Supporting information for:
Computational study on the reaction of CH3SCH2CH3 with OH radical: mechanism and enthalpy of formation
Jia Caoa, Wenliang Wang,a, Yue Zhang,a, Weina Wanga, Tianlei Zhanga, Jian Lvb, Chunying Lib
aSchool of Chemistry and Materials Science, Shaanxi Normal University, Xi’an 710062, People′sRepublic of China
bXi'an Modern Chemistry Research Institute, Xi'an 710065, People′sRepublic of China
1.Calculation details ofTST,RRKM rate constantandMorse potential function
Rate constants are computed by the conventional transition state (TST) theory withWigner tunneling correction.Rate constant for the reaction is calculated by the combination of equation (1), (2), (3) and (4) based on the steady state analysis and equilibrium hypothesis,
(1)
(2)
(3)
For the reaction ()with MES and OH as reactants directly, rate constant is computed by equation (4).
(4)
(5)
Where QTS, QMES and QOH are the total partition functions of transition state and reactant, respectively.ETS, EMES and EOH are the total energies of the transition state and isolated reactants, respectively. kB is Boltzmann’s constant. h is Planck’s constant. v is the imaginary frequency of the transition state. σ is the Wigner tunneling correction. All of the TST rate constant calculations are performed by using VKLab version 1.0 program.
Unimolecular reaction rate constant is calculated by using Rice-Ramsperger-Kassal-Marcustheory (RRKM). The expression for the RRKM rate constant at a given energy E is expressed as
Where is the sum of states of the transition state,is the reactant’s density of states, E0 is the reaction critical energy (including zero point energy), and h is Planck’s constant. Calculations of and with a grain size of 10.0 cm-1are performed using the Beyer-Swinehart-Rabinovith algorithm. The pressure dependence of rate constant is treated by one-dimentional (1D) master equation calculations using the Boltzmannprobability of the complex.The energetic and molecular parameters (molecular mass, moments of inertia, enthalpies of formation, vibrational frequencies, Lennard-Jones sigma, Lennard-Jones sigma epsilon) were used in the rate constant calculation.All of the RRKMrate constant calculation was employed by using chemrate program.
To describe the association reaction in absence of the transition state for the barrierless process CH3SCH2CH3+OH→RC[HO•••S(CH3)CH2CH3], the Morse potential function is used to approximate the minimum energy path.In the above equation, R is the reaction coordinate (i.e., the distance between the two bonding atoms), De is the bonding energy excluding zero point energy, and Re is the equilibrium values of R. The potential function is computed by scanning the S-O bond of the RC from 2.04 Å to 5.04 Å with an interval step size of 0.15 Å, and other geometric parameters are full optimized without symmetry constraint.
2. Figure and Table from calculation
Tables and Figures / PageTable S1 / The energetic of the complex RC [HO···S(CH3)CH2CH3] at the different levels of theory / S4
Table S2 / Rotational constantand vibrational frequencies data for the reactants, complex and transition state / S5
Table S3 / The calculatedrate constant (incm3molecule-1s-1)over the temperature range of 200-900K / S6
Table S4 / The predicted branching ratios of hydrogen abstraction channels and addition channels in the temperature of 200-900K. / S7
Figure S1 / Optimized geometries of all the species. Bond lengthsare in angstroms and anglesare in degrees. / S8
Figure S2 / Optimized geometries of pre-product complex at the MP2/6-31+G(2d,p) level of theory. PC1a, PC1b, PC1c, PC2a, PC2b, PC3a, PC3b and PC3c are the pre-product complex of Path R1a, R1b, R1c, R2a, R2b, R3a, R3b and R3c, respectively. Bond lengthsare in angstroms and anglesare in degrees. / S10
Figure S3 / The classical potential energy (VMEP), the vibrationally adiabatic ground-state potential energy (VaG) and the zero-point energy ZPE curve as a function of reaction coordinate s [(amu)1/2bohr] at the CCSD(T)/6-311+G(2d,p)//MP2/6-31+G(2d,p)+ZPE level for Path R1a, R2a and R3a. / S11
Figure S4 / The fitted Morse curve for the association process CH3SCH2CH3+OHRC [HO···S(CH3)CH2CH3]at the MP2/6-31+G(2d,p) level of theory. / S13
Figure S5 / Optimized complex geometries of CH3S(OH)CH2CH3and 3O at the MP2/6-31+G(2d,p) level of theory. / S14
Figure S6 / The unimolecular dissociation rate constant RC[HO···S(CH3)CH2CH3]TS1aP1(CH2SCH2CH3+H2O) at 300 K. / S15
Table S1Zero point energies (ZPE), electronic energies(E)and relative energies ERof the RC [HO···S(CH3)CH2CH3] (unit in kcal·mol-1)
Methods / E(CH3SCH2CH3+OH) / E(RC) / ER(RC)a / ER(RC)+ZPECCSD(T)/6-311++G(d,p)//MP2/6-31+G(2d,p) / -371550.68 / -371555.59 / -4.91 / -1.95
CCSD(T)/6-31+G(2d,p)//MP2/6-31+G(2d,p) / -371525.41 / -371534.38 / -8.96 / -6.00
CCSD(T)/6-311+G(2df,p)//MP2/6-31+G(2d,p) / -371637.41 / -371646.19 / -8.77 / -5.81
CCSD(T)/6-311+G(3df,p)//MP2/6-31+G(2d,p) / -371646.87 / -371656.79 / -9.91 / -6.95
CCSD(T)/6-311+G(3df,2p)//MP2/6-31+G(2d,p) / -371654.27 / -371664.41 / -10.14 / -7.17
CCSD(T)/6-311+G(3df,2pd)//MP2/6-31+G(2d,p) / -371550.68 / -371673.04 / -10.22 (-10.13)b / -7.26
ZPE[MP2/6-31+G(2d,p)] / 72.30 / 75.26
aER=E(RC)-E(CH3SCH2CH3+OH)
bFrom reference [17] at theCCSD(T)/6-311+G(3df,2pd)//MP2/6-31+G(2d,p) level (excluding zero point energy)
Table S2. Moments of inertia and vibrational frequencies for the reactants, complexes and transition states computed at the MP2/6-31+G(2d,p) level of theory
Species / IA, IB, IC/a.u. / Frequencies (cm-1)MES / 114.5, 568.4, 648.8 / 81, 181, 195, 250, 350, 698, 749, 799, 983, 986 1013, 1060, 1102, 1275, 1307, 1383,
1434, 1504, 1516, 1521, 1528, 1538, 3102, 3105, 3105, 3161, 3195, 3201, 3204,3218,
OH / 3.2, 3.2 / 3817
RC / 331.1, 647.4, 802.5 / 89, 114, 162, 192, 235, 276, 309, 357, 488, 694, 755, 788, 817, 975, 992, 1014, 1068, 1107, 1283, 1311, 1370, 1428, 1485, 1493, 1501, 1526, 1541, 3107, 3114, 3119, 3189, 3199, 3223, 3228, 3242, 3836
iso-RC / 341.8, 646.0, 821.3 / 75, 99, 124, 170, 205, 228, 275, 354, 510, 684, 709, 761, 785, 972, 985, 1008, 1054, 1105, 1276, 1304, 1379, 1430, 1491, 1496, 1504, 1526, 1543, 3108, 3113, 3116, 3185, 3199, 3221, 3222, 3239, 3794
TS1a / 355.9, 936.3, 1150.5 / 1660ί, 51, 76, 97, 190, 218, 248, 324, 358, 693, 725, 780, 801, 910, 971, 1013, 1059,1101, 1107, 1278, 1311, 1322, 1435, 1438, 1478, 1521, 1529, 1537, 3106, 3113, 3141, 3175, 3198, 3205, 3239, 3797
TS1b / 356.7, 970.2, 1220.2 / 1449ί, 48, 74, 86, 124, 202, 247, 329, 356, 630, 694, 773, 800, 918, 983, 1014, 1061, 1095, 1123, 1278, 1313, 1340, 1429, 1435, 1497, 1519, 1529, 1537, 3105, 3112, 3143, 3174, 3197, 3205, 3236, 3810
TS1c / 164.7, 1298.7, 1374.4 / 1923ί, 13, 70, 95, 180, 184, 248, 306, 351, 683, 725, 770, 800, 885, 968, 1009, 1057, 1077, 1108, 1276, 1276, 1307, 1433, 1435, 1478, 1517, 1528, 1537, 3106, 3113, 3142, 3173, 3198, 3206, 3236, 3795
TS2a / 485.8, 680.8, 1024.6 / 1382ί, 73, 75, 123, 180, 197, 226, 236, 354, 667, 712, 748, 864, 975, 989, 996, 1035, 1108, 1168, 1199, 1299, 1385, 1433, 1468, 1503, 1521, 1522, 1529, 3105, 3109, 3136, 3197, 3205, 3213, 3225, 3792
TS2b / 497.0, 692.2, 1088.1 / 1096ί, 65, 82, 104, 146, 184, 203, 242, 350, 621, 717, 751, 848, 957, 989, 1000, 1046, 1102, 1142, 1208, 1301, 1383, 1432, 1503, 1519, 1522, 1530, 1541, 3104, 3107, 3134, 3195, 3207, 3210, 3225, 3809
TS3a / 319.5, 919.6, 1082.1 / 1903ί, 53, 108, 151, 183, 201, 333, 353, 383, 659, 706, 748, 871, 929, 987, 996, 1020, 1068, 1145, 1240, 1292, 1338, 1384, 1471, 1492, 1503, 1507, 1518, 3100, 3108, 3146, 3166, 3209, 3222, 3232, 3746
TS3b / 264.9, 1131.5, 1256.5 / 1734ί, 35, 65, 68, 131, 187, 198, 346, 365, 663, 711, 749, 793, 925, 986, 994, 1020, 1069, 1145, 1253, 1297, 1343, 1384, 1440, 1494, 1504, 1505, 1519, 3091, 3104, 3146, 3159, 3202, 3219, 3230, 3809
TS3c / 171.4, 1454.7, 1588.4 / 1610ί, 52, 66, 75, 86, 185, 198, 305, 371, 657, 735, 772, 816, 905, 986, 991, 1047, 1070, 1127, 1264, 1293, 1331, 1383, 1427, 1503, 1503, 1516, 1521, 3105, 3115, 3152, 3177, 3207, 3220, 3236, 3810
TS4 / 265.0, 1191.8, 1317.2 / 1587ί, 76, 129, 161, 185, 205, 250, 303, 327, 462, 715, 767, 784, 951, 980, 990, 1103, 1122, 1197, 1227, 1246, 1382, 1405, 1414, 1458, 1506, 1517, 3111, 3141, 3143, 3215, 3226, 3249, 3335, 3344, 3826
TS5 / 331.1, 697.5, 796.6 / 556ί, 49, 131, 171, 224, 263, 309, 368, 464, 588, 636, 677, 710, 777, 989, 997, 1067, 1081, 1182, 1278, 1313, 1427, 1463, 1467, 1486, 1525, 1541, 3101, 3103, 3137, 3169, 3192, 3211, 3297, 3307, 3771
TS6 / 311.4, 725.5, 851.0 / 584ί, 74, 107, 146, 187, 212, 283, 318, 461, 618, 672, 740, 854, 900, 964, 987, 1042, 1090, 1176, 1243, 1366, 1423, 1477, 1495, 1511, 1525, 1529, 3073, 3100, 3141, 3155, 3191, 3207, 3219, 3259, 3768
TS7 / 294.2, 625.3, 787.6 / 1980ί, 84, 164, 190, 216, 223, 289, 341, 381, 423, 663, 722, 791, 898, 964, 979, 1010, 1068, 1096, 1277, 1300, 1360, 1436, 1479, 1486, 1500, 1527, 1538, 3108, 3111, 3112, 3186, 3199, 3218, 3226, 3243.
TS8 / 281.2, 613.9, 766.1 / 1449ί, 111, 188, 218, 247, 328, 382, 497, 571, 622, 666, 679, 790, 840, 917, 958, 1007, 1071, 1098, 1171, 1278, 1303, 1346, 1435, 1443, 1483, 1527, 1540, 1762, 3110, 3112, 3185, 3201, 3218, 3231, 3355
TS9 / 287.4, 645.0, 797.9 / 1670ί, 100, 135, 222, 228, 294, 343, 434, 496, 570, 727, 735, 784, 867, 989, 995, 1052, 1064, 1129, 1186, 1334, 1351, 1364, 1441, 1486, 1499, 1513, 1532, 1765, 3081, 3110, 3154, 3179, 3231, 3241, 3262
S1
Table S3 The calculatedrate constant (incm3molecule-1s-1)over the temperature range of 200-900K.
T/K / k1a / k1b / k1c / k2a / k2b / k3a / k3b / k3c / k5 / k6 / ktotal200 / 1.76E-12 / 1.45E-12 / 3.18E-16 / 2.12E-11 / 1.75E-11 / 2.32E-15 / 1.05E-16 / 1.20E-16 / 6.70E-30 / 6.45E-30 / 4.19E-11
245 / 1.46E-12 / 1.43E-12 / 1.71E-15 / 1.08E-11 / 1.03E-11 / 5.32E-15 / 6.83E-16 / 7.59E-16 / 6.16E-27 / 6.38E-27 / 2.40E-11
298.15 / 1.33E-12 / 1.50E-12 / 6.89E-15 / 6.71E-12 / 7.21E-12 / 1.08E-14 / 3.20E-15 / 3.49E-15 / 1.45E-24 / 1.58E-24 / 1.68E-11
350 / 1.30E-12 / 1.63E-12 / 1.88E-14 / 5.10E-12 / 5.96E-12 / 1.83E-14 / 9.70E-15 / 1.04E-14 / 6.32E-23 / 7.15E-23 / 1.40E-11
400 / 1.34E-12 / 1.81E-12 / 4.02E-14 / 4.35E-12 / 5.42E-12 / 2.77E-14 / 2.24E-14 / 2.39E-14 / 9.94E-22 / 1.15E-21 / 1.30E-11
450 / 1.41E-12 / 2.02E-12 / 7.53E-14 / 3.98E-12 / 5.20E-12 / 3.96E-14 / 4.46E-14 / 4.71E-14 / 8.75E-21 / 1.02E-20 / 1.28E-11
500 / 1.52E-12 / 2.27E-12 / 1.28E-13 / 3.81E-12 / 5.18E-12 / 5.41E-14 / 7.96E-14 / 8.35E-14 / 5.12E-20 / 6.03E-20 / 1.31E-11
550 / 1.65E-12 / 2.57E-12 / 2.03E-13 / 3.76E-12 / 5.29E-12 / 7.17E-14 / 1.31E-13 / 1.37E-13 / 2.22E-19 / 2.63E-19 / 1.38E-11
600 / 1.80E-12 / 2.90E-12 / 3.04E-13 / 3.80E-12 / 5.49E-12 / 9.25E-14 / 2.03E-13 / 2.11E-13 / 7.71E-19 / 9.15E-19 / 1.48E-11
650 / 1.98E-12 / 3.28E-12 / 4.36E-13 / 3.91E-12 / 5.78E-12 / 1.17E-13 / 3.00E-13 / 3.11E-13 / 2.24E-18 / 2.67E-18 / 1.61E-11
700 / 2.18E-12 / 3.71E-12 / 6.04E-13 / 4.07E-12 / 6.14E-12 / 1.45E-13 / 4.27E-13 / 4.40E-13 / 5.69E-18 / 6.77E-18 / 1.77E-11
750 / 2.41E-12 / 4.18E-12 / 8.14E-13 / 4.27E-12 / 6.56E-12 / 1.78E-13 / 5.87E-13 / 6.04E-13 / 1.29E-17 / 1.54E-17 / 1.96E-11
800 / 2.65E-12 / 4.70E-12 / 1.07E-12 / 4.51E-12 / 7.03E-12 / 2.15E-13 / 7.87E-13 / 8.07E-13 / 2.67E-17 / 3.17E-17 / 2.18E-11
850 / 2.93E-12 / 5.27E-12 / 1.38E-12 / 4.78E-12 / 7.56E-12 / 2.57E-13 / 1.03E-12 / 1.05E-12 / 5.12E-17 / 6.08E-17 / 2.43E-11
900 / 3.23E-12 / 5.89E-12 / 1.74E-12 / 5.09E-12 / 8.15E-12 / 3.04E-13 / 1.32E-12 / 1.35E-12 / 9.21E-17 / 1.09E-16 / 2.71E-11
In table,k1a,k1b, k1c, k2a, k2b, k3a, k3b, k3c,k5 andk5represent total rate constants ofPath R1a, R1b, R1c, R2a, R2b, R3a, R3b, R3c, R5 and R6, respectively.ktotal is the sum of k1a, k1b, k1c,k2a, k2b,k3a, k3b, k3c,k5 andk6.
Table S4The predicted branching ratios over the temperature of 200-900K
T / k1/ktotal / k2/ktotal / k3/ktotal / k5/ktotal / k6/ktotal200 / 7.66E-02 / 9.24E-01 / 6.09E-05 / 1.60E-19 / 1.54E-19
245 / 1.20E-01 / 8.79E-01 / 2.82E-04 / 2.57E-16 / 2.66E-16
298.15 / 1.69E-01 / 8.27E-01 / 1.04E-03 / 8.63E-14 / 9.40E-14
350 / 2.11E-01 / 7.93E-01 / 2.74E-03 / 4.51E-12 / 5.11E-12
400 / 2.45E-01 / 7.52E-01 / 5.69E-03 / 7.65E-11 / 8.85E-11
450 / 2.74E-01 / 7.17E-01 / 1.02E-02 / 6.84E-10 / 7.97E-10
500 / 2.99E-01 / 6.86E-01 / 1.66E-02 / 3.91E-09 / 4.60E-09
550 / 3.20E-01 / 6.56E-01 / 2.46E-02 / 1.61E-08 / 1.91E-08
600 / 3.38E-01 / 6.28E-01 / 3.43E-02 / 5.21E-08 / 6.18E-08
650 / 3.54E-01 / 6.02E-01 / 4.52E-02 / 1.39E-07 / 1.66E-07
700 / 3.67E-01 / 5.76E-01 / 5.71E-02 / 3.21E-07 / 3.82E-07
750 / 3.78E-01 / 5.51E-01 / 6.99E-02 / 6.58E-07 / 7.86E-07
800 / 3.86E-01 / 5.28E-01 / 8.30E-02 / 1.22E-06 / 1.45E-06
850 / 3.94E-01 / 5.06E-01 / 9.63E-02 / 2.11E-06 / 2.50E-06
900 / 4.02E-01 / 4.87E-01 / 1.10E-01 / 3.40E-06 / 4.02E-06
In table,k1 (k1=k1a+k1b+k1c) is rate constant for channel R1. k2 (k2=k2a+k2b) is rate constant of channel R2, k3 (k3=k3a+k3a+k3c) is rate constant of channel R3, ktotal is the sum of k1, k2,k3,k5 andk6.The k1a,k1b, k1c, k2a, k2b, k3a, k3b, k3c,k5 andk6represent total rate constants ofPath R1a, R1b, R1c, R2a, R2b, R3a, R3b, R3c, R5 and R6, respectively.
S1
Fig. S1Optimized geometries of all the species at the MP2/6-31+G(2d,p) level of theory. a, b, c, d, e are from references [43-47], respectively. Bond lengthsare in angstroms and anglesare in degrees.
Fig. S2 Optimized geometries of pre-product complex at the MP2/6-31+G(2d,p) level of theory. PC1a, PC1b, PC1c, PC2a, PC2b, PC3a, PC3b and PC3c are the pre-product complex of Path R1a, R1b, R1c, R2a, R2b, R3a, R3b and R3c, respectively. Bond lengthsare in angstroms and anglesare in degrees. The relative energies to the reactants were shown in parentheses calculated at the CCSD(T)/6-311+G(3df,p)//MP2/6-31+G(2d,p)+ZPE level of theory (in kcalmol-1). As describe in Fig. S2, the geometries and energies of PC1a, PC1b and PC1c were nearly same, which suggests Path R1a, R1b and R1c, via transition state TS1a, TS1b and TS1c, respectively, connect to the same pre-product complex (denoted PC1). The similar conclusion can be obtained for the Path (R2a and R2b. R3a and R3b), and therefore they were not discussed in present paper.In the paper, “PC1a, PC1b and PC1c” were labeled as “PC1”,“PC2a and PC2b” were labeled as “PC2”, “PC3a and PC3b” were labeled as “PC3ab”,because of the similar energies and geometries,
Fig. S3The classical potential energy (VMEP), the vibrationally adiabatic ground-state potential energy [(VaG=VMEP+ZPE)] and the zero-point energy (ZPE) curve as a function of reaction coordinate s [(amu)1/2bohr]at the CCSD(T)/6-311+G(2d,p)//MP2/6-31+G(2d,p)+ZPE level for Path R1a, R2a and R3a.
Fig. S4 The Morse curve for the association process CH3SCH2CH3+OHRC [HO···S(CH3)CH2CH3]. The solid line is the potential and points are calculated at the MP2/6-31+G(2d,p) level of theory.
Fig. S5 Optimized complex geometries of CH3S(OH)CH2CH3and 3O2at the MP2/6-31+G(2d,p) level of theory. Bond lengthsare in angstroms and anglesare in degrees. The relative energies of complexes to the reactants [CH3S(OH)CH2CH3+3O2] were shown in parentheses calculated at the CCSD(T)/6-311+G(2d,p)//MP2/6-31+G(2d,p)+ZPE level of theory (in kcalmol-1). As seen in figure S5, The O atom in 3O2 is adducted to the H atom of OH group in RC, as well as O atom in 3O2 is adducted to the S atom in RC are considered. The relative energy of complex [(OO•••HO)•••S(CH3)CH2CH3] and [(OO) •••S(OH)(CH3)CH2CH3]to the sum energy of RC + 3O2 is -10.18 and -11.77kcalmol-1, respectively. It can be found that O atom in 3O2 is adducted to the H atom of OH group in RC is more stable than O atom in 3O2 is adducted to the S atom by 0.96 kcalmol-1. [(OO•••HO)•••S(CH3)CH2CH3] and [(OO) •••S(OH)(CH3)CH2CH3]are possiblecomplexesfor the adduct of CH3S(OH)CH2CH3with 3O2in the atmosphere.
Fig.S6Fall-off region of the reaction RC [HO···S(CH3)CH2CH3]TS1aP1(CH2SCH2CH3+H2O) rate constant as a function of pressure (0.01-10 atm)at 300 K.
S1
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e-mail: (W. L. Wang). (Y. Zhang)