New Reaction Classes in the Kinetic Modeling of Low Temperature Oxidation of n-alkanes

Transcription

1 Supplemental Material for paper New Reaction Classes in the Kinetic Modeling of Low Temperature Oxidation of n-alkanes Eliseo Ranzi, Carlo Cavallotti, Alberto Cuoci, Alessio Frassoldati, Matteo Pelucchi, Tiziano Faravelli Dept. di Chimica, Materiali e Ingegneria chimica G. Natta, Politecnico di Milano (September 2014) This file contains Details of calculations performed for H-abstractions from the hydroperoxyl substitution site (section S1), for ketohydroperoxide decomposition through the Korcek mechanism (section S2), and for the molecular decomposition of acetyl-methyl-hydroperoxide (section S3). Structures and vibrational frequencies of the 3 reaction pathways investigated theoretically: H-abstractions from the site of the hydroperoxyl substitution (section S4), the Korcek ketohydroperoxide decomposition pathway (section S5), and the molecular decomposition of acetyl-methylhydroperoxide (section S6). In section S7 it is discussed how the minimum energy structures of the KHP isomers were located, while in section S8 it is reported a comparison between the computational prediction for the rate constant of cyclization of 2-formyl-ethyl-hydroperoxide performed in this work and the procedure adopted by Jalan et al.[2013]. 1

2 S1. H-abstractions from the hydroperoxyl substitution site As mentioned in the text, simulations were performed for the two minimum energy isomers of C 4-1KHP (2-acetylethyl-hydroperoxide, CH 3COCH 2CH 2OOH), whose structures are reported in Figure S1. Though it might be argued that the rotational conformers are likely to be much more than the two considered in this analysis, it is also true that the rate constant for H-abstraction will be determined mostly by the relative orientation of the OH radical with respect to the - CH 2OOH group, which is well described by the cis and trans transition states, and by the possible orientations of the - CH 2- group connected to the -CH 2OOH group, which are two and correspond to the two isomers here considered. More details on how the two isomers were found are reported in section S7. The rate constants for these reactions were computed using the Rigid Rotor - Harmonic Oscillator (RRHO) approximation, as the analysis of the vibrational frequencies of transition states (TSs) and reactants showed that the contribution to the vibrational partition functions coming from internal torsional modes, which would be better described using a hindered rotor model, does not change substantially between TSs and reactants, so that their contribution to the partition functions evens out in the rate constant estimation. Of the four transition states (each one with two optical isomers), three have submerged energy barriers. The barrier heights computed at the CBS-QB3 level for the minimum energy structure for the cis and trans conformations are and 0.13 kcal/mol, while those computed for the second conformer are and -0.3 kcal/mol. The presence of negative energy barriers is indicative of the existence of a precursor state, as it is known for this class of reactions. In these cases the rate constant is determined both by the rate of formation of the precursor complex and by its rate of reaction to give the desired product, which is in competition with decomposition to reactants. This is usually well described using two states transition state theory [Greenwald et al., 2005]. In the present investigation the rate of formation of the precursor complex was not considered and the rate constant was determined using conventional transition state theory, thus providing an upper limit to the real rate constant. Given the low values of the energy barriers it is reasonable to expect that, at the temperatures considered in this study the reaction flux will be controlled by the inner transition state, as the density of states of the outer transition state will be significantly larger and the difference in energy between the inner and outer transition state is minimal. Figure S1: Structures of the minimum energy conformer (a) and of the isomer (b) of C 4-1KHP that is closest in energy (+0.6 kcal/mol) considered to calculate H-abstraction rates from the OH radical and structures of the cis (c) and trans (d) transition states calculated for the minimum energy conformer. 2

3 S2. Ketohydroperoxide decomposition through the Korcek mechanism Structures and vibrational frequencies of stationary points of the investigated PES were determined at the M062X/6-311+G(d,p) level of theory. The barrier height was computed at the CCSD(T) level with extension to the complete basis set limit for C 3CHP, while the barrier heights for C 4-1KHP and C 4-2KHP (2-formyl-isopropyl-hydroperoxide, CHOCH 2CHOOHCH 3) cyclization were computed at the CBS-QB3 level and corrected for the difference between the CBS-QB3 and CCSD(T)/CBS energy barriers computed for the C 3CHP cyclization reaction. The reason why it was preferred to re-calculate the rate constant for C 3CHP is that the CCSD(T)/CBS energy barrier computed for this reaction is about 1 kcal/mol smaller than that computed by Jalan et al. at the CCSD(T)/cc-pVTZ level. As the CCSD(T)/CBS level of theory is more accurate than that of the previous calculations, it was decided to re-estimate the rate constant. This served also as a benchmark to test the level of uncertainty for the estimation of the rate constants of the Korcek mechanism for C4-hydroperoxides. Channel specific rate constant for CP decomposition were computed using the rate parameters calculated by Jalan for the decomposition of the CP species formed by C 3-KHP cyclization. Figure S2: Structures of a) C 3CHP, b) C 4-1KHP, and c) C 4-2KHP and torsional modes considered as 1D rotors (shown in Figure for C 4-2KHP) to estimate the rovibrational partition function of the reactant when calculating the cyclization rate. The conformational analysis of the reactants was here performed using a 1D hindered rotor model on 1D relaxed potential energy scans for the four torsional modes highlighted in Figure S2. As pointed out by Jalan et al., the use of an ensemble of 1D rotors to perform the conformational analysis for a KHP species is a gross approximation as it neglects the fact that the torsional motions are coupled. Neglecting this aspect corresponds to neglecting the contribution of many rotational isomers to the density of states of the reactant. An estimation of the expected error was performed by Jalan for C 3CHP. It was thus found that the 1D hindered rotor approach underestimates the rovibrational partition function of the reactant by a factor of 7 at 600 K with respect to a more accurate calculation performed considering explicitly the 27 possible isomers of C 3CHP and calculating the vibrational partition function including anharmonic corrections. In the present work the rate constant of C 3CHP cyclization to the cyclic peroxide intermediate (CP) was first calculated as described above using the 1D rotor approximation adopting as reference structure the minimum energy isomer of the reactant. While the calculated rovibrational partition function of the reactant is similar to that determined by Jalan, the rate constant differs only by a factor of 2.7 at 600 K, when calculated at parity of energy barrier. The reason is that not including anharmonic corrections both for the reactant and the transition state leads to an error cancellation effect. To improve the estimation of the rate constant two conformers were used to calculate the rovibrational partition function of the reactants: the minimum energy structure of the reactant and the structure of the 3

4 conformer that is closest in energy and that cannot be generated by a single rotation of one of the torsional angles, but requires at least the rotation of two angles. This way the 1D torsional analysis can be performed for the two conformers minimizing the risk of double counting of the same configurations. The two conformers considered for this analysis differ only by 0.2 kcal/mol for C 3CHP at the CBS-QB3 level and correspond to the two lowest energy isomers found by Jalan et al. The rate constant estimated at 600 K using a rovibrational partition function calculated performing a Boltzmann weight of the two partition functions of the two isomers differs only by a factor of 1.5 from the value calculated by Jalan when using the same energy barrier to calculate the rate constant. If the comparison is performed using the CCSD(T)/cc-pVTZ value computed on the geometry optimized in the present calculations the difference decreases to a factor of 1.1. A more extended comparison between the two computational approaches is reported in section S8, though it is important to emphasize that the good agreement between the two approaches is in part due to a cancellation of errors, and that at 1000 K the difference between the approaches increases to a factor of 2. It is here also important to point out that the Eckart tunneling correction factor is in good agreement with the VTST/SCT prediction above 400 K (the difference is below 10%), while the tunneling factor is overestimated by a factor of 2.5 at 300 K. On the basis of these results it is reasonable to expect that the rate constant estimation for KHP cyclization performed as outlined above is within the uncertainty factor of three that was desired for the present analysis at least up to 700 K. Table S1. Energy barriers and relative energies for the reactions of cyclization of C 3CHP, C 4-2KHP, and C 4-1KHP to the cyclic peroxide intermediate whose decomposition represent an important pathway for the formation of acids and aldehydes. Energy barriers estimated at different levels of theory are reported in kcal/mol. The energy of the conformer considered in the simulations relative to that of the minimum energy structure and corrected for ZPE is reported in kcal/mol. Energy Barrier (kcal/mol) Level of Theory a,b C 3CHP CHOCH 2CHOOHCH 3 CH 3COCH 2CH 2OOH CBS-QB3 b M062X/6-311+G(d,p) CCSD(T)/cc-pVTZ c CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/CBS Level of Theory Relative Energy of Conformer (kcal/mol) CBS-QB M062X/6-311+G(d,p) a) all calculations performed on geometries determined at the M062X/6-311+G(d,p) level except for CBS-QB3 energies; b) Zero point energies are not included; c) the energy barrier computed by Jalan et al. using the same basis set is The difference with respect to the value here reported is probably due to the different basis sets used to determine the structure of the transition state: g(d,p) (here) vs. MG3S. 4

5 Table S2: Rate constants for the decomposition of C 3CHP, C 4-2KHP, and C 4-1KHP to the reaction products that can be formed from the decomposition of the CP intermediate through the Korcek mechanism interpolated between 400 and 1000 K in the modified Arrhenius form:. Reaction A α Ea (cal/mol) C 3CHP CH 3COOH + H 2CO 5.7E C 3CHP HCOOH + CH 3CHO 4.7E C 4-2KHP CH 3COOH + CH 3CHO 1.4E C 4-2KHP CH 3COCH 3 + HCOOH 3.4E C 4-1KHP CH 3COOH + CH 3CHO 3.5E

6 S3. Molecular decomposition of acetyl-methyl-hydroperoxide. Simulations were performed determining the geometries of reactants and transition state using a minimal active space of 4 electrons in 4 orbitals, including the σ and σ* orbitals of the O-O peroxyl bond and the σ and σ* orbitals of the C-C acetyl-methylhydroperoxyl bond for the three body decomposition reactions and an active space of 6 electrons in 6 orbitals that included the σ and σ* orbitals of the O-O peroxyl bond, the σ and σ* orbitals of the O-H hydroxyl bond, and the π and π* orbitals of the carbonyl, for the cyclization reaction. The structure of the three transition states and of the reactant are shown in Figure S3. As it can be observed in Figure S3b and S3c, the transition states for the three body reactions are characterized by the partial rotation of the OH group towards the oxygen atom of formaldehyde. The transition state of the cyclization reaction, though similar to the one that was found for C 3CHP, C 4-1KHP, and C 4-2KHP, has some substantial differences. In particular the C-O length of the forming bond is 1.82 Å, with respect to the 1.72 Å found for the C 3CHP cyclization transition state, while the H-O forming and breaking bond lengths are 1.22 Å and 1.26 Å, while those found for C 3CHP are 1.32 Å and 1.17 Å, respectively. These differences are probably due to the different number of atoms involved in the cyclization transition state, which are five for the Korcek mechanism and four in this case, thus determining a considerable increase of the molecular strain. Figure S3: Minimum energy structures of acetyl-methyl-hydroperoxide (a) and of three transition states leading to: b) three body decomposition (cis transition state), c) three body decomposition (trans transition state), and d) cyclization to a cycloperoxy intermediate. The analysis of the barrier heights reported in Table 2 in the text reveals some interesting aspects of this reacting system. The first is that cyclization is energetically unfavored with respect to dissociation, which is different from what found for the peroxy cyclization reaction previously considered when studying the Korcek mechanism and is most reasonably due to the strain related to the formation of a 4 membered cyclic species. The second is that the energy barrier of the decomposition reactions is smaller than the reaction energy change, which is calculated to be 47.9 kcal/mol at the CBS-QB3 level of theory. This is not due to a computational error, as a similar reaction energy of 47.4 kcal/mol was determined at the CASPT2/aug-cc-pVTZ level using a (6e,6o) active space and imposing a 10 Å separation between the three fragments. The difference between energy barrier and reaction energy is thus probably due to a residual interaction between the three fragments at the transition state that will lead, following dissociation, to the formation of a precursor complex. The already mentioned establishment of an interaction between OH and formaldehyde does probably contribute significantly to the stabilization of the transition state. 6

7 S4. Structures and vibrational frequencies calculated for H-abstraction from 2-acetyl-ethyl-hydroperoxide Well 1 (Minimum Energy Structure) CBS-QB3 C O C C O O C H H H H H H H H

8 Well 2 (Conformer) CBS-QB3 C C O C C O O H H H H H H H H

9 Cis Transition state for minimum energy reactant CBS-QB3 C C C C O O O H H H H H H H H O H

10 Trans Transition state for minimum energy reactant CBS-QB3 C C C C O O O H H H H H H H H O H

11 Cis Transition state for conformer CBS-QB3 C C C C O O O H H H H H H H H O H

12 Trans Transition state for conformer CBS-QB3 C C C C O O O H H H H H H H H O H

13 S5. Structures and vibrational frequencies calculated for the Korcek ketohydroperoxide decomposition pathway Cyclization of 2-formyl-ethyl-hydroperoxide (HCOCH2CH2OOH) HCOCH2CH2OOH Reactant: minimum energy structure (M062X/6-311+G(d,p) ultrafine grid) C C C O O O H H H H H H

14 HCOCH2CH2OOH Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C C H H C O O O H H H H

15 HCOCH2CH2OOH cyclization transition state (M062X/6-311+G(d,p) ultrafine grid) C H C C O O O H H H H H

16 Cyclization of 2-acetyl-ethyl-hydroperoxide (CH3COCH2CH2OOH) CH3COCH2CH2OOH Reactant: minimum energy structure (M062X/6-311+G(d,p) ultrafine grid) C O C C O O C H H H H H H H H

17 CH3COCH2CH2OOH Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C C O C C O O H H H H H H H H

18 CH3COCH2CH2OOH transition state (M062X/6-311+G(d,p) ultrafine grid) C O C C O O C H H H H H H H H

19 Cyclization of 2-formyl isopropyl-hydroperoxide (HCOCH2CHOOHCH3) HCOCH2CHOOHCH3 Reactant: minimum energy structure (M062X/6-311+G(d,p) ultrafine grid) C O C C O O H H H H C H H H H

20 HCOCH2CHOOHCH3 Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C O O C C O H H H C H H H H H

21 HCOCH2CHOOHCH3 cyclization transition state (M062X/6-311+G(d,p) ultrafine grid) C O C C O O H H H H C H H H H

22 S6. Molecular decomposition pathways for acetyl-methyl-hydroperoxide Acetyl-methyl-hydroperoxide minimum energy structure. CASPT2(4e,4o)/cc-pVTZ H C C O C O O H H H H H

23 Transition state Acetyl-methyl-hydroperoxide CH3CO + H2CO + OH cis. CASPT2(4e,4o)/cc-pVTZ C C C O H H O H H H O H

24 Transition state Acetyl-methyl-hydroperoxide CH3CO + H2CO + OH trans. CASPT2(4e,4o)/cc-pVTZ C C O C O O H H H H H H

25 Transition state Acetyl-methyl-hydroperoxide cyclic peroxide. CASPT2(6e,6o)/cc-pVTZ C C C O H H O H H H O H

26 S7. Conformational Analysis An extensive conformational analysis was performed in this work with the intent of locating the minimum energy structure to use as reference for the calculation of rate constants, as well as to determine the structure of the conformer that lies closest in energy to the minimum energy conformer. The approach here adopted consisted in performing several 1D relaxed potential energy scans starting from different conformations. In particular, four 1D potential energy scans were performed for each one of the two structures that were considered for the cyclization reactions of the 3 different KHPs species here considered. It was thus confirmed that the two structures considered in the calculation are the minimum energy structure and conformational isomer with the closest energy. In addition, the extensive conformational analysis performed by Jalan et al. was exploited in order to determine first guesses for the minimum energy structures. Indeed, it was confirmed that the two minimum energy structures here found for 2-formyl-ethyl-hydroperoxide are the same located by Jalan et al and that the two structures found for 2-formyl isopropyl-hydroperoxide and for 2-acetylethyl-hydroperoxide are similar to those that can be obtained from 2-formyl-ethyl-hydroperoxide by substitution of a H atom with a methyl group. 26

27 S8. Comparison between the computational prediction for the rate constant of cyclization of 2-formyl-ethylhydroperoxide performed in this work and the MS-T model. As mentioned in the text, the procedure here adopted to determine the CHP cyclization rate constant suffers for the shortcomings related to the use of an approximate procedure to perform the conformational analysis for the reactant, which is based on 1D relaxed potential energy scans. It has however been reported in section four of the paper that including the two minimum energy isomers in the simulations improves considerably the agreement with the data calculated by Jalan et al. performing a more extensive conformational analysis and including anharmonic contributions in the calculations. It is thus useful to compare more in detail the two approaches in order to understand differences and similarities, which may be useful to improve the estimation of rate parameters for reactants having a large number of conformers. S8.1 Number of conformers The total number of different conformers identified by Jalan is 27. In the present analysis the total number of different conformers that was found through 1D relaxed potential energy scans are 7 for the minimum energy structure and 9 for the second isomer, so that, including the starting wells, a total of 18 wells are found. Of these 18 structures however only 16 are independent, as one structure coincides and one is an optical isomer. This analysis shows that using the 1D hindered rotor approach using more than one reference structure allows improving considerably the sampling of the conformational space, though some care should be placed in order to avoid counting twice the same structure. Also, though the structures not found in the present conformational analysis are most likely the highest energy conformers, it is very reasonable that the underestimation of the density of states that is performed neglecting these conformers will lead to more sensible errors with the increase of the temperature. S8.2 1D Conformational analysis The level of accuracy of the present calculations can be judged comparing the F factors computed using the 1D rotor approximation with one and two conformers with those computed by Jalan using the 27 conformers and accounting for anharmonicities through the MS-T method. The F factor is defined as the ratio between the rovibrational partition function calculated considering all the possible conformers and the anharmonic effects and the one that is computed in the rigid rotor harmonic oscillator approximation using a single reference structure. The comparison is performed in Tables S1 and S2. Table S3. F factors computed at different levels of theory. F Factor Temperature 1D HR on 1 conformer 1D HR on 2 conformers MS-T model (Jalan et al.)

28 Table S4. Ratio of F factors of transition state and reactant. F Factors ratio Temperature 1D HR on 1 conformer 1D HR on 2 conformers MS-T model (Jalan et al.) E-2 3.1E-2 1.7E E-2 2.1E-2 1.2E E-2 1.4E-2 1.0E E-2 1.2E-3 9.0E-3 As it can be observed, the data reported in Table 1 show that the difference between the 1D HR model on 1 conformer and the MS-T model is a factor of 6-8, while it decreases to a factor of 3-4 including the second conformer. Even more interestingly, the difference between the MS-T model and the level of theory used in the present work decreases considerably when the comparison is performed between the ratios of the F factors computed between transition state and reactant. As in the present model we did not compute anharmocities, the improvement in the agreement between the two models is determined by the simplification of the anharmonic corrections computed for the transition state and those computed for the reactant, which will be similar for most internal modes. S8.3 Tunneling corrections The tunneling corrections calculated using the asymmetric Eckart model are reported in table S3, where they are compared with the value determined using the SCT/VTST model (Jalan et al.). The difference between the two models is minimal in the investigated temperature range, while it grows up to a factor of 2 at 300 K. Table S5. Tunneling correction factors calculated using the Eckart model and compared with those determined by Jalan at the SCT/VTST level. Q Tunneling Temperature Asymmetric Eckart SCT/VTST (Jalan)

29 References Greenwald, E. E.; S. W. North; Y. Georgievskii; S. J. Klippenstein, The Journal of Physical Chemistry A 109 (27) (2005) Jalan, A., I. M. Alecu, R. Meana-Pañeda, J. Aguilera-Iparraguirre, K. R. Yang, S. S. Merchant, D. G. Truhlar, and W. H. Green. New Pathways for Formation of Acids and Carbonyl Products in Low-Temperature Oxidation: The Korcek Decomposition of γ-ketohydroperoxides. J. Am. Chem. Soc. 2013, 135,