Substituent Effects on the Reaction Rates of Hydrogen Abstraction in

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Energy Fuels 2010, 24, 2857–2867 Published on Web 04/26/2010

: DOI:10.1021/ef1001953

Substituent Effects on the Reaction Rates of Hydrogen Abstraction in the Pyrolysis of Phenethyl Phenyl Ethers Ariana Beste*,† and A. C. Buchanan, III‡ †

Computer Science and Mathematics Division and ‡Chemical Sciences Division, Oak Ridge National Laboratory, Post Office Box 2008, MS 6367, Oak Ridge, Tennessee 37831-6367 Received February 19, 2010. Revised Manuscript Received April 7, 2010

We report reaction profiles and forward rate constants for hydrogen abstraction reactions occurring in the pyrolysis of methoxy-substituted derivatives of phenethyl phenyl ether (PhCH2CH2OPh, PPE), where the substituents are located on the aryl ether ring (PhCH2CH2OPh-X). We use density functional theory in combination with transition-state theory, and anharmonic corrections are included within the independent mode approximation. PPE is the simplest model of the abundant β-O-4 linkage in lignin. The mechanism of PPE pyrolysis and overall product selectivities have been studied experimentally by one of us, which was followed by computational analysis of key individual hydrogen-transfer reaction steps. In the previous work, we have been able to use a simplified kinetic model based on quasi-steady-state conditions to reproduce experimental R/β selectivities for PPE and PPEs with substituents on the phenethyl ring (X-PhCH2CH2OPh). This model is not applicable to PPE derivatives where methoxy substituents are located on the phenyl ring adjacent to the ether oxygen because of the strongly endothermic character of the hydrogen abstraction by substituted phenoxy radicals as well as the decreased kinetic chain lengths resulting from enhanced rates of the initial C-O homolysis step. Substituents decelerate the hydrogen abstraction by the phenoxy radical, while the influence on the benzyl abstraction is less homogeneous. The calculations provide insight into the contributions of steric and polar effects in these important hydrogentransfer steps. We emphasize the importance of an exhaustive conformational space search to calculate rate constants and product selectivities. The computed rate constants will be used in future work to numerically simulate the pyrolysis mechanism, pending the calculation of the rate constants of all participating reactions.

typically studied using simplified models.4-6 The various lignin model compounds represent the different linkages and functional groups in lignin. The most common linkage in lignin is the arylglycerol-β-aryl ether (β-O-4) linkage, for which the simplest model is phenethyl phenyl ether (PhCH2CH2OPh, PPE). The pyrolysis of PPE at 330-425 °C follows a free-radical chain mechanism,6 shown in Scheme 1, to produce phenol plus styrene and benzaldehyde plus toluene as the principal products. Britt et al.7,8 investigated the influence of several methoxy and hydroxy substituents on the thermal decomposition of PPE using high-temperature, flash vacuum pyrolysis techniques8 as well as slow pyrolysis in the liquid phase.7 Under both conditions, the pyrolysis rate and product distribution were found to be significantly influenced by the substituents. Understanding the origin of the substituent effects is a difficult task because the substituents can alter multiple reaction steps in Scheme 1: the homolytic initiation (reaction 1), competitive hydrogen abstraction reactions (reactions 2, 6, and 7), radical rearrangement (reaction 4), and/or radical scission (reactions 3 and 5). The strength of computational studies lies in the ability to probe individual reaction steps. To obtain a detailed understanding of the mechanism of the thermal decomposition of substituted

Introduction Lignin is an abundant natural biopolymer strengthening the cell walls of vascular plants. Despite its potential to serve as a source of clean chemicals and fuels,1 lignin has found only limited industrial applications. Most of the lignin obtained as a byproduct of the pulping industry is consumed as fuel, although its use as a natural adsorbent2 or as a syngas base3 has been investigated. The complicated structure of lignin and the dependence of its chemical behavior upon the isolation process3 make the development of novel, economically viable processing techniques difficult. Reviews on the gasification and thermochemical conversion of biomass are available (refs 2 and 4 and references therein). Lignin is decomposed through pyrolysis. This is an extremely complex chemical process, whose fundamental basis is *To whom correspondence should be addressed: Oak Ridge National Laboratory, Post Office Box 2008, MS 6367, Oak Ridge, TN 378316367. Telephone: 865-241-3160. Fax: 865-574-0680. E-mail: bestea@ ornl.gov. (1) Mohan, D.; Pittman, C. U., Jr.; Steele, P. H. Energy Fuels 2006, 20, 848. (2) Suhas Carrott, P. J. M.; Ribeiro Carrott, M. M. L. Bioresour. Technol. 2007, 98, 2301. (3) Baumling, S.; Broust, F.; Bazer-Bachi, F.; Bourdeaux, T.; Herbinet, O.; Ndiaye, F. T.; Ferrer, M.; Lede, J. Int. J. Hydrogen Energy 2006, 31, 2179. (4) Beste, A; Buchanan, A. C., III; Britt, P. F.; Hathorn, B. C.; Harrison, R. J. J. Phys. Chem. A 2007, 111, 12118. (5) Kawamoto, H.; Horigoshi, S.; Saka, S. J. Wood Sci. 2007, 53, 168. Kawamoto, H.; Horigoshi, S.; Saka, S. J. Wood Sci. 2007, 53, 268. r 2010 American Chemical Society

(6) Britt, P. F.; Buchanan, A. C., III; Malcolm, E. A. J. Org. Chem. 1995, 60, 6523. (7) Britt, P. F.; Kidder, M. K.; Buchanan, A. C., III Energy Fuels 2007, 21, 3102. (8) Britt, P. F.; Buchanan, A. C., III; Cooney, M. J.; Martineau, D. R. J. Org. Chem. 2000, 65, 1376.

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of theory in combination with variational transition-state theory19,20 can provide accurate rate constants. However, the size of our target system (substituted PPE) requires the use of more cost-effective methods. In addition, our systems are not rigid and contain on the order of 10 frequencies below 100 cm-1, which are expected to have large anharmonic contributions. Favorably for PPE, the R/β selectivity is determined by the ratios of rate constants for similar reactions (same reactants) and error cancellation occurs for systematic errors in activation energies, tunneling, and recrossing phenomena. We included anharmonic effects, which are not expected to be systematic, through a diagonal correction for low-frequency modes based on a semi-classical WignerKirkwood expansion.21 The experimental value6 for the total R/β selectivity in the pyrolysis of PPE is 3.1 ( 0.3 at 648 K. Using cost-effective density functional theory (DFT) in combination with transition-state theory and applying quasisteady-state kinetic conditions for radical intermediates, we obtained a calculated R/β selectivity of 2.4 at 648 K in good agreement with experimental values. We extended our efforts to study the substituent effects on the R/β selectivity of the pyrolysis of substituted PPE. Methoxy and hydroxy substituents were introduced in the para position of the phenethyl ring (X-PhCH2CH2OPh), and the R/β selectivity increased compared to PPE,22 correlating nicely with the observed experimental trend (MeO-PPE > HO-PPE > PPE).7 The strongest effect of the substituents was observed for the R pathway of the hydrogen abstraction by the phenoxy radical, which was enhanced by the substituents. In contrast, the rates for the β pathway and the pathways of abstraction by the less electrophilic benzyl radical decreased. In the currently presented work, we calculate the reaction energies and barriers for the hydrogen abstraction reactions relevant in the pyrolysis of methoxy-substituted PPE in the ortho, di-ortho, and para position of the phenyl ring adjacent to the ether oxygen (PhCH2CH2OPh-X) as well as the corresponding forward rate constants for the hydrogen abstraction reactions. As we will show, the reaction profiles are quite different from the reaction profiles for PPE with substituents located on the opposite ring,22 which leads to the breakdown of the simplified steady-state kinetic model to calculate the total R/β selectivity used in refs 4 and 22.

Scheme 1. Radical Chain Mechanism of the Pyrolysis of Phenethyl Phenyl Ether (PhCH2CH2OPh, PPE)6

PPE, we launched a series of computational investigations. We are aware of only a few other computational studies on lignin model compounds focusing on conformational9,10 and mechanical11 aspects. Mechanistic analysis12 was performed for the thermal decomposition of a small intermediate in lignin combustion. The activation barrier for the reverse reaction of the initial homolytic cleavage of the carbon-oxygen bond (reaction 1 in Scheme 1) is expected to be small, and valuable information can be obtained by calculating the bond dissociation enthalpies (BDEs) of the carbon-oxygen and carbon-carbon bond breaking. We recently found13 significant substituent effects on the carbon-oxygen BDE when the substituents are located at the phenyl ring adjacent to the ether oxygen. Interestingly, the carbon-carbon BDE is not substantially influenced by substituents on either ring. One of the key experimental results for the pyrolysis of PPE is the R/β selectivity, referring to the product distribution derived from the hydrogen abstraction at either the R or β position of PPE. The total R/β selectivity is a composite of the R/β selectivities in the hydrogen abstraction reactions by the phenoxy radical (reaction 2 in Scheme 1), the benzyl radical (reaction 6 in Scheme 1), and the phenethyl radical (reaction 7 in Scheme 1). Experimental findings6 suggested that the phenethyl abstraction contributes only little to the product distribution for PPE, and we focused our computational work on the hydrogen abstraction by the chain-carrying phenoxy and benzyl radicals.4 The calculation of R/β selectivities requires knowledge of the rate constants for the participating reactions. The computation of absolute rate constants is a challenging task, and calculated rate constants can differ by orders of magnitude to each other and experimental values.14-18 For small and rigid molecules, a high level

Computational Details All calculations were carried out with the NWChem program package.23 We used the unrestricted density functional method to obtain the equilibrium and transition-state structures. We chose the M06-2X functional, which is part of the recent developed family of kinetic functionals by Zhao and Truhlar.24 It showed excellent performance for reaction barriers of hydrogen abstraction reactions (mean-squared error of -0.98 kcal/mol in barrier heights for the BBH7 database containing hydrogen abstraction reactions25). Previously, we successfully computed bond

(9) Simon, J. P.; Eriksson, K.-E. L. J. Mol. Struct. 1996, 384, 1. (10) Agache, C.; Popa, V. I. Chem. Mon. 2006, 137, 55. (11) Elder, T. Biomacromolecules 2007, 8, 3619. (12) Da Silva, G.; Bozzelli, J. W. J. Chem. Phys. A 2007, 111, 7987. (13) Beste, A.; Buchanan, A. C., III J. Org. Chem. 2009, 74, 2837. (14) Chen, X.; Zhang, X.; Han, K.; Varandas, A. J. C. Chem. Phys. Lett. 2006, 421, 453. (15) Wang, W.; Feng, L.; Wang, W.; Luo, Q.; Li, Q. J. Mol. Struct. 2006, 764, 53. (16) Phillips, D. L.; Zhao, C.; Wang, D. J. Phys. Chem. A 2005, 109, 9653. (17) Zhang, Y.; Li, Q. S.; Zhang, S. J. Mol. Struct. 2004, 682, 163. (18) Chan, W.-T.; Hamilton, I. P.; Pritchard, H. O. J. Chem. Soc., Faraday Trans. 1998, 19, 2303.

(19) Garrett, B. C.; Truhlar, D. G. J. Chem. Phys. 1979, 70, 1593. (20) Garrett, B. C.; Truhlar, D. G. J. Am. Chem. Soc. 1979, 101, 4534. (21) Wigner, E. P. Phys. Rev. 1932, 40, 749. Kirkwood, J. G. Phys. Rev. 1933, 44, 31. (22) Beste, A.; Buchanan, A. C.; Harrison, R. J. J. Phys. Chem. A 2008, 112, 4982. (23) Kendall, R. A.; Apra, E.; Bernholdt, D. E.; Bylaska, E. J.; Dupuis, M.; Fann, G. I.; Harrison, R. J.; Ju, J. L.; Nichols, J. A.; Nieplocha, J.; Straatsma, T. P.; Windus, T. L.; Wong, A. T. Comput. Phys. Commun. 2000, 128, 260. (24) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. (25) Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2008, 4, 1849.

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Figure 1. Equilibrium geometries for (a) PPE, (b and f) p-methoxy PPE, (c and e) o-methoxy PPE, and (d) di-o-methoxy PPE.

below 110 cm-1, anharmonic corrections were incorporated through an independent mode approximation. Each transition state possesses 9-11 frequencies below 110 cm-1. The anharmonic one-dimensional potentials were obtained as a fit to a fourthorder polynomial of the energies of displaced geometries along the normal modes. We used the semi-classical WignerKirkwood expansion to calculate the anharmonic, vibrational partition functions.4 Anharmonic partition functions for lowfrequency modes were also used to calculate equilibrium constants.

dissociation enthalpies of substituted PPE13 with the M06-2X functional. We used a mixed basis set4 for optimizations and transition-state searches. The energies were calculated with a 6-311þþG** basis set. All energy differences were zeropoint-corrected. Vibrational analysis was performed for equilibrium geometries and transition states. Partial atomic charges were computed by a fitting procedure of the quantum mechanical electrostatic potential on selected grid points. To ensure that the conformational space was well-sampled, we pre-optimized the transition states with fixed hydrogen-benzyl (phenoxy) and fixed hydrogen-PPE distances distinct by different orientations of the aromatic rings and the methoxy substituents. Optimization to a minimum of most coordinates, except the reaction coordinate, facilitated subsequent saddle point searches. Convergence to a saddle point was most often achieved when the starting structure for the transition-state search resembled the transition state closely. We, therefore, applied an iterative strategy; i.e., once a transition state was localized for a PPE derivative, we used the equivalent starting structure for the pre-optimization of all other derivatives. The original searches included four orientations of the attacking radical per PPE derivative described by a linear hydrogen bridge, an angle of around 100° between the hydrogen bridge and the aromatic plane of the attacking radical and a dihedral angle between the carbon-ether oxygen bond, the hydrogen bridge, and the bond of the radical center to the aromatic ring of the attacking radical of about 0°, 90°, 180°, and 270° (the angles were adjusted if strong sterical hindrance was encountered). Similarly, we re-optimized starting structures of unsuccessful transition-state searches using hydrogen-PPE and hydrogen-benzyl (phenoxy) distances from successful searches of similar transition states. The final hydrogen-PPE and hydrogen-benzyl (phenoxy) distances are embedded in the figures of the transition states in the Supporting Information and range from 1.28 to 1.40 A˚ for the hydrogen-PPE distance and from 1.19 to 1.37 A˚ for the hydrogen-benzyl (phenoxy) distance. We obtained multiple transition states for each reaction channel. The rate constants were calculated with transition-state theory, including a Wigner tunneling correction.26 The harmonic quantum approximation was used to calculate the vibrational partition functions for frequencies above 110 cm-1. For frequencies

Results and Discussion Our starting point was the calculation of the equilibrium structures of PPE and its derivatives. Structures a-d of Figure 1 show their lowest energy conformations. Notice that PPE, p-methoxy PPE, and o-methoxy PPE share the same lowest energy conformation. The steric hindrance introduced by the addition of another methoxy group in di-o-methoxy PPE makes a conformation favorable where the phenyl ring adjacent to the ether oxygen is rotated by 90°. The energy profiles for the rotation of the phenyl ring adjacent to the ether oxygen are given in the Supporting Information. For PPE, the only minimum along the rotational coordinate is found at 0°, which is the conformation shown in Figure 1a. We find a similar situation for p-methoxy PPE. The o-methoxy derivative possesses a second minimum at 105°, which is 0.6 kcal/mol higher in energy than the minimum at 0° and separated by an energy barrier of 2.3 kcal/mol. The additional conformer is given in Figure 1e. The rotation of the phenyl ring by 180° in o-methoxy PPE leads to a maxima on the potential energy surface; i.e., the conformation where the methoxy group is on the bottom in Figure 1c is not stable. For di-o-methoxy PPE and the only minimum is found at 90°; i.e., the equivalent conformer to PPE, and its para- and orthosubstituted derivatives does not exist. All PPE conformers given in Figure 1 show the phenyl ring opposite the ether oxygen in the same orientation. The rotation of this phenyl ring in PPE does not lead to additional minima (see the Supporting Information). Because the substituents are located on the phenyl ring adjacent to the ether

(26) Henriksen, N. E.; Hansen, F. Y. Theory of Molecular Reaction Dynamics; Oxford University Press: New York, 2008; pp 153-155.

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try. For conformer e, also the two R- and two β-hydrogen atoms are not equivalent. In addition, the radical can attack the PPE derivatives at different angles. These factors account for the large conformational space that we need to sample. In total, we identified 117 transition states for hydrogen abstraction reactions on the conformers shown in Figure 1. A reaction path is assigned to each transition state. The transition states can be viewed in the Supporting Information. The numbering follows the energetic order; i.e., the lowest number corresponds to the group of transition states containing the energetically lowest transition state derived from the lowest reactant conformer. We find very similar transition states for the different PPE derivatives, where their energetic order is often influenced by the substituent. The distinct rotation of the phenyl ring adjacent to the ether oxygen in conformers a, b, c, and f on one hand and conformers d and f on the other hand remains in the transition states. Generally, stronger steric effects can be observed when substituents are located in an ortho position. For instance, for the hydrogen abstraction by the o-methoxy phenoxy radical on the R position of conformer e characterized by TS37 (see the Supporting Information), we only found the transition states where the methoxy substituent points away from the attacking radical (TS37e and TS37f) and not toward the phenoxy radical. In some cases, we could not localize the equivalent transition state to a previously obtained transition state of a different conformer, despite extensive searches. For example, we identified TS27a (see the Supporting Information) as a transition state for the abstraction of the β-hydrogen of conformer b by p-methoxy phenoxy. We could not find the corresponding transition state for conformer f. This shows that a small perturbation can qualitatively alter the M06-2X potential energy surface. The disappearance of a saddle point becomes more likely the more shallow the potential energy surface around the extreme point. The located transition states possess on the order of 10 frequencies below 100 cm-1, which indicates that along these degrees of freedom the extreme points are situated in a shallow region of the potential. Vibrational analysis revealed for most transition states one imaginary frequency. However, three of the transition states (TS22c, TS46, and TS47) showed an additional spurious imaginary frequency not exceeding i10 cm-1. As previously discussed,4,22 these low imaginary frequencies are indicative of numerical inaccuracies and the breakdown of the harmonic approximation. The Supporting Information contains the harmonic potentials along the low imaginary modes obtained by displacement and a quadratic fitting procedure. For the three transition states in question, the minimum occurs at zero displacement. The energetically lowest transition structures for the hydrogen abstraction reactions on PPE (reactions 2 and 6) are given in Figure 2. Equivalently, the lowest transition states for p-methoxy, o-methoxy, and di-o-methoxy PPE are shown in Figures 3-5. The lowest transition states for o-substituted PPE are shown in Figure 4. The lowest transition states for di-o-substituted PPE are shown in Figure 5. The transition states for PPE and p-methoxy PPE are very similar. The substituent effects on the transition-state geometries become apparent for o-methoxy PPE. Whereas the lowest benzyl transition state for the R channel is derived from conformer c, all other transition states in Figure 4 are derived from conformer e. In particular, steric hindrance prevents the equivalent transition state to TS8 and TS21b to be the lowest in

Table 1. Equilibrium Constants and Mole Fraction for the Rotation of the Phenyl Ring in o-Methoxy PPE and the Rotation of the Methoxy Group in p-Methoxy PPE at 618 K K phenyl rotation in o-OCH3PPE

0.77

methoxy rotation in p-OCH3PPE

1.04

mole fractions Figure 1c 0.56 Figure 1b 0.49

Figure 1e 0.44 Figure 1f 0.51

oxygen, we did not repeat the rotation of the opposite phenyl ring for the PPE derivatives. Another concern is the orientation of the methoxy groups in conformers b, c, and d. A rotation of the methoxy group in p-methoxy PPE of 180° results in a minimum structure shown in Figure 1f). Conformer f is 0.3 kcal/mol higher in energy than conformer b, with a rotational barrier of 2.3 kcal/mol. The energy profile for the rotation is given in the Supporting Information. In contrast, the rotation of the methoxy group by 180° in o-methoxy PPE and either or both methoxy groups in di-o-methoxy PPE does not yield an equilibrium structure. On the basis of this analysis, we consider the six conformers in Figure 1 to be reactants for the hydrogen abstraction reactions 2 and 6 in Scheme 1. We assume thermal equilibrium between conformers c and e and conformers b and f. The mole fraction of each conformer is determined by the equilibrium constant K = (QP/QR)e-ΔE/kT, where ΔE is the energy difference between conformers, and QR and QP are the partition functions of the reactants (c and b) and products (e and f). Table 1 gives the equilibrium constants and mole fractions for the relevant conformers. The latter serves as a weight factor for the calculation of the rate constants. Notice, that the equilibrium constant for conformers b and f is slightly larger than 1, even though conformer f is higher in energy than conformer b. This is due to the relatively large molecular partition function of conformer f. The ratio of the molecular partition functions of conformers f and b is 1.30, whereas the energetic contribution to the equilibrium constant is 0.80. The second reactants in the hydrogen abstraction reactions 2 and 6 of Scheme 1 are the benzyl and phenoxy radicals. In the reactions investigated here, the benzyl radical does not carry substituents. Initially, the conformation of the phenoxy radicals depends upon the conformation of the PPE derivatives because they are formed through PPE cleavage, i.e., reactions 1 and 3 of Scheme 1. The barriers for the rotation of the methoxy group are high, i.e., 5.5 kcal/mol for the rotation of the methoxy group in p-methoxy phenoxy and 6.1 kcal/mol for the rotation of the methoxy group in o-methoxy phenoxy. Convergence problems prevented us from obtaining the rotational barriers in di-o-methoxy phenoxy, but we assume similarly high barriers. The energy profiles for the rotation of the methoxy group in p-methoxy phenoxy and o-methoxy phenoxy are given in the Supporting Information. Because of the high energy barriers for the methoxy rotation in the phenoxy radicals, we only consider phenoxy conformers that correspond to the dissociation products of the conformers shown in Figure 1. For either the R or β pathway, there are two equivalent hydrogen atoms in PPE that can be abstracted by the benzyl or phenoxy radical and each radical has two equivalent sides of attack. This symmetry is partially reduced by the introduction of substituents. Conformers b, c, d, and f still possess equivalent hydrogen atoms, but the corresponding phenoxy radicals have two distinct sides of attack. Only the di-o-methoxy phenoxy radical formed from conformer d maintains symme2860

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Figure 2. Lowest transition-state structures for hydrogen abstraction reactions (2 and 6) on PPE: b, hydrogen-benzyl distance in angstroms; p, hydrogen-phenoxy distance in angstroms; and e, hydrogen-ether distance in angstroms.

Figure 3. Lowest transition-state structures for hydrogen abstraction reactions (2 and 6) on p-methoxy PPE: b, hydrogen-benzyl distance in angstroms; p, hydrogen-phenoxy distance in angstroms; and e, hydrogen-ether distance in angstroms.

energy for the R abstraction by the o-methoxy phenoxy radical. Similarly, we observe that for the R abstraction by the benzyl radical on di-o-methoxy PPE steric hindrance destabilizes an equivalent transition state to TS1, TS15a, and TS28a; instead, the benzyl radical in TS45 avoids contact with the substituted phenyl ring. The phenoxy transition state of the R channel for di-o-methoxy PPE, i.e., TS51, is the corresponding transition state to the transition state for o-methoxy PPE, i.e., TS39c. Larger structural rearrangements are visible in TS54 compared to the phenoxy transition states of the less substituted PPE derivatives. In all transition states, we observe that the hydrogen-benzyl and hydrogen-ether distances in the benzyl transition states are similar but the hydrogen-phenoxy distances in the phenoxy transition states are significantly smaller than the hydrogen-ether distances when the more polarized phenoxy radical abstracts the hydrogen atom. Figures 6 and 7 display the reaction profiles for the hydrogen abstraction reactions 1 and 2 based on the lowest energy

transition states described above. The energies of all transition states that were found are tabulated in the Supporting Information. The reaction energies of the benzyl abstraction are only slightly altered by the substituents. The reaction barriers are lowered by o-methoxy substituents by about 1 kcal/mol. The substituent in the para position has little influence on the reaction barriers. The R/β-barrier differences, which affect the product selectivity, vary within only 0.6 kcal/mol. In contrast, the reaction energies for the R and β channels of the phenoxy abstraction are strongly influenced by the substituents and are between 5 and 6 kcal/mol higher than for PPE. Also, the reaction barriers for substituted PPE differ significantly from the PPE barriers. The p-methoxy substituent increases the reaction barriers for the R and β channels. The o-methoxy substituents decrease the barrier for the R abstraction, whereas the β barrier stays the same for o-methoxy PPE and increases for di-o-methoxy PPE. The latter might be caused by an increased steric effect in the β transition state. The 2861

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Figure 4. Lowest transition-state structures for hydrogen abstraction reactions (2 and 6) on o-methoxy PPE: b, hydrogen-benzyl distance in angstroms; p, hydrogen-phenoxy distance in angstroms; and e, hydrogen-ether distance in angstroms.

Figure 5. Lowest transition-state structures for hydrogen abstraction reactions (2 and 6) on di-o-methoxy PPE: b, hydrogen-benzyl distance in angstroms; p, hydrogen-phenoxy distance in angstroms; and e, hydrogen-ether distance in angstroms.

R/β-barrier difference varies over a wide range, from 0.2 to 3.5 kcal/mol, which strongly impacts the R/β selectivity of the phenoxy abstraction. The lowest energy transition state for β-hydrogen abstraction by the o-methoxy phenoxy radical (TS40d) shown in Figure 7 is slightly unusual in that the energy for this transition state is lower than the energy of the products. This implies that the reverse reaction could have a negative Arrhenius activation energy. Such reactions have been observed in hydrogen atom transfers for highly polar reactants, where pre-reactive interactions in the entrance channel (e.g., van der Waals complexes or hydrogen bonding) permit barriers to form below the reactant energies. Examples observed include hydrogen-transfer reactions of C2H5• with HBr, C4H9O• with

O2, and HO• with HONO2. These examples and the basis for such reaction behavior have been discussed in a recent review.27 How polar effects and electron delocalization influence reaction barriers of hydrogen abstraction reactions on PPE and PPE derivatives was discussed in refs 4 and 22. Again, we observe that electron delocalization is less pronounced in the transition states than in the product radicals, causing the R/βbarrier difference to be small compared to the R/β-product energy difference. The polar effect was used to explain the stabilization of the β transition states of the electrophilic phenoxy radical relative to the R transition states by charge donation from the adjacent ether oxygen, which decreases the (27) Donahue, N. M. Chem. Rev. 2003, 103, 4593.

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Figure 6. Reaction profile based on the lowest transition states for the hydrogen abstraction reactions on substituted PPE by the benzyl radical. Energies are given in kcal/mol. For simplicity, we only show the product energies that include radicals derived from the lowest energy conformers of the corresponding PPE derivative.

Figure 7. Reaction profile based on the lowest transition states for the hydrogen abstraction reactions on substituted PPE by substituted phenoxy radicals. Energies are given in kcal/mol. For simplicity, we only show the product energies that include radicals derived from the lowest energy conformers of the corresponding PPE derivative.

R/β-barrier gap. The differences between the charges of the lowest phenoxy β transition states and the reactants are given in the Supporting Information. Comparing the polarization

of transition states and the charge donation by the ether oxygen gives a qualitative assessment of the polar effect. On one hand, we see strong polarization in the phenoxy β 2863

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Table 2. Substituent Effects on Reaction Energies of the Phenoxy Abstraction in kcal/mola

p-methoxy PPE o-methoxy PPE di-o-methoxy PPE

radical effect (phenoxy)

ground-state effect (phenol)

substituent effect on R PPE

total substituent effect on R channel

substituent effect on β PPE

total substituent effect on β channel

3.99 2.89 2.53

-1.76 -3.47 -2.21

0.31 0.39 0.45

6.06 6.75 5.19

-0.32 -0.16 0.55

5.43 6.20 5.29

a Total substituent effects are divided into radical effect on phenoxy, ground-state effect on phenol, and substituent effect on PPE and corresponding radical combined. The total substituent effect on the reaction energy of the R channel is the sum of the first, the negative of the second, and the third column, and the total substituent effect on the reaction energy of the β channel is the sum of the first, the negative of the second, and the fifth column.

Figure 8. Arrhenius plots for the R- and β-hydrogen abstraction reactions on PPE, p-methoxy PPE (pPPE), o-methoxy PPE (oPPE), and di-omethoxy PPE (di-oPPE) by benzyl and phenoxy radicals. Rate constants were computed in the temperature range of 580-660 K. Table 3. Activation Energies and Arrhenius Pre-factors Derived from Calculated Rate Constants in the Temperature Range of 580-660 K (Figure 8) benzyl abstraction R channel

PPE p-methoxy PPE o-methoxy PPE di-o-methoxy PPE

phenoxy abstraction β channel

R channel

β channel

Ea (kcal/mol)

ln A

Ea (kcal/mol)

ln A

Ea (kcal/mol)

ln A

Ea (kcal/mol)

ln A

11.6 11.5 11.4 11.3

16.3 15.7 15.9 16.7

13.9 13.5 13.4 12.9

16.8 16.6 16.7 16.5

11.7 14.0 12.3 11.9

16.4 15.9 15.7 15.1

12.4 15.0 13.0 15.2

16.9 16.6 16.1 16.5

transition states of PPE, o-methoxy PPE, and di-o-methoxy PPE. On the other hand, charge donation from the ether oxygen seems small for o-methoxy PPE. The R/β-barrier differences for the phenoxy abstractions follow the trend: ΔE (PPE) = 0.2 kcal/mol, ΔE (p-methoxy PPE) = 0.9 kcal/ mol, ΔE (o-methoxy PPE) = 1.0 kcal/mol, and ΔE (di-omethoxy PPE) = 3.5 kcal/mol. A weak polar effect in the transition state of p-methoxy PPE compared to PPE is consistent with a larger barrier difference for p-methoxy PPE. The same conclusion cannot be drawn for o- and di-o-substituted PPE, which we believe is a consequence of an increased steric effect in the β transition states relative to the R transition states, masking the electronic effect. The substituent effect on the reaction energies of the phenoxy abstraction (Figure 7) is remarkably large. Figure 6 shows that the substituent effects on the PPE derivatives and their corresponding radicals is small because the substituent effect on the reaction energies of the benzyl abstraction is small and the second reactant; i.e., benzyl, does not carry substituents. Therefore, the reason for the reaction energy differences of the phenoxy abstraction must be the strong influence of the substituents on phenol and/or the phenoxy radical. The total substituent effect originating from the phenoxy/phenol system can be divided into radical and ground-state effects, as illustrated in the Supporting Informa-

tion. Table 2 summarizes the contributions to the substituent effects on the reaction energies of the phenoxy abstraction. We observe that the substituent effects on the phenoxy radical and phenol dominate the total substituent effect. The phenoxy radical is stabilized while phenol is destabilized by the methoxy substituents. The phenoxy and phenol effects are additive, resulting in a large total substituent effect for the R and β channels. Figure 8 shows the Arrhenius plots in the temperature range of 580-660 K obtained by calculating the rate constants for the R and β channels of the hydrogen abstraction reactions by the benzyl and phenoxy radicals (reactions 2 and 6) for PPE, p-methoxy PPE, o-methoxy PPE, and di-o-methoxy PPE using 117 transition states. The activation energies and Arrhenius prefactors derived from these plots are given in Table 3. Conclusions, which could be drawn from the 0 K energy profiles of Figures 6 and 7 employing only the lowest energy transition state, do not necessarily coincide with the trends in the reaction rates. For example, according to Figure 6, the benzyl radical R abstraction on o- and di-omethoxy PPE should be accelerated in comparison to the R abstraction on PPE and p-methoxy PPE; instead, the hydrogen abstractions on o-methoxy PPE and p-methoxy PPE are decelerated, and only the abstraction on di-o-methoxy PPE is accelerated in comparison to PPE. In fact, the activation 2864

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Table 4. Total R/β Selectivities and Individual R/β Selectivities for the Benzyl and Phenoxy Hydrogen Abstraction on PPE Derivatives at 618 Ka total selectivity

PPE p-methoxy PPE o-methoxy PPE di-o-methoxy PPE a

benzyl selectivity

phenoxy selectivity

this work

experimental

experimentalb

3.7 1.9 2.5 4.7

1.1 1.1 1.2 3.6

1.7 1.4 1.5 3.7

3.8 ( 0.3 3.0 ( 0.03 4.6 ( 0.1 7.3 ( 0.4

3.7 ( 0.3 2.7 ( 0.03 4.0 ( 0.1 5.1 ( 0.4

Experimental values are taken from ref 7. b Homolysis contribution is subtracted.

energies obtained from the Arrhenius plots for the benzyl radical R abstraction on the different PPE derivatives are all very similar. This is not only a finite temperature effect but can also be contributed by the inclusion of energetically higher transition states relative to the lowest transition state. For instance, two energetically higher transition states than TS1 (0.9 and 1.8 kcal/mol) were included in the calculation of the benzyl R-abstraction rate on PPE. Only one additional transition state was found for p-methoxy PPE, which is 1.8 kcal/mol higher than TS15a. This explains why the R abstraction on PPE is faster than on p-methoxy PPE even though the reaction barriers in Figure 6 are the same. Similarly, the number of transition states included to calculate the rate on o-methoxy PPE is smaller, which counteracts the effect of the lower energy barrier for TS28a. The number of transition states for di-o-methoxy PPE is the same as that for PPE, and the barrier corresponding to TS45 is lower than that for PPE, which results in an accelerated reaction rate. The finite temperature rates for the β abstraction by the benzyl radical follow the expectation from Figure 6, where the abstraction on di-o-methoxy PPE is fastest, followed by o-methoxy PPE, p-methoxy PPE, and PPE. In contrast to the 0 K energy profile of the phenoxy abstraction in Figure 7, we observe a clustering of the abstraction rates according to the substitution pattern on PPE. The hydrogen abstraction for the R and β channels by the phenoxy radical is fastest for PPE, followed by o- and di-omethoxy PPE, and the abstraction on p-methoxy PPE is slowest. An exception is the β abstraction on di-o-methoxy PPE, which is sterically hindered. The forward reaction rates have been used in a simplified kinetic model4,22 invoking the quasi-steady-state approximation for the radical chain reaction to compute the total R/β selectivity of the pyrolysis mechanism shown in Scheme 1. The total R/β selectivities and the individual R/β selectivities for the benzyl and phenoxy abstraction, given by the ratio of the forward rate constants, are tabulated for the different PPE derivatives in Table 4. We observe that the total R/β selectivities are underestimated in comparison to experimental values, which will be discussed in more detail below. Within the kinetic model, the phenoxy selectivity dominates the total selectivity4,22 but for the phenoxy abstraction, the R pathways (except for di-o-methoxy PPE) are only slightly favored in comparison to the β pathways, resulting in small total R/β selectivities. In earlier work,4 we investigated the hydrogen abstraction reactions on PPE using the B3LYP functional and obtained a R/β selectivity of 2.4 at 648 K; the experimental value is 3.1 ( 0.3 at 648 K. Comparing the B3LYP R/β selectivity with the M06-2X R/β selectivity of Table 4 suggests that the B3LYP functional may be better suited for the calculation of product selectivities of β-O-4 model compounds than the M06-2X functional, which, in other work,24,25 was found to have better kinetic properties than the B3LYP functional. In ref 4, we reported activation barriers obtained with B3LYP for the

hydrogen abstraction by the benzyl radical to be 18.8 kcal/mol for the R pathway and 21.2 kcal/mol for the β pathway, with corresponding prefactors of 17.2 and 17.2. The experimental activation energies are 14.4 kcal/mol for the R channel and 17.6 kcal/mol for the β channel, with prefactors of 19.1 and 19.6, respectively, with relatively large error bars.28 The B3LYP activation energies overestimate the experimental values by 4.4 and 3.6 kcal/mol. The M06-2X functional (see Table 3) underestimates the experimental energies by 2.8 and 3.7 kcal/mol. Because the R/β-barrier difference is very similar for the two functionals (2.4 and 2.3 kcal/mol), the worsening agreement of the R/β selectivity when using the M06-2X must have a different origin. With the B3LYP functional, we located two transition states for the R pathway and two transition states for the β pathway of the hydrogen abstraction by benzyl and three transition states for the R pathway and two transition states for the β pathway of the hydrogen abstraction by phenoxy on PPE.4 In contrast, with the M062X functional, we found three transition states for the R pathway and four transition states for the β pathway of the hydrogen abstraction by benzyl and three transition states for the R pathway and four transition states for the β pathway of the hydrogen abstraction by phenoxy on PPE. Each transition state defines a reaction channel, and the forward rate constants for the benzyl and phenoxy abstractions are the sum of the rate constants corresponding to the individual transition states. In Table 5, we list M06-2X R/β selectivities for a varying number of transition states (for better comparison, we omit tunneling corrections in the rate constants because they have not been included in the B3LYP values). When only the lowest transition states of each pathway are included (combination 1111 in Table 5), the total R/β selectivity is low, where the individual selectivity of the phenoxy radical is the dominating contribution. For transition-state combination 3434, the total and the individual R/β selectivities are even lower, because for the benzyl and the phenoxy abstraction an additional reaction path is available for the β channel compared to the R channel. Transition-state combination 2232 has the highest total R/β selectivity, which can mainly be attributed to the higher selectivity for the phenoxy abstraction because of the larger number of R transition states compared to β transition states. In fact, the total M06-2X R/β selectivity calculated with the same transition-state combination as used for the B3LYP value gives nearly the same total R/β selectivity, i.e., 2.5 for M06-2X and 2.4 for B3LYP. The above analysis emphasizes the importance of the conformational space search to the calculation of rate (28) The best experimental rate constant for a reference reaction (2allylbenzyl radical abstracting hydrogen from meta-xylene; Franz, J. A.; Alnajjar, M. S.; Barrows, R. D.; Kaisaki, D. L.; Camaioni, D. M.; Suleman, N. K. J. Org. Chem. 1986, 51, 1446) has an error of 0.7 kcal/mol in the activation energy and 0.4 in log A. The group additivity parameters (from Benson's book, ref 58 in ref 13) have errors associated with them as well. An overall estimate of the errors in the experimental values is 1-2 kcal/ mol for the activation energies and 2.5 for ln A.

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Table 5. Total R/β Selectivities and Individual R/β Selectivities for the Benzyl and Phenoxy Hydrogen Abstraction on PPE at 618 K Including a Varying Number of Transition Statesa number of transition states benzyl abstraction

phenoxy abstraction

R

β

R

β

benzyl selectivity

phenoxy selectivity

total selectivity

1 2 3

1 2 4

1 3 3

1 2 4

4.8 5.5 3.7

1.2 2.0 1.1

1.9 2.5 1.7

a

Selectivities were obtained using the M06-2X functional. Italic selectivities incorporate the same number of transition states as used to compute the B3LYP selectivities in ref 4.

constants and selectivities. The Supporting Information includes a table of the reaction barriers for all 117 transition states. For example, the β abstraction by the phenoxy radical on PPE can proceed through four different transition states; the lowest 0 K barrier is 10.0 kcal/mol, followed by 10.9, 11.0, and 11.3 kcal/mol. The calculated rate constant at 618 K when only the lowest transition state is used is 256. When the second transition state is also included, the rate constant increases by a factor of 2.0; when the first three transition states are taken into account, the rate constant increase by a factor of 2.6; and when all four transition states are considered, the rate constant increases by a factor of 3.5. The conformational search depends upon the computational method used to solve the electronic structure problem. Particularly, when transition states are located in shallow regions of the potential energy surface, the use of a different functional can change the character of an extremum to a point with more than one imaginary frequency. Because the region around the transition states for the hydrogen abstraction reaction considered here is shallow (see the discussion above), consistency in the computational approach is pertinent. Table 4 shows that the experimental trend in the total R/β selectivities is not well-reproduced by the computational values outside of the noticeable increase in selectivity for the di-o-methoxy PPE case. One factor is that the experimental values shown in column five and reported in ref 7 include contributions from the initial C-O homolysis step (reaction 1 in Scheme 1), which is negligible for PPE but becomes increasingly important for the methoxy-substituted PPEs. This is a consequence of the significantly reduced C-O BDEs for the methoxy derivatives (5.1-5.5 and 8.6 kcal/mol for one and two methoxy substituents, respectively),13 which results in much shorter kinetic chain lengths.7 In column six of Table 4, we have subtracted the contribution of homolysis to the R/β selectivities, which decreases the selectivies and brings them closer to the calculated values. This adjustment is based on the amount of ethylbenzene formed as a product. However, because hydrogen abstraction by phenethyl radicals to form ethylbenzene now becomes significant (reactions 7a and 7b in Scheme 1), these steps must be explicitly taken into account in the kinetic model and can no longer be ignored for these derivatives. Another key factor that is different between the hydrogen abstraction reactions on previously studied PPE derivatives containing substituents on the phenethyl ring22 and the reactions reported here is that the methoxy substituents considerably destabilize phenol and stabilize the phenoxy radical as discussed above. This leads to the increase of the product energies of the phenoxy abstraction to an extent that the reverse reaction rate becomes significant. Strong participation of the reverse reaction is expected for the β pathways of the phenoxy abstraction (see Figure 7) on p-methoxy PPE,

o-methoxy PPE, and di-o-methoxy PPE, where the product energies are comparable or even higher than the transitionstate energies. Inclusion of these reverse steps would increase the R/β selectivities toward the experimental values. We conclude that the simplified steady-state kinetic model used to compute the total R/β selectivity of previously studied PPE derivatives is not applicable for the pyrolysis mechanisms of PPE derivatives where methoxy substituents are located on the phenyl ring adjacent to the ether oxygen. Instead, the reverse reaction rates need to be included in the kinetic model, as well as hydrogen abstraction steps involving phenethyl radicals, which does not lead to a simple analytical expression. In future work, we will compute rate constants for these steps and also include the phenyl shift and β-scission reactions of the pyrolysis mechanism shown in Scheme 1. This will enable us to use the calculated rate constants in a numerical simulation of the entire mechanism, understand more clearly the impact of substituents on product selectivities, and provide quantitative input for more complicated kinetic modeling of lignin pyrolysis, which is of current interest.29 Conclusion We studied the hydrogen abstraction reactions on substituted PPE by the benzyl and phenoxy radicals using DFT, in particular, the M06-2X functional. These reactions are part of the radical chain mechanism of the thermal decomposition of PPE and PPE derivatives, which serve as model compounds for the β-O-4 linkage in lignin. The investigated derivatives carry para-, ortho-, and di-ortho-methoxy substituents on the phenyl ring adjacent to the ether oxygen. The search for transition states was based on six reactant ether conformers, which implicitly determined the conformation of the phenoxy radicals. This choice was supported by potential energy profiles for the rotation of the phenyl rings and the methoxy substituents. We located 117 transition states, which were used to compute the rate constants for R- and β-hydrogen abstraction reactions. The rate constants were calculated within transition-state theory, including a Wigner tunneling correction. Anharmonic corrections were incorporated within the independent mode approximation using the semi-classical Wigner-Kirkwood approximation to calculate the one-dimensional anharmonic vibrational partition function. We have shown the strong dependence of the rate constants on the number of transition states included. Transition states about 1 kcal/mol higher in energy than the lowest transition state contribute significantly to the rate constant and can increase the rate constant by a factor of 2. Methoxy substituents decelerate the hydrogen abstractions by the phenoxy radicals. In comparison to PPE, (29) Hou, Z.; Bennett, C. A.; Klein, M. T.; Virk, P. S. Energy Fuels 2010, 24, 58.

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the benzyl radical abstraction rate of the β hydrogen is slightly increased by the substituents and the abstraction rate of the R hydrogen is decreased for p- and o-methoxy PPE but increased for di-o-methoxy PPE. The calculations provide insight into the role of steric and polar effects in these important hydrogen-transfer steps. The rate constants were used to calculate the overall R/βproduct selectivities, employing a simplified quasi-steadystate kinetic model found to be successful in reproducing experimental product selectivities in previous work.4,22 However, for the current PPE derivatives where methoxy substituents are located on the phenyl ring adjacent to the ether oxygen, the selectivities are not well-reproduced and the simplified kinetic model is not applicable. This is a consequence of the strongly endothermic character of the hydrogen abstractions by the substituted phenoxy radicals, which requires the reverse reactions be taken into account. Furthermore, our recent studies showed that the methoxy substituents lead to significantly lower C-O BDEs,13 which result in increased rates of homolysis and much shorter kinetic chain lengths. Taken together, the consequence is that a simple

analytical expression describing the kinetics cannot be derived. The calculated rate constants will be used in future work to numerically simulate the pyrolysis mechanism, which will require the computation of the rate constants of all participating reactions. Acknowledgment. This research was sponsored by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy. This research was performed in part using the resources of the Center for Computational Sciences at Oak Ridge National Laboratory under Contract DE-AC05-00OR22725. Supporting Information Available: Potentials for phenyl and methoxy rotation in PPE and methoxy-substituted PPE, images of all transition states, harmonic potentials of spurious imaginary modes of three transition states, table of activation energies corresponding to individual transition states, polarization in selected transition states, and scheme to illustrate ground and radical substituent effects in phenol and phenoxy radicals. This material is available free of charge via the Internet at http:// pubs.acs.org.

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