-pairs at transition states, a ubiquitous feature of Brønsted acid catalysis, contain less stable conjugate anions. The dependences of rate constants on DPE further suggest that activation energies change by much less than the commensurate change in DPE because the higher energy needed to deprotonate weaker acids is largely recovered at transition states via electrostatic interactions between cationic reactants and the conjugate anion. Isomerization rate constants of C6 alkanes changed similarly with DPE, in spite of large differences in their values. Cyclopropyl carbenium ions mediate each of these isomerizations at transition states of kinetically-relevant steps. Their similar charge distributions interact with conjugate anions equally via electrostatic interactions at transition states; as a result, they compensate for interactions between protons and anions equally and cause similar sensitivities to acid strength. Reactants with lower rate constants have transition state cations with less stable gas-phase analogs, however, because these are properties of non-interacting cations, they are catalyst independent and do not influence a reaction's sensitivity to DPE. Rate constants for water elimination from H-bonded alkanol intermediates are more sensitive to DPE for bimolecular CH3OH dehydration than previously reported for unimolecular butanol dehydration. Unimolecular dehydration transition states have more localized charges than bimolecular dehydration transition states where cationic charges are distributed across multiple reactant molecules. The localized cations at unimolecular dehydration transition states more closely resemble protons and are more effective at interacting with conjugate anions, causing weaker effects of DPE. The effects of DPE are weaker for CH3OH dehydration when rate constants measure transition states from reacting intermediates that are ion-pairs (than from uncharged H-bonded intermediates) because conjugate anions are present at both species and affect their stabilities similarly.
Zeolites are significantly weaker acids than Keggin POM clusters according to their DPE values, yet their reactivities fall within the range of POM clusters for these probe reactions. Larger alkane isomerization rate constants are measured on zeolite BEA than are predicted from its DPE value because significant van der Waals forces stabilize confined cyclopropyl carbenium ions at transition states and overcompensate for any additional entropy loss caused by confinement. Transition state solvation reduces isomerization activation energies because they are measured with respect to gas-phase reactants that are unconfined. Confinement of acid sites within the channels of BEA favors alkyl shift reactions over those that change the degree of hydrocarbon branching and also favor reactions that have less branched transition states. Confinement preferentially stabilizes those transition state cations that best interact with zeolite channel walls via van der Waals contacts. The effects of confinement are weaker for CH3OH dehydration when bimolecular transition states are measured with respect to intermediates where both CH3OH reactants are confined than intermediates where one of the CH3OH is unconfined in the gas-phase.
These relations demonstrate how fundamental properties of solid acids such as their acid strengths and their confining environments, influence stabilities of relevant intermediates and transition states, and by inference influence reactivity, according to their charges and the sizes of confined species. The effects of acid strength are strongest when uncharged reactive intermediates form transition state cations that interact weakly with conjugate anions because of their diffuse charges. The effects of acid strength weaken as transition states become more similar to a proton or as reacting intermediates also become ion-pairs. The effects of confinement are determined by van der Waals stabilization of transition states; these effects are most pronounced when reactants or reacting intermediates are unconfined. The success of these relations indicates the importance of using well-defined acids whose properties can be assessed unambiguously, counting the number of active sites directly during reactions, and interpreting reactivity as chemical events.
The effects of composition on the DPE values and reactivities of Keggin clusters are investigated further using density functional theory (DFT) because their well-defined structures permit reliable calculations of their properties by theoretical methods. DPE values are dissected into energy terms that reflect covalent and electrostatic interactions between protons and anions by using thermochemical cycles. Similar thermochemical cycles describing interaction energies between conjugate anions and organic cations indicate how catalyst composition influences reactivity through the stabilities of transition states and intermediates, specifically shown here for CH3OH dehydration. Central atoms of Keggin clusters influence the densities of delocalized electrons in anions, which determine their electrostatic interactions with cations, while addenda atoms influence both covalent and electrostatic interactions between ions. Central atoms influence the stabilization of protons and organic cations because they both interact with the delocalized electrons. The charge distributions of cations determine how strongly changes in the anionic distribution affect electrostatic interactions. Protons are the cation that is most sensitive to changes in the anion because of their localized charges and close proximities to anions. Addenda atoms influence the stabilities protons much more strongly than ion-pair transition states or intermediates, because the latter have much weaker covalent interactions with anions than the former. As a results, solid acids with different covalent contributions to OH bonds cannot be compared directly using DPE values as the descriptor for acid strength in structure-function relations, because ion-pair transition states do not recover covalent interactions that must be overcome to deprotonate the catalyst. H-atom addition energies (HAE), which are also accessible for Keggin clusters from DFT, probe the local abilities of catalysts to accept H-atoms and electrons. HAE values are accurate descriptors of alkane and alkanol oxidative dehydrogenation (ODH) reactions, because H-atom addition and kinetically-relevant H-abstraction steps in ODH reactions both transfer electrons to unoccupied metal atom orbitals, the energies of which are consequential for ODH rates and HAE values.
