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
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 -1.03 and 0.13 kcal/mol, while those computed for the second conformer are -1.47 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
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
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 35.2 34.4 35.2 M062X/6-311+G(d,p) 37.0 36.4 37.2 CCSD(T)/cc-pVTZ c 35.1 - - CCSD(T)/aug-cc-pVDZ 35.2 - - CCSD(T)/aug-cc-pVTZ 34.3 - - CCSD(T)/CBS 34.1 - - Level of Theory Relative Energy of Conformer (kcal/mol) CBS-QB3 0.2 0.4 0.7 M062X/6-311+G(d,p) 0.01 0.4 0.5 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 34.7. 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: 6-311+g(d,p) (here) vs. MG3S. 4
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 5.7E1 2.13 27500 C 3CHP HCOOH + CH 3CHO 4.7E1 2.15 25100 C 4-2KHP CH 3COOH + CH 3CHO 1.4E6 0.939 28700 C 4-2KHP CH 3COCH 3 + HCOOH 3.4E5 1.13 26100 C 4-1KHP CH 3COOH + CH 3CHO 3.5E1 2.2 25700 5
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
S4. Structures and vibrational frequencies calculated for H-abstraction from 2-acetyl-ethyl-hydroperoxide Well 1 (Minimum Energy Structure) CBS-QB3 C -0.580500-0.799452-0.098132 O -0.185810-0.110059-1.018344 C 0.135808-2.096976 0.252329 C -0.167926-3.226046-0.758933 O -0.169012-2.798642-2.108225 O 1.128319-2.218232-2.398787 C -1.789743-0.411479 0.718828 H 1.207963-1.892998 0.229513 H -0.129294-2.445417 1.254086 H -1.181118-3.617628-0.624189 H 0.548016-4.042156-0.608848 H 0.930621-1.281356-2.204632 H -2.247009 0.487437 0.308477 H -2.516756-1.230141 0.729819 H -1.495174-0.235663 1.758858 57.6673 135.0366 148.3946 200.3736 217.956 344.5355 387.8145 499.3175 527.8962 623.0862 639.9277 748.9779 829.8333 893.7647 945.1388 962.8954 1017.3753 1063.5457 1109.6837 1189.6536 1263.9097 1271.8597 1334.5162 1384.3379 1400.2633 1458.4669 1461.1458 1472.8824 1478.9922 1485.7759 1772.4277 3017.7057 3026.0978 3055.334 3072.3131 3080.7983 3108.4055 3143.5313 3600.1186 7
Well 2 (Conformer) CBS-QB3 C -0.084343 0.175091 0.220429 C -0.536897-1.040108-0.559433 O -1.412849-0.948038-1.397362 C 0.175617-2.345629-0.241312 C -0.507692-3.649128-0.674096 O -0.591795-3.798365-2.085562 O -1.913655-3.410403-2.529211 H 0.384886-2.380654 0.834868 H -0.436470 0.091877 1.254413 H 1.006844 0.235542 0.258141 H -0.498065 1.077755-0.226520 H 1.157915-2.282885-0.728828 H -1.508403-3.747756-0.246447 H 0.101630-4.489462-0.324858 H -1.871373-2.441527-2.405619 52.9308 114.0102 136.1012 190.0153 221.9505 310.9325 431.7647 456.9764 510.7518 605.8368 642.0982 741.8036 810.8673 891.4424 958.0094 971.9748 1002.8364 1062.4999 1110.02 1185.8279 1243.162 1294.6526 1370.8712 1386.7533 1401.9754 1434.5302 1463.6094 1470.9504 1477.8727 1492.5838 1776.3318 3011.3705 3030.1232 3030.3628 3047.0756 3087.4189 3088.3065 3143.601 3579.0829 8
Cis Transition state for minimum energy reactant CBS-QB3 C -1.650267-0.297818 0.735348 C -0.555389-0.893152-0.113347 C -0.033913-2.278251 0.250620 C -0.377583-3.351278-0.799067 O -0.286141-2.950992-2.134973 O 1.052874-2.456078-2.382110 O -0.089136-0.294339-1.064578 H 1.053669-2.213772 0.324226 H -0.413395-2.613833 1.217986 H -1.395312-3.741803-0.708364 H 0.360249-4.227999-0.609593 H 0.925888-1.513690-2.141209 H -1.949715 0.670711 0.338209 H -2.510930-0.974243 0.763769 H -1.302523-0.185864 1.767610 O 1.720791-4.817204-0.515916 H 2.076720-4.320909-1.275164-312.6858 95.3746 210.1787 351.5394 528.3900 724.3267 892.7150 1020.6751 1186.2665 1325.8927 1407.9537 1473.2879 1916.5611 3074.6104 3145.3007 57.2796 147.3479 234.2488 386.3798 648.5680 774.0811 928.4313 1074.5087 1252.5231 1334.9737 1459.1753 1482.0337 3026.9929 3081.7637 3527.8655 78.6204 168.0436 340.4541 502.2787 663.9191 839.1356 958.8124 1098.0676 1272.4730 1386.3121 1463.6073 1764.1675 3064.2329 3111.6671 3706.0215 9
Trans Transition state for minimum energy reactant CBS-QB3 C -1.804995-0.481760 0.774705 C -0.656488-0.851243-0.124708 C 0.172673-2.077747 0.250874 C -0.125355-3.273425-0.655636 O -0.186389-2.992852-2.028532 O 1.016158-2.270379-2.417929 O -0.404680-0.231737-1.141349 H 1.228161-1.813925 0.141799 H -0.003082-2.381307 1.285281 H -1.213388-3.644329-0.428854 H 0.521977-4.130743-0.430966 H 0.703552-1.353247-2.273286 H -2.303944 0.411364 0.401689 H -2.500884-1.327634 0.794710 H -1.457429-0.321170 1.799873 O -2.652148-3.652605-0.329269 H -2.820494-3.453716-1.267307-420.2480 38.2766 83.4445 111.7044 156.6723 182.5004 190.2585 211.6784 263.4266 303.3822 388.6920 495.7184 526.8227 645.8870 664.5898 703.5528 743.1467 835.6795 886.0595 912.1361 966.9422 1032.0514 1056.9300 1099.6088 1183.1470 1247.8389 1254.4524 1296.5879 1373.9224 1388.4626 1421.4470 1462.6721 1462.8702 1475.7287 1477.7774 1683.8913 1766.9371 3018.3962 3025.0084 3053.1662 3085.7349 3102.5970 3143.6009 3550.5429 3724.2406 10
Cis Transition state for conformer CBS-QB3 C -0.487751-0.113944 0.347733 C -0.488686-1.137786-0.753331 C 0.293936-2.429092-0.513262 C -0.510926-3.733955-0.565102 O -0.967257-4.163412-1.813790 O -2.115688-3.391740-2.237137 O -1.082671-0.948173-1.798950 H 0.788574-2.390715 0.460244 H -1.072438-0.532731 1.174486 H 0.523314 0.074584 0.719198 H -0.949355 0.810632 0.004940 H 1.075443-2.474585-1.281849 H -1.434001-3.607322 0.155856 H 0.086677-4.569646-0.190794 H -1.721114-2.512935-2.433395 O -2.601914-2.962938 0.664312 H -3.085538-2.995349-0.181243-436.4980 53.1558 83.0777 117.2776 150.3827 179.2718 235.3872 253.8178 326.4910 407.4774 407.9333 474.5460 520.1055 606.5040 682.2648 733.6072 776.7697 834.2792 885.5384 919.2826 982.4001 1021.3679 1070.3673 1081.5301 1195.2915 1211.6265 1243.9836 1319.5835 1367.3430 1386.5929 1416.1443 1455.7814 1467.4345 1477.5501 1507.2591 1660.9735 1767.7966 3025.2753 3029.0122 3077.0109 3088.8084 3092.0246 3146.0704 3477.7511 3698.7830 11
Trans Transition state for conformer CBS-QB3 C -0.030079 0.134311 0.156040 C -0.497461-1.121554-0.544381 C 0.136702-2.426264-0.082077 C -0.547554-3.697151-0.568961 O -0.468648-3.862449-1.970148 O -1.757302-3.569062-2.557736 O -1.331780-1.071722-1.427494 H 0.197031-2.430379 1.012382 H -0.436536 0.152198 1.173069 H 1.059347 0.152704 0.246530 H -0.380748 1.012369-0.384160 H 1.176343-2.424659-0.432228 H -1.587084-3.788496-0.246277 H 0.027438-4.573139-0.121879 H -1.782444-2.598427-2.433750 O 1.190584-5.618972-0.003151 H 1.115512-5.895991-0.933698-129.1441 41.3689 61.7378 76.2935 103.6222 139.5242 190.7212 214.6975 242.4117 313.9961 435.3035 459.3439 493.9079 608.9010 636.1246 657.4425 748.9951 811.4299 891.9888 951.4482 966.8513 997.3997 1067.6576 1104.9524 1185.0942 1239.2996 1293.6807 1357.7051 1372.5204 1391.4257 1409.3781 1435.0031 1463.3605 1475.6634 1490.0786 1770.1915 2236.5974 3025.4852 3032.9741 3057.8621 3084.5894 3090.1835 3144.0443 3564.4790 3719.9393 12
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 -0.532487-0.782048-0.059289 C 0.199480-2.054967 0.281293 C -0.218217-3.169614-0.693623 O -0.257011-2.725668-2.031815 O 1.040269-2.265343-2.380923 O -0.147825-0.026273-0.914228 H -1.474880-0.571966 0.480762 H 1.270480-1.874812 0.181507 H -0.021014-2.371067 1.302853 H -1.241319-3.504287-0.506177 H 0.462318-4.019849-0.592452 H 0.932013-1.304885-2.281111 105.1473 145.7188 222.3564 242.1558 383.9686 495.0058 522.6491 567.9149 832.6065 893.5199 952.0837 999.4492 1020.2852 1122.3879 1156.6181 1241.8216 1276.2571 1345.0054 1393.5009 1428.0971 1459.1891 1480.4983 1491.7067 1850.1899 2979.0038 3070.2923 3095.9593 3128.4744 3156.9029 3742.5472 13
HCOCH2CH2OOH Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C -0.466468 1.064638 0.389748 C 0.986698 1.055821-0.064674 H 1.073316 1.479273-1.072706 H 1.603885 1.693139 0.579732 C 1.616948-0.308884-0.109177 O 1.036851-1.340796 0.113131 O -1.275206 0.323516-0.512257 O -1.734322-0.860877 0.115964 H -0.948981-1.430057 0.058887 H -0.844412 2.090132 0.398330 H -0.578016 0.643570 1.390236 H 2.690937-0.331090-0.374567 108.7344 150.7004 191.2719 237.8731 376.9826 497.5126 525.6023 640.0965 770.0614 863.5136 939.6747 974.2572 1020.3740 1123.5867 1137.4737 1256.9515 1294.6419 1391.5556 1398.6295 1426.3680 1441.7784 1476.9147 1492.2230 1853.1333 2976.0967 3054.1179 3079.6422 3090.5006 3138.7491 3735.6327 14
HCOCH2CH2OOH cyclization transition state (M062X/6-311+G(d,p) ultrafine grid) C -0.018631-0.906637-0.470622 H 0.695930-0.078439-0.411529 C 0.320087-2.162684 0.305357 C -0.080715-3.288819-0.641823 O 0.481760-2.937420-1.907272 O 0.255180-1.552501-2.041790 O -1.260642-0.647685-0.751582 H 1.385632-2.208761 0.533633 H -0.264701-2.182465 1.225423 H -1.168833-3.360002-0.723212 H 0.346412-4.258237-0.390993 H -0.864166-1.247934-1.859039-1566.8225 211.1291 306.1250 412.0369 467.8949 610.2257 652.1783 740.7523 884.4111 926.8211 937.5785 994.0170 1071.2851 1082.9035 1129.8109 1219.5058 1268.2787 1324.3203 1329.2893 1357.2037 1386.3121 1469.3434 1500.7874 1524.7123 2004.5399 3081.3466 3083.9900 3104.8698 3163.8568 3171.7221 15
Cyclization of 2-acetyl-ethyl-hydroperoxide (CH3COCH2CH2OOH) CH3COCH2CH2OOH Reactant: minimum energy structure (M062X/6-311+G(d,p) ultrafine grid) C -0.507346-0.777908-0.062290 O -0.060555-0.040347-0.910527 C 0.206526-2.073346 0.276488 C -0.214849-3.173506-0.711382 O -0.266959-2.711642-2.043480 O 1.028904-2.253889-2.400958 C -1.796715-0.481722 0.656626 H 1.280116-1.903999 0.191021 H -0.024503-2.401954 1.292262 H -1.235884-3.513382-0.519719 H 0.467044-4.024994-0.630390 H 0.941256-1.298451-2.241010 H -2.270040 0.401244 0.233115 H -2.467240-1.342436 0.583213 H -1.591370-0.322475 1.718848 51.2039 129.1781 148.4772 203.5905 222.1949 365.3134 396.3651 511.7780 527.0655 543.6869 641.8301 771.2648 856.6854 937.5000 963.9331 990.0994 1043.9211 1101.7750 1136.5814 1200.6363 1274.2502 1280.7669 1348.9754 1390.0659 1409.5971 1463.2932 1468.3854 1476.3702 1486.7155 1493.7956 1836.4513 3064.1635 3067.7498 3094.1828 3123.6946 3129.2141 3155.5713 3187.8463 3726.0868 16
CH3COCH2CH2OOH Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C -0.044329 0.178239 0.180234 C -0.561949-1.071279-0.487604 O -1.512901-1.036501-1.234952 C 0.166861-2.359710-0.164426 C -0.505452-3.617978-0.695964 O -0.513655-3.622984-2.115739 O -1.837417-3.450097-2.591647 H 0.301428-2.423401 0.921427 H -0.306202 0.146144 1.241797 H 1.044489 0.228562 0.115437 H -0.494763 1.057407-0.275448 H 1.174615-2.275202-0.587642 H -1.531862-3.710457-0.336806 H 0.057803-4.498122-0.374272 H -1.971318-2.498311-2.445796 48.5782 102.4236 147.8365 168.0348 216.6686 314.0579 439.7204 472.6686 512.9400 543.3228 630.3102 762.6689 821.8472 934.8505 966.4917 1010.2251 1017.9201 1117.2844 1131.8202 1199.2582 1253.5479 1301.9307 1386.9263 1399.3861 1416.7884 1437.9954 1468.8901 1481.6303 1482.5908 1491.5413 1837.1530 3056.3678 3068.5168 3075.6088 3095.1606 3135.5651 17
CH3COCH2CH2OOH transition state (M062X/6-311+G(d,p) ultrafine grid) C -0.012307-0.905029-0.451394 O -1.277672-0.688638-0.687155 C 0.358742-2.188706 0.269764 C -0.090344-3.303270-0.667847 O 0.415227-2.953564-1.954541 O 0.164741-1.575069-2.088141 C 0.916586 0.269451-0.347766 H 1.432914-2.245406 0.451299 H -0.182874-2.224135 1.216271 H -1.182172-3.364682-0.698326 H 0.336288-4.277996-0.436615 H -0.948066-1.273214-1.782101 H 0.629352 1.027614-1.074534 H 0.802635 0.691894 0.655009 H 1.955411-0.025457-0.491634-1646.3482 168.7420 195.9978 243.8462 306.6282 380.3997 422.6832 488.2321 588.4271 640.4242 656.3377 816.7163 905.4877 946.8121 975.8240 1003.1537 1058.3008 1082.4119 1092.8639 1207.1984 1220.7879 1270.7067 1335.2090 1375.0723 1387.4960 1406.3396 1461.1352 1469.7433 1484.2147 1503.7381 1526.2205 1963.2895 3071.4428 3076.7595 3099.5584 3149.5692 3157.9845 3167.1563 3185.1990 18
Cyclization of 2-formyl isopropyl-hydroperoxide (HCOCH2CHOOHCH3) HCOCH2CHOOHCH3 Reactant: minimum energy structure (M062X/6-311+G(d,p) ultrafine grid) C -0.546381-0.767091-0.069064 O -0.167853 0.004422-0.913013 C 0.200636-2.030179 0.271909 C -0.201764-3.162960-0.694257 O -0.243686-2.696832-2.036178 O 1.038373-2.191686-2.384905 H -1.497058-0.577383 0.464169 H 1.271574-1.842904 0.171479 H -0.017238-2.342446 1.295386 H -1.246810-3.441217-0.522916 C 0.701391-4.375409-0.544893 H 0.899396-1.237151-2.269077 H 0.371041-5.169027-1.215713 H 1.726861-4.105124-0.800200 H 0.678166-4.746924 0.481713 94.9556 133.5386 194.2346 217.0973 226.8374 291.4976 370.6845 459.2493 523.1083 552.6969 612.3530 804.1086 908.4683 948.5992 981.6250 996.7165 1017.3338 1120.7292 1145.9425 1176.4987 1248.6220 1296.8543 1361.4962 1383.2098 1411.4637 1425.1064 1460.5190 1478.4970 1488.7727 1505.8326 1849.2871 2976.4524 3074.2583 3079.8507 3090.4696 3148.5683 3153.3541 3164.5012 3745.0479 19
HCOCH2CHOOHCH3 Reactant: conformer (M062X/6-311+G(d,p) ultrafine grid) C -0.444072 1.065289 0.386397 O -1.213658 0.294682-0.540520 O -1.734126-0.857434 0.097628 C 1.013364 1.038718-0.062779 C 1.624002-0.334726-0.113689 O 1.040145-1.357774 0.138360 H 1.104182 1.471370-1.067566 H 1.641296 1.659948 0.587308 H -0.961459-1.446163 0.090105 C -1.006978 2.476455 0.411866 H -0.543292 0.595051 1.367243 H 2.690139-0.372254-0.408383 H -2.044957 2.452986 0.743389 H -0.432152 3.113429 1.087854 H -0.974880 2.911006-0.589810 84.3351 138.6203 178.8829 230.1031 235.0912 312.1136 362.1052 388.4494 528.4869 538.3666 678.8799 765.0476 861.5659 907.0325 974.0431 979.4705 1063.3103 1120.2369 1161.2584 1170.8174 1259.2762 1318.7368 1381.3532 1401.8757 1415.2806 1424.5788 1441.0686 1474.2891 1490.3177 1503.9600 1852.0941 2973.4200 3047.9914 3067.2971 3084.2240 3104.9210 3142.6501 3161.1438 3755.0523 20
HCOCH2CHOOHCH3 cyclization transition state (M062X/6-311+G(d,p) ultrafine grid) C -0.013982-0.879300-0.482043 O -1.258267-0.605387-0.741209 C 0.322769-2.134548 0.293664 C -0.095240-3.276754-0.631104 O 0.447139-2.919640-1.912631 O 0.222445-1.536298-2.052223 H 0.710278-0.058449-0.439126 H 1.392131-2.193723 0.508122 H -0.248617-2.144976 1.222644 H -1.187659-3.298176-0.709875 C 0.459972-4.639474-0.287329 H -0.890472-1.223381-1.849996 H 0.175802-5.370160-1.045421 H 1.548739-4.600575-0.225307 H 0.060615-4.966183 0.674160-1566.9805 158.1057 216.9835 241.5798 300.6290 395.3161 465.8432 483.9120 622.1293 636.4761 743.3117 867.9871 905.9062 910.4103 982.8969 1015.8402 1065.0940 1127.1799 1153.9909 1194.4691 1229.2174 1301.3641 1319.9961 1343.1459 1384.7433 1400.3590 1431.1003 1466.2277 1489.4211 1505.6018 1516.3822 2005.3801 3067.4720 3074.6229 3077.8746 3095.4623 3155.2485 3157.1410 3160.1605 21
S6. Molecular decomposition pathways for acetyl-methyl-hydroperoxide Acetyl-methyl-hydroperoxide minimum energy structure. CASPT2(4e,4o)/cc-pVTZ H 1 1-0.2591264967-0.4509659998 0.0476080402 C 2 6-0.3900558719-1.3258643974-0.6039925898 C 3 6-0.1182086280-2.5925467905 0.1794402323 O 4 8 0.3620049392-2.5823231498 1.3067104928 C 5 6-0.4782297687-3.9035529312-0.5169149905 O 6 8 0.0259980596-5.0383205830 0.1495330081 O 7 8-0.7211747489-5.1308963540 1.4080943904 H 8 1 0.3146219915-1.2598462618-1.4510288753 H 9 1-0.0202430519-3.9247924469-1.5220841413 H 10 1-1.5776244359-3.9567447734-0.6371461360 H 11 1-1.4096735534-1.3378035371-1.0243145498 H 12 1-0.2036674349-4.4822817752 1.9223531187 71.18 114.05 201.81 274.40 350.03 449.33 472.62 521.69 649.67 801.33 827.37 876.69 977.41 1075.00 1117.59 1212.46 1278.15 1377.12 1400.66 1411.96 1429.24 1460.59 1475.02 1783.47 3068.01 3087.30 3144.31 3179.51 3223.46 3728.57 22
Transition state Acetyl-methyl-hydroperoxide CH3CO + H2CO + OH cis. CASPT2(4e,4o)/cc-pVTZ C 1 6-0.9157987723 0.3959627705-1.0329764352 C 2 6-0.4190792958 0.3969274126 0.7865645992 C 3 6 0.7755245635 1.2947665722 0.9686674513 O 4 8 0.1250762448 0.1083834142-1.6868127963 H 5 1-1.2360053173 1.4637187049-0.9693026331 H 6 1-1.7505931725-0.3309283341-0.9483260331 O 7 8-1.0573308563-0.2500601786 1.5479021846 H 8 1 0.3854914636 2.2882099160 1.2484792997 H 9 1 1.4002123389 0.8987617972 1.7825223762 H 10 1 1.3390798936 1.3541021888 0.0311243206 O 11 8 1.5646396094-1.0092046949-0.4784074728 H 12 1 1.2723503006-1.6316855688-1.1674348608-455.91 83.95 112.77 141.38 183.67 214.99 259.92 289.79 369.90 457.54 526.65 561.91 811.18 915.44 1011.35 1034.52 1136.21 1246.58 1355.05 1429.06 1445.16 1472.60 1536.32 1931.59 2945.22 3065.72 3099.60 3209.26 3264.27 3811.63 23
Transition state Acetyl-methyl-hydroperoxide CH3CO + H2CO + OH trans. CASPT2(4e,4o)/cc-pVTZ C 1 6-0.5329352169-1.5878813744-0.1195778761 C 2 6 0.5801213646-2.5792437143-0.3171629181 O 3 8 1.7636328183-2.4759589666-0.3064368349 C 4 6-0.2833067260-4.4253353345-0.6871603198 O 5 8-1.5058376558-4.2421396316-0.5002024773 O 6 8-2.5790004139-6.1897945724-0.8342172537 H 7 1-0.1376326142-0.5793833823 0.0748722343 H 8 1-1.1659115835-1.6151154927-1.0197558303 H 9 1 0.1473677327-4.4360407547-1.7133909029 H 10 1 0.3536221152-4.9321710463 0.0710724923 H 11 1-1.1544933870-1.9554799461 0.7112157417 H 12 1-2.9482794334-5.8238327841-0.0112920553-105.64 40.17 56.59 83.30 121.89 144.34 192.45 223.03 320.61 382.81 495.86 512.30 733.89 922.49 999.14 1081.77 1156.78 1242.24 1354.56 1439.11 1446.56 1497.77 1653.51 1957.27 2983.05 3058.64 3096.52 3214.05 3227.58 3811.93 24
Transition state Acetyl-methyl-hydroperoxide cyclic peroxide. CASPT2(6e,6o)/cc-pVTZ C 1 6-0.6458089705 0.9061834898-0.5889592727 C 2 6-0.1643850997 0.0316057606 0.5801667049 C 3 6 0.4748273978 0.6697134457 1.7773621647 O 4 8-0.0108865766 0.1871920407-1.6433967865 H 5 1-0.2708646570 1.9431522211-0.5276754071 H 6 1-1.7420006405 0.8874505189-0.7036554288 O 7 8-0.6623863889-1.1707148316 0.6804437122 H 8 1-0.3375601738 1.0858367237 2.4008781158 H 9 1 1.0001848223-0.0966492352 2.3647345388 H 10 1 1.1561362080 1.4853763957 1.4977245529 O 11 8 0.9515399290-0.5518529584-0.7365231090 H 12 1 0.0957041499-1.3532415710-0.2658527851-1850.85 135.12 146.91 230.53 371.18 448.54 551.83 644.26 660.36 767.70 866.74 957.96 1021.99 1053.76 1071.97 1188.68 1223.66 1292.67 1362.98 1402.27 1453.14 1476.55 1499.60 1552.34 1963.43 3082.65 3088.28 3166.05 3189.55 3232.20 25
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
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.) 400 14.7 32.1 124.2 500 22.2 48.2 174.9 600 32.7 67.1 220.3 700 43.4 80.7 258.2 27
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.) 400 6.7E-2 3.1E-2 1.7E-2 500 4.5E-2 2.1E-2 1.2E-2 600 3.1E-2 1.4E-2 1.0E-2 700 2.3E-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) 400 6.1 6.3 500 2.75 3.0 600 1.94 2.1 700 1.61 1.7 28
References Greenwald, E. E.; S. W. North; Y. Georgievskii; S. J. Klippenstein, The Journal of Physical Chemistry A 109 (27) (2005) 6031-6044 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, 11100 11114 29