Temperature and pressure dependent rate coefficients for the reaction of vinyl radical with molecular oxygen

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1 Paper # 070RK-0274 Topic: Reaction Kinetics 8 th U. S. National Combustion Meeting rganized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Temperature and pressure dependent rate coefficients for the reaction of vinyl radical with molecular oxygen C. Franklin Goldsmith, Lawrence B. Harding, James A. Miller, Stephen J. Klippenstein Chemical Sciences and Engineering Division Argonne National Laboratory, Argonne, IL A theoretical treatment for the kinetics of vinyl radical (C 2 H 3 ) with molecular oxygen is presented. The C 2 H 3 2 potential energy surface (PES) was computed using high-level ab initio methods, with accuracy comparable to HEAT, W4, or focal-point calculations. The vinyl 2 interaction potential was computed using multi-reference configuration interaction and multi-reference perturbation theory (with six electrons in four orbitals for 2 and three electrons in three orbitals for C 2 H 3 ), and the corresponding capture rate was computed using variable reaction coordinate transition state theory (VRC-TST). Additional multi-reference calculations were performed for several transition states, including the decomposition of vinylperoxy to form vinoxy and the isomerization of dioxiranylmethyl to oxiranyloxy, which are critical to the overall branching between the two dominant product channels, vinoxy and HC CH 2. Temperature and pressure-dependent rate constants are computed by solving the Master Equation. A double-exponential-down model is used to describe the effects of supercolliders in collisional energy transfer. 1. Introduction The reaction of the vinyl radical (C 2 H 3 ) with molecular oxygen is of fundamental importance in high-temperature oxidation chemistry. At high temperatures, alkyl radicals will fragment via betascission to form smaller radicals and a corresponding alkene. In this regard, the combustion of ethylene (C 2 H 4 ) is central to the combustion of all larger hydrocarbons. The cleavage of this final carbon-carbon bond occurs through the oxidation of either the vinyl or the ketenyl radical (HCC): C 2 H 4 R C 2 H 3 RH [R1] C 2 H 3 2 products [R2] C 2 H 3 C 2 H 2 H [R3] C 2 H 2 HCC H [R4] HCC 2 C C 2 H [R5a] HCC 2 C C H [R5b] Whether the vinyl oxidation pathway [R2] or the ketenyl oxidation pathway [R4-R5] has the higher flux depends upon the temperature, with higher temperatures favoring the decomposition of vinyl and thence the ketenyl pathway. Although the temperature and pressure dependence of the rate

2 coefficient for vinyl decomposition is well known [Miller and Klippenstein 2004], the temperature and pressure dependence of the vinyl 2 rate coefficients remains poorly understood. A thorough, quantitative analysis is complicated by the complexity of the potential energy surface (PES), which in addition to the initial adduct, vinylperoxy has several bimolecular product channels: C 2 H 3 2 CH 2 CH [R2a] vinoxy [R2b] acetylene H 2 [R2c] glyoxal H [R2d] ketene H [R2e] formaldehyde HC [R2f] C CH 3 [R2g] C 2 CH 3 [R2h] riginally, the dominant pathway was assumed to be acetylene H 2, [R2c]. However, Slagle et al. found that the primary product channel was CH 2 HC, [R2f], for the temperature range 297 and 602 K [Slagle et al. 1984]. This result was followed by several theoretical analyses of the potential energy surface that helped to explain the prompt formation of CH 2 HC [Westmoreland 1992, Bozzelli and Dean 1993, Carpenter 1993, Carpenter 1995, Mebel et al. 1996, Lopez et al. 2009]. ne consequence of the theoretical analyses was that vinoxy could be the primary product channel at higher temperatures. The temperature at which vinoxy becomes the primary product channel depends upon the relative barrier heights of a few key transition states, as seen in Figure 1. The corresponding energies for the minima and transition states on the PES are in Tables 1 and 2, respectively. The lowest energy path for vinylperoxy, W1, is isomerization to dioxiranyl-methyl, W3, via TS3. Dioxiranyl-methyl can isomerize to oxiranyloxy, W5, via TS8. xiranyloxy, in turn, will rapidly isomerize to either formyl-methoxy, W6, via TS11, or to formyloxyl-methyl, W7, via TS10; in either case, it is a simple beta-scission to form CH 2 HC. Effectively, the transition state for the isomerization of dioxiranyl-methyl to oxiranyloxy, TS8, acts as the bottleneck to CH 2 HC formation. According to Mebel et al. [Mebel et al. 1996], the temperature at which the rate constant for vinoxy exceeds that for CH 2 HC is approximately 800 K in 760 of N 2. In subsequent work, Carpenter demonstrated that the key transition state TS8 has a strong multi-reference character [Carpenter 2001]. Using multi-reference perturbation theory (CASPT2), Carpenter obtained a transition-state barrier height that was 11.5 kcal/mol lower in energy than that originally obtained in Mebel et al. If that were the case, then the barrier height for TS8 would be lower than that for TS3, which would significantly raise the temperature at which vinoxy becomes the dominant product channel, possibly rendering it kinetically irrelevant. In a response to Carpenter, Mebel and Kislov use both couple cluster (CCSD(T)) and multi-reference configuration interaction (MRCI) with larger basis sets to study this transition state in greater detail [Mebel and Kislov 2005]. They obtained transition-barrier heights that were between 7-8 kcal/mol lower in energy than in Mebel et al. The energies obtained by Mebel and Kislov were computing using the same geometries as by Carpenter [Carpenter 2001]. Although Carpenter presents CASPT2(23,15) energies, the geometry optimization was done using CASSCF(23,15). Despite the large active space, CASSCF is nonetheless a poor method for geometry optimization. Consequently, neither Carpenter s nor Mebel and Kislov s barrier height can be assumed to be quantitatively accurate. The unresolved nature of this key transition state is critical to understanding the branching ratio between vinoxy versus 2

3 CH 2 HC. The location of this switching temperature will have profound consequences for kinetic modeling, since vinoxy is chain branching but nearly thermo-neutral (e.g. -7 kcal/mol in Table 1), whereas CH 2 HC is chain propagating but highly exothermic (-87.2 kcal/mol). To address this problem, the present work presents the most thorough analysis to date of the C 2 H 3 2 potential energy surface. 2. Methods For each stationary point on the potential energy surface, geometry optimization and normal mode analysis was performed using UCCSD(T)/cc-pvtz. The optimized geometry was used for several post-ccsd(t) corrections, similar to those included in HEAT [Tajti et al. 2004] and W4 [Karton et al. 2004] methods to obtain thermochemical accuracy below 1 kj/mol. The total zero-point corrected electronic energy at zero Kelvin, relative to vinyl 2, was computed as follows. First the CCSD(T) energy at the complete basis-set limit, E CCSD(T)/av z, was extrapolated from CCSD(T) calculations with quadruple and quintuple zeta basis sets. Next, corrections for higher level excitations, E CCSDT(Q)/cc-pvdz, were computing from the difference between CCSDT(Q)/cc-pvdz and CCSD(T)/cc-pvdz energies. Corrections for core-valence correlations, E c.v., were determined from the difference in the CCSD(T)/cc-pcv z energies if the core electrons are frozen (uncorrelated) or not. Lastly, relativistic effects, E rel., are approximated from the difference in CI energy with and without using the Douglas-Kroll one-electron integrals. E = E CCSD(T)/av z E CCSDT(Q)/cc-pvdz E c.v. E rel. ZPE (E1) E CCSD(T)/av z = E CCSD(T)/av5z ( E CCSD(T)/av5z - E CCSD(T)/avqz )*0.8 (E2) E CCSDT(Q)/cc-pvdz = E CCSDT(Q)/cc-pvdz - E CCSD(T)/cc-pvdz (E3) E c.v. = E CCSD(T)/cc-pcv z, all - E CCSD(T)/cc-pcv z, valence (E4) E CCSD(T)/cc-pcv z = E CCSD(T)/cc-pcvqz ( E CCSD(T)/cc-pcvqz - E CCSD(T)/cc-pcvtz )* (E5) E rel. = E CI/aug-cc-pcvtz,DK - E CI/aug-cc-pcvtz,non-relativistic (E6) 3. Results and Discussion The zero-point corrected electronic energies at 0 K, relative to vinyl 2, are summarized in Tables 1 and 2. The thick black line in Figure 1 indicates the reaction path for the primary product channel at lower temperatures, CH2 HC, [R2f]. The chain-branching pathway for vinoxy, [R2b], is shown in blue. It is also possible for the dissociating atom to abstract the H atom from the middle carbon of vinoxy via a roaming mechanism, leading to ketene H [R2e]. The other product channel formed directly from vinylperoxy is acetylene H 2, [R2c], shown in red. xiranyloxy will undergo one of two ring-opening reactions. ne pathway yields formyl-methoxy, which, in addition to decomposing to CH 2 HC, also can decompose to glyoxal H, [R2d]. The other ring-opening isomer from oxiranyloxy is formyloxyl-methyl, which, in addition to decomposing to CH 2 HC, also can undergo a 4-member ring internal H abstraction to form methoxyl-formyl (CH 3 C), which can decompose to either C methoxy, [R2g], or C2 methyl, [R2h]. 3

4 10 energy (kcal/mol) H C C H 2 HC H H C 2 CH 3 Figure 1: Potential energy surface for vinyl 2. Table 1: intermediates and products on the vinyl 2 potential energy surface. # name structure T1 energies relative to vinyl 2 (kcal/mol) CBS ZPE T/Q c.v. rel. Total R vinyl W1 vinylperoxy W2 2-hydroperoxylvinyl H W3 dioxiranyl-methyl W4 dioxetanyl W5 oxiranyloxy W6 formyl-methoxy W7 formyloxylmethyl W8 methoxyl-formyl P1 vinoxy

5 P2 acetylene H 2 P3 P4 P5 P6 P7 glyoxal H ketene H formaldehyde HC C methoxy C2 methyl H 2 H C H HC C C 2 CH Table 2: transition states on the vinyl 2 potential energy surface # reaction T1 energies relative to vinyl 2 (kcal/mol) CBS ZPE T/Q c.v. rel. Total TS 1 R to P1 TS 2a W1 to P1 TS 2b W1 to P4 (roaming) TS 3 W1 to P TS 4 W1 to W TS 5 W1 to W TS 6 W1 to W TS 7 W2 to P TS 8 W3 to W TS 9 W4 to W TS 10 W5 to W TS 11 W5 to W TS 12 W7 to W TS 13 W7 to P TS 14 W8 to P TS 15 W8 to P TS 16 W6 to P TS 17 W6 to P Also presented in Tables 1 and 2 are the T1 diagnostics from the UCCSD(T)/cc-pvtz calculations. For several stationary points, the T1 diagnostic is between 0.03 and 0.04 (e.g for H 2 ), which suggests modest multi-reference effects. The uncertainties for these stationary points will be somewhat larger; nonetheless, the post-ccsd(t) corrections (particularly the higher-order excitations) should help to compensate. Multi-reference calculations were essential for four of the transition states. First, the reaction coordinate for the vinyl 2 entrance channel, TS1, is 5

6 barrierless. Second, the reaction coordinate for vinylperoxy decomposition to vinoxy, TS2, has a low-lying excited state, and the - bond distance at the first-order saddle point is greater than 2 Å. Lastly, even though both TS8 and TS9 are well-defined tight transition states, the T1 diagnostics are and 0.117, respectively, which indicates a strong multi-reference character. These four transition states will be discussed individually in the following sections. TS1: vinyl 2 vinylperoxy interaction potential The minimum active space considered for the initial capture of the vinylperoxy adduct is 9 electrons in 7 orbitals: 6 electrons in the 4 π, π* orbitals in oxygen, 2 electrons in the π, π* orbitals in vinyl, plus the singularly occupied orbital in vinyl. The minimum energy path (MEP) was calculated as a function of C- distance, from r = 1.39 Å (the vinylperoxy equilibrium geometry) to r = 20 Å. For each fixed distance r, the remaining degrees of freedom were optimized using CASPT2(9,7)/cc-pvtz. Subsequent MRCI(9,7)/cc-pvtz calculations were performed on the CASPT2 geometries. For these types of reactions, the dynamic bottleneck typically is in the region of 2 to 5 Å. The results of the CASPT2 and MRCI calculations for this region are shown in Figure 2. $#$%!*#$%!"!#$%&'()*,-./&!)#$%!(#$%!'#$%,-./ !789:%,-./01234!;<8=>?3@!AB1>566!789:%,-./01234!;<8=>?3@!C1D<B1>566!789:%,-./01234!E37D1!AB1>566!789:%,-./01234!E37D1!C1D<B1>566!789:%,F)-/ !789:%!&#$%!"#$% )% )#&% (% (#&% '% '#&% &% #&'0/& Figure 2: Minimum energy path for vinyl 2. From Figure 2, it is clear that there is substantial disagreement between the two methods, with a discrepancy of nearly 2 kcal/mol between 2.4 and 2.6 Å. For the MRCI calculations, the Davidson and Pople corrections (MRCIQ) improve the agreement with the CASPT2 calculations. In a separate work, one of the authors has demonstrated that the error introduced by the internal contractions used in the MRCI implementation in Molpro is greatest at the saddlepoint, and the results in Figure 2 appear to confirm this finding. The CASPT2 and MRCI calculations were repeated using both larger basis sets and larger active spaces. The (11,9) active space included the 2 electrons in the 2 σ, σ* orbitals, and the (13,11) active space additionally included the 2 electrons in the C-C σ, σ* orbitals in vinyl. MRCI(13,11) calculations were not performed. The same reference CASPT2(9,7)/cc-pvtz geometries were used for all calculations. For each active space, the calculations were repeated using both the cc-pvtz and cc-pvqz basis sets. The complete basis set limit was then estimated from the triple and quadruple zeta calculations, using an expression 6

7 analogous to (E5). The results for the basis set and active space expansion for r = 2.6 Å are summarized in Table 3. Also included in Table 3 are coupled-cluster calculations with increasingly higher-order excitations with a substantially smaller basis set. The coupled-cluster calculations appear to be converging with higher-order excitations. The CASPT2 and MRCI calculations were repeated using this basis set for comparison. The CASPT2 and MRCIQ calculations are both in reasonable agreement with the CCSDTQ(P) value, differing by 0.4 and kcal/mol, respectively. It is difficult to conclude whether excitations beyond CCSDTQP would converge more to the CASPT2 or MRCIQ values. Compared to the vdz(p/s) basis set calculations, the disagreement between CASPT2 and MRCIQ is larger when the cc-pvtz and cc-pvqz basis sets are used. However, at the highest level considered, the differences between the CASPT2 and MRCIQ methods appear to have stabilized and are within 0.7 kcal/mol along the reaction coordinate. Uncertainty of ± 0.7 kcal/mol will have a non-negligible impact on the rate constants at room temperature. Global uncertainty analysis and comparison with experimental data at room temperature will help to determine whether the CASPT2 or MRCIQ potentials are more accurate. Table 3: vinyl 2 interaction potential at r = 2.6 Å, relative to infinite separation. Method potential (kcal/mol) Single reference (9e7o) (11e9o) (13e11o) CCSDT/vdz(p/s) 0.2 CCSDT(Q)/vdz(p/s) -0.1 CCSDTQ/vdz(p/s) -0.4 CCSDTQ(P)/vdz(p/s) -0.6 CASPT2/vdz(p/s) MRCI/vdz(p/s) MRCIQ/vdz(p/s) MRCIQ/vdz(p/s) MRCIQ/vdz(p/s) MRCIQ/vdz(p/s) CASPT2/cc-pv z MRCI/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z TS2: vinylperoxy vinoxy The vinylperoxy vinoxy reaction is complicated by the presence of low-lying excited states. At infinite separation, the vinoxy complex is three-fold degenerate, with the degeneracy resulting from the four electrons in three orbitals in the isolated -atom. As the - bond distance decreases, the CC dihedral angle approaches 90 degrees; the isolated -atom is perpendicular to the plane of heavy atoms, with one singularly occupied p-orbital aligned with the singularly occupied orbital of the vinoxy oxygen. nce bonding between the two oxygen atoms begins, the terminal oxygen atom is now two-fold degenerate. Finally, as the - distance decreases to the equilibrium value in vinylperoxy, the CC dihedral angle rotates to 180 degrees, and the degeneracy on the terminal oxygen is broken, resulting in an A state, with the A state roughly 24 kcal/mol higher in energy. 7

8 Single reference methods are ill-suited to handle the presence of low-lying excited electronic states in the transition-state region. The minimum active space considered for this reaction is seven electrons in six orbitals: the aforementioned four electrons in three p-orbitals for the -atom, plus three electrons in three orbitals for vinoxy. Although vinoxy is a resonantly stabilized radical with the radical site predominantly localized on the terminal carbon, for the purposes of this reaction the unpaired electron is confined to the terminal oxygen, with the remaining two electrons in the carboncarbon π, π* orbitals. An additional active space of nine electrons in eight orbitals was considered, which includes the two electrons in the carbon-oxygen σ, σ* orbitals. The transition state geometry was optimized using CASPT2(7,6)/cc-pvtz. Normal mode analysis confirmed that the geometry is a first-order saddle point. The same geometry was used for subsequent CASPT2 and MRCI calculations for both the (7,6) and (9,8) active spaces, using both cc-pvtz and cc-pvqz basis sets. The results are summarized in Table 4. For vinoxy at infinite separation (r = 20 Å), a three-state calculation was performed, with equal weighting for the three electronic states. For the transition state, a two-state calculation was performed, with dynamical weighting for the two states. Depending upon the method, active space, and basis set, the nearly-degenerate excited state was between 1.4 and 1.8 kcal/mol above the ground state. For the CASPT2 calculations, as the active space and basis set are increased, the barrier height relative to vinoxy goes from positive to negative. The MRCI calculations, in contrast, all exhibit a positive barrier height. Table 4: TS2: vinylperoxy to vinoxy. Barrier height is relative to vinoxy. method barrier height (kcal/mol) (7e6o) (9e8o) CASPT2/cc-pvtz CASPT2/cc-pvqz CASPT2/cc-pv z MRCI/cc-pvtz MRCI/cc-pvqz MRCI/cc-pv z MRCIQ/cc-pvtz MRCIQ/cc-pvqz MRCIQ/cc-pv z MRCIQ/cc-pvtz MRCIQ/cc-pvqz MRCIQ/cc-pv z MRCIQ/cc-pvtz MRCIQ/cc-pvqz MRCIQ/cc-pv z MRCIQ/cc-pvtz MRCIQ/cc-pvqz MRCIQ/cc-pv z

9 TS8: dioxiranyl-methyl oxiranyloxy As discussed in the introduction, the transition state for the isomerization of dioxiranyl-methyl to oxiranyloxy is a bottleneck in the pathway leading to the primary product channel, CH 2 HC. If the barrier height is decreased, then the temperature at which vinoxy becomes the primary product channel increases. The minimum active space considered for this transition state is three electrons in three orbitals: two electrons in the - σ, σ* orbitals, plus the singularly occupied orbital on the terminal carbon. Two additional active spaces were considered: the (7,7) active space includes the four C- σ, σ* orbitals, and the (9,9) active space also includes the C-C σ, σ* orbitals. For each active space, the geometry was optimized using CASPT2/cc-pvtz. Subsequent calculations were performed using the cc-pvqz basis set to allow for complete basis set extrapolation. Additional MRCI calculations were performed on the CASPT2 geometries. The results are listed in Table 5, along with the corresponding values from Mebel et al [Mebel et al. 1996], Carpenter [Carpenter 2001], and Mebel and Kislov [Mebel and Kislov 2005]. It is difficult to state conclusively what the optimum value is. For the purposes of rate coefficients, the calculations should be repeated with a value of 20 ± 4 kcal/mol to test for sensitivity. Table 5: TS 8: dioxiranyl- methyl to oxiranyloxy. Barrier heights are relative to dioxiranyl- methyl. Method Barrier height (kcal/mol) Single (3e3o) (7e7o) (9e9o) (23e15o) reference UCCSD(T)/cc-pvtz 16.0 CASPT2 (RS2C)/cc-pv z MRCI/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z Mebel et al Carpenter 12.5 Mebel and Kislov TS9: dioxetanyl formyl-methoxy In addition to the pathway through dioxiranyl-methyl, there is also a four-membered ring that can be formed from vinylperoxy, dioxetanyl. The ring-opening transition state for the isomerization of dioxetanyl to formyl-methoxy has an unusually high multi-reference character. This channel is expected to play a minor role in the flux to CH 2 HC, since the transition state barrier height is 12 kcal/mol higher than the competing barrier height for dioxiranyl-methyl formation. The minimum active space considered for this transition state is three electrons in three orbitals: two electrons in the - σ, σ* orbitals, plus the singularly occupied orbital on the radical carbon. Two additional active spaces were considered: the (7,6) active space includes the CH 2 - σ, σ* orbitals plus the lone pair on the oxygen adjacent to the radical carbon, and the (9,8) active space also includes the CH- σ, σ* orbitals. For each active space, the geometry was optimized using CASPT2/cc-pvtz. Subsequent calculations were performed using the cc-pvqz basis set to allow for 9

10 complete basis set extrapolation. Additional MRCI calculations were performed on the CASPT2 geometries. The results are listed in Table 6, along with the corresponding value from Mebel et al [Mebel et al. 1996]. Table 6: TS 9: dioxetanyl to formyl- methoxy. The barrier heights are relative to dioxetanyl. Method Barrier height (kcal/mol) Single (3e3o) (7e6o) (9e8o) reference UCCSD(T)/cc-pvtz 4.1 CASPT2 (RS2C)/cc-pv z MRCI/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z MRCIQ/cc-pv z Mebel et al Conclusions A number of issues remain regarding the C 2 H 3 2 potential energy surface. At the present level of theory and computational resources, it will be difficult to resolve the uncertainty in the C 2 H 3 2 interaction potential. For TS8, resolving the large uncertainty in the barrier height will involve more sophisticated analyses such as higher-order couple-cluster excitations and consideration of the splitting between the doublet and quartet state. VRC-TST rate constant calculations will be performed. The uncertainties in the potential energy surface will be propagated through the RRKM/ME calculations into uncertainty predictions for the rate coefficients [Goldsmith et al. 2013]. Global uncertainty analysis and careful examination of all experimental data will help to resolve some of these and other key issues [Burke et al. 2013]. Acknowledgements This research was supported by the U.S. Department of Energy, ffice of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract No. DE-AC02-06CH CFG gratefully acknowledges financial support from the Argonne Director s Postdoctoral Fellowship. References Bozzelli, J.W., and Dean, A.M. J. Phys. Chem. (1993) 97, Burke, M.P., Klippenstein, S.J., and Harding, L.B. Proc. Comb. Inst. (2013) 34, Carpenter, B.K. J. Am. Chem. Soc. (1993) 115, Carpenter, B.K. J. Phys. Chem. (1995) 99, Carpenter, B.K. J. Phys. Chem. A (2001) 105, Goldsmith, C.F., Tomlin, A.S., and Klippenstein, S.J. Proc. Comb. Inst. (2013) 34, Karton, A., Rabinovich, E., Martin, J.L.M., Ruscic, B., J. Chem. Phys. (2006) 125, Lopez, J.G., Rasmussen, M.U.A., Gao, Y., Marshall, P., and Glarborg, P. Proc. Comb. Inst. (2009) 32,

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