Protonated Isobutene in Zeolites: tert‐Butyl Cation or Alkoxide?

Substantially red-shifted as a result of hydrogen-bond formation with the zeolite framework: This characteristic of a CH infrared band can be used to identify the tert-butyl carbenium ion in zeolite ferrierite (see picture). Above 120 K, this complex becomes more stable than the tert-butoxide or the isobutoxide of ferrierite. Acid zeolite catalysts are industrially used for a variety of hydrocarbon transformation processes. Initially it was assumed that these reactions follow mechanisms known from chemistry in superacidic media, and involve carbocations as intermediates formed upon protonation of hydrocarbons by Brønsted acid sites. 1 However, NMR spectroscopic studies failed to find simple carbenium ions as intermediates, and instead produced evidence for surface alkoxides. 2, 3 Around the same time, quantum chemical calculations employing small cluster models showed that alkoxides are minima on the potential energy surface (PES) and, hence, intermediates, while carbenium ions represent saddle points on the PES and are only present as extremely short-lived transition states. 4 So far, evidence for persistent carbenium ions has only been produced for cyclic alkenyl or aromatic carbenium ions by NMR, 5 UV/Vis, 6 and IR spectroscopy7 or computational techniques. 8 Among the carbenium ions derived from small alkenes, the tert-butyl cation has attracted much interest because it is more stable than primary or secondary carbenium ions; the competing formation of tert-butoxide may be sterically hindered. Previous computational studies have shown that, depending on the framework and the position at the zeolite wall to which they are bound, tert-butoxides may be as unstable as the tert-butyl cation. 9–12 Only the embedded cluster study by Boronat et al. 12 reports a local minimum on the PES for the tert-butyl cation in mordenite. It is, however, about 26 kJ mol−1 less stable than the adsorption π complex of isobutene with the Brønsted site. Nevertheless, all experimental attempts13, 14 to produce evidence for either the tert-butyl cation or an alkoxide have been unsuccessful so far, and the existence of tert-butyl cations in zeolites remains controversial. Herein we report density functional theory (DFT) calculations for the reaction of isobutene with H-ferrierite (H-FER, 1) with formation of the π complex 2 (Scheme 1). We applied periodic boundary conditions to a large simulation cell of dimensions 1870×1417×1496 pm3. 15 We show that the complex with the tert-butyl cation (4) —one possible structure formed upon proton transfer to isobutene in 2—is a local minimum on the potential energy surface. For the first time we have evaluated entropy contributions to assess the stability of 4 relative to the adsorption π complex 2 and other possible proton transfer products, that is, surface alkoxides (3, 5), at finite temperatures. Reactions considered for the protonation of isobutene in H-FER (1). Our simulation cell of H-FER (1) has the composition HAlSi71O144. After aluminum substitution at the crystallographic position T2, 16 the proton is most stable at O7. 15 We used the Perdew–Burke–Ernzerhof (PBE) density functional17 with a plane wave basis set. 18 Stationary points obtained by relaxation of the positions of all atoms in the cell are characterized by harmonic frequencies, from which zero-point vibrational energies, finite temperature energy, and entropy contributions are obtained. 19 All calculations employed the CPMD code. 20 The calculated structures and the corresponding reaction energies are shown in Figure 1 and Table 1. Formation of the π complex of isobutene with the Brønsted acidic site is exothermic (2, ΔE0=−6. 6 kJ mol−1). In contrast, chemisorption of isobutene is an endothermic process. Of the two different alkoxides, the isobutoxide (5) is more stable than the tert-butoxide (3). The longer CO bond in tert-butoxide (161 pm) compared to isobutoxide (151 pm) indicates increased steric constraints due to the three methyl groups at the CO carbon atom. Both the adsorbed isobutene and the tert-butyl cation are connected by hydrogen bonds to the zeolite framework. The corresponding bond lengths are 190. 2 and 242. 5 pm for r (AlOH⋅⋅⋅C1) and r (AlOH⋅⋅⋅C2) in the π complex and 174. 0 pm for r (AlO⋅⋅⋅HC) in the carbenium ion structure. The carbenium ion complex 4 is electronically least favored. It is 46 kJ mol−1 less stable than the adsorption π complex, while isobutoxide is 14 kJ mol−1 and tert-butoxide is 27 kJ mol−1 less stable. Portions of the structures calculated for the π complex of isobutene in ferrierite (2), for the tert-butyl cation in ferrierite (4), and for the tert-butoxide (3) and isobutoxide (5) of ferrierite. Compound ΔE ΔE0 ΔH298 ΔG298 2 −9. 4 −6. 6a −4. 9 40. 4 3 17. 2 35. 0 27. 5 119. 0 4 36. 2 32. 2 34. 9 76. 0 5 4. 8 24. 4 18. 8 96. 8 Similar relative energies have been found in a previous DFT (PW91) study for chabasite, ZSM-22, and mordenite11 as well as in a B3PW91 study on mordenite. 12 The density functionals that are currently used do not properly account for dispersion interactions (see, e. g. , references 21, 22). This results in too low energies of adsorption, but may also change the relative energies of chemisorbed species compared to adsorption π complexes and carbenium ions. 15 Future refinements of the present results by explicit inclusion of dispersion interactions may be obtained by an MP2/DFT hybrid technique23 or by adding a damped dispersion term. 22 The results obtained with the PBE/PW91 family of functionals require less correction than those with functionals including Becke exchange. 21, 22, 24 Inclusion of zero-point vibrations and finite temperature effects stabilizes the tert-butyl carbenium ion relative to the chemisorbed species (see ΔE0 and ΔH298 in Table 1). An important new finding of the present study is the effect of entropy on the Gibbs energy: At temperatures higher than about 120 K, the tert-butyl cation complex 4 becomes favored over the alkoxides (3, 5, Figure 2). The different slopes for the change in Gibbs energy for the alkoxides compared to the π complex and the carbenium ion reflect different entropy contributions. The existence of an additional covalent bond in the alkoxides (CO) limits the mobility of the hydrocarbon species, and suggests a lower entropy compared to the other two structures. Plot of the Gibbs energy ΔGT as a function of temperature T (at 1 atm) for the formation of 2–5 from isobutene and H-FER (1). The vibrational states obtained from our frequency calculations are shown in Figure 3 (the vibrational frequencies can be found in the Supporting Information). A nearly continuous vibrational region from 1250 cm−1 down to far infrared with a window between about 1000 and 800 cm−1 is seen for unloaded H-FER (1) as well as for the hydrocarbon-containing structures. This is characteristic of zeolite lattice vibrations. The calculated frequencies for the zeolitic OH and OD stretching modes in unloaded H-FER (3643 and 2652 cm−1, respectively) compare well with experimental data (3609 and 2663 cm−1, respectively). 25 Quantitative agreement is not expected because of the limited accuracy of DFT and neglected anharmonicities. The vibrational spectra of structures 2–5 approximately resemble superpositions of those of the unloaded zeolite and the gas-phase species. In the isobutene π complex 2, hydrogen bond formation shifts the zeolitic OH and OD stretching mode by −819 and −585 cm−1, respectively. Corresponding measurements on deuterated forms of different zeolites yield somewhat smaller OD shifts: −416 cm−1 (mordenite) 14 and −388 cm−1 (faujasite). 26 It is known27 that the PBE functional overestimates OH frequency shifts upon hydrogen bond formation. Vibrational spectra calculated for isobutene and the tert-butyl cation (both in the gas phase) as well as for structures 1–5. A significant change is predicted for the IR spectrum of the carbenium ion complex 4: Only 8 instead of 9 vibrational modes are seen in the CH stretching region around 3000 cm−1; the remaining mode corresponding to the O⋅⋅⋅HC hydrogen bond is found at 2245 cm−1, that is, well separated from the others. This is a new prediction which may help to identify the tert-butyl cation as a transient species in future laser-spectroscopic experiments. 28 Supporting information for this article is available on the WWW under http: //www. wiley-vch. de/contents/jc₂002/2005/z501002ₛ. pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.