J. Phys. Chem. B 2004, 108, 971-980 971 DFT-Based Reaction Pathway Analysis of Hexadiene Cyclization via Carbenium Ion Intermediates: Mechanistic Study of Light Alkane Aromatization Catalysis Yogesh V. Joshi, Aditya Bhan, and Kendall T. Thomson* School of Chemical Engineering, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed: July 28, 2003; In Final Form: NoVember 4, 2003 We conducted density functional theory calculations to identify the complete cyclization mechanism (ring formation and ring expansion) for protonated hexadiene in the gas-phase as a precursory means of studying aromatization of light alkanes in acidic zeolite catalysts. We identify the rate-determining step to consist of ring expansion from a methylcyclopenta carbenium precursor to a stable cyclohexa carbenium intermediate, exhibiting an activation barrier of 9.6 kcal/mol and proceeding through a bicyclic intermediate starting from a secondary cyclopentyl carbocation. This pathway for ring closure was preferred over tertiary precursor expansion and direct cyclization to a cyclohexyl carbocation. Expecting carbocation intermediates to be represented by alkoxide species near Brønsted acid sites, we calculated the relative stability of primary, secondary, and tertiary alkoxide analogues to cyclopentyl carbocation intermediates involved in ring expansion and notice a reversal of stability relative to gas-phase carbocation stabilities (i.e., primary > secondary > tertiary stability). However, on the basis of the notion that transition state stability depends heavily on carbocation character of the transition state, even in alkoxide-based chemistry, we conclude that ring expansion would nevertheless constitute the rate-determining step in a zeolite-catalyzed mechanism. 1. Introduction Cyclizations involving C(6+) olefins are believed to occur via carbocation/alkoxide-based pathways relatively independent The conversion of light hydrocarbons to aromatics provides of oligomerization.18 Further, aromatization studies involving the potential for large economic gains by substantially increasing cyclohexane and methyl cyclohexane over Ga/H-ZSM-5 result the value of liquefied petroleum gas (LPG) feedstocks. Aromatic in a very low production of light alkanes, suggesting that once compounds, particularly BTX (benzene, toluene, and xylene), naphthenic intermediates are formed they are rapidly dehydro- contribute high-octane components to the gasoline pool (120+ genated over gallium sites, forming their respective aromatic octane value) and are important feedstock components for isomers.42 Experimental investigations of carbocation chemistry, downstream petrochemical processing. As a consequence, over dating back to Olah’s successful attempt of stabilizing carbo- the last 50 years there has been a considerable drive to develop - cations in superacid solutions, exist and provide important economically viable aromatization routes in industry.1 5 How- insight into potential cyclization mechanisms.43-46 For example, ever, aromatization catalysts suffer from a number of deficien- Saunders et al.47 give experimental evidence for protonated cies. Monofunctional acid catalysts exhibit relatively low cyclopropane intermediates for several carbocation reactions, aromatics yields which is due to preferentially high cracking, 6-10 reporting activation energies for various reactions using line isomerization, and â-scission reactivity. Bifunctional metal/ 1 - - - shape analysis of H NMR data. Further, there have been several H-ZSM-5 catalysts using Ga,11 26 Zn,27 34 and Pt10,7,35 40 experimental investigations aimed at studying the isomerization dramatically improve aromatics yields but are prone to deactiva- of alkylcyclopentyl cations.48-51 However, there has not been tion via coking31 and, although better than purely acidic a complete investigation of ring formation via carbocation routes catalysts, are nevertheless limited in both aromatics yield and specifically aimed at understanding the catalytic steps toward selectivity toward H versus CH byproducts. 2 4 aromatization in acid zeolite systems. The goal of ongoing research in this area is the development of highly H selective catalysts for light paraffin aromatization The goal of this work was to use electronic density functional 2 V (for reviews of this subject see the references).20,10,41 Critical theory (DFT) calculations to in estigate possible mechanisms V to this goal is an effort to clearly elucidate reaction pathways for hexadiene cyclization ia carbenium ion intermediates. We and mechanisms for aromatization. Aromatization of even single concentrated on gas-phase (noncatalytic) carbocation mecha- component feedstocks is complex, involving a large number nisms in order to derive a simple theoretical baseline for model- reaction steps, many of which are not well understood or are ing heterogeneous cyclization based on carbenium/alkoxide only postulated. However, it is generally agreed that the relevant chemistry in zeolites, which is the subject of future work in reactions for conversion of light alkanes to aromatics consists our research group. Most of the previous theoretical work on of (1) alkane C-H activation to alkoxide/carbenium complexes, ring closure mechanisms has been of gas-phase cyclization via 52,53 (2) dehydrogenation to olefins, (3) oligomerization to higher free radical pathways in combustion processes. For example, olefins, (4) rapid isomerization, (5) â-scission, (6) cyclization, it was reported that the rate-determining step for soot formation 54 and (7) dehydrogenative aromatization.10,41 is the cyclization to first benzene. More detailed calculations of ring formation52 and ring expansion53 involving free radical * Corresponding author. Phone: (765) 496-6706. FAX: (765) 494- intermediates have subsequently been reported. Theoretical 0805. E-mail: [email protected]. studies of cyclization starting from C(6+) hydrocarbons are not 10.1021/jp036205m CCC: $27.50 © 2004 American Chemical Society Published on Web 12/24/2003 972 J. Phys. Chem. B, Vol. 108, No. 3, 2004 Joshi et al. SCHEME 1: Cyclization of the C6 Diene via Carbenium Ion Intermediate, Catalyzed by Solid Acids unprecedented. An MNDO study of ring expansion was reported bond attacks the positive cationic charge center, closing the ring. by Viruela-Martin et al.,55 and recently there has been a detailed The resulting alkylcyclopenta carbenium ions can then undergo study of five-membered ring expansion with relevance to sterol a series of hydride transfers to form stable tertiary carbenium biosynthesis.56 A recent ab initio study of carbenium ion ions, which subsequently undergoe ring expansion to form the reactions involved in sterol synthesis57 also points out interesting cyclohexa carbenium ion. results about ring formation. However, the precursors used for In the catalytic cyclization route, the carbenium ion inter- these investigations were C(8+) molecules, which contain mediates are assumed to reside in the vicinity of active Brønsted fundamentally different alkyl groups (compared to C6 mol- sites, possibly as stabilized alkoxide compounds. However, we ecules) attached to the five-membered ring. It is known that felt it was useful to first study gas-phase carbenium ion aromatization of light alkanes using zeolite catalysts has high cyclization mechanisms, as this will provide a basis for selectivity for toluene and benzene. Hence, a separate consid- hypothesizing catalytic routes. We will eventually verify the eration for cyclization concentrating on C6 carbenium ions as kinetic feasibility of similar elementary steps involved in zeolite- precursors is desired and perhaps more relevant to zeolite catalyzed cyclization. We will use the resulting intermediate chemistry. We present here details of proposed gas-phase geometries as starting guesses for full DFT studies involving cyclization mechanisms of hexadiene conversion to benzene embedded cluster models of zeolite sites. based on carbenium ion chemistry. This work represents the first step in understanding cyclization mechanisms in zeolite 3. Computational Methods catalysts, the subject of future investigations in our group. This rest of this paper is organized as follows. Section 2 All calculations were carried out using the B3LYP hybrid 58 + describes the particulars of our hypothesized cyclization mech- density functional with a 6-311 G(2d,p) basis set for all atoms.59 All structures were optimized to tight convergence anism, providing the rationale for this study. In section 3 we 60 describe the computational details of our calculations. In section criteria using the GAUSSIAN 98 commercial code. We believe 4 we present the results of our calculations, laying out the this choice of functional and basis set is the best for the type of mechanisms for different parts of the cyclization and presenting system we are investigating. In its original formulation the the energetic analysis of intermediates and transition states for parameters in the B3LYP functional were determined by least- the following components/steps: (4.1) precursor geometries, squares fitting to the G2 set of atomic and molecular energy (4.2) activation of the precursor, (4.3) ring formation, (4.4) data. Almost half of this set is related to ionization energies of various atoms and molecules. We also opted for the MP2 hydride transfer, (4.5) ring expansion, and (4.6) direct cyclization + as an alternative mechanism. In section 5 we present a discussion optimized 6-311 G(2d,p) single-ú core, triple-ú valance