ARTICLE pubs.acs.org/JPCA
Quantum Chemical and Theoretical Kinetics Study of the O(3P) þ CS2 Reaction Vahid Saheb* Department of Chemistry, Shahid-Bahonar University of Kerman, Kerman 76169, Iran ABSTRACT: The triplet potential energy surface of the O(3P) þ CS2 reaction is investigated by using various quantum chemical methods including CCSD(T), QCISD(T), CCSD, QCISD, G3B3, MPWB1K, BB1K, MP2, and B3LYP. The thermal rate coefficients for the formation of three major products, CS þ SO (3Σ), OCS þ S (3P) and CO þ S2 (3Σg) were computed by using transition state and RRKM statistical rate theories over the temperature range of 2002000 K. The computed k(SO þ CS) by using high-level quantum chemical methods is in accordance with the available experimental data. The calculated rate coefficients for the formation of OCS þ S (3P) and CO þ S2 (3Σg) are much lower than k(SO þ CS); hence, it is predicted that these two product channels do not contribute significantly to the overall rate coefficient.
’ INTRODUCTION The reaction of oxygen atom O(3P) with carbon disulfide, CS2, has received considerable scrutiny because of its importance in CS2O2 chemical lasers.127 Three possible exothermic channels have been identified for this reaction: 3
∑
Oð3 PÞ þ CS2 fCS þ SOð Þ fOCS þ Sð3 P Þ 3 fCO þ S2 ð g Þ
∑
R1 R2 R3
It is revealed by several experimental studies that the major primary step is the reaction channel R1, which provides CS for producing chemical CO lasers through the important secondary reaction Oð3 PÞ þ CS f COq þ Sð3 P Þ
R4
The modeling of the chemical kinetics of CS2 þ O2 laser systems has revealed that the products of routes R2 and R3 could affect the laser performance.10,11 Hancock and Smith have shown that OCS produced by route R2 selectively relaxes the lower excited states of COq, and intensifies laser output from higher levels.11 Suart et al. have reported that the power of a CO chemical laser is enhanced upon the addition of “cold” CO, N2O, and OCS.7 This effect is explained by a vibrationvibration energy transfer mechanism. In pioneering studies, Smith et al. used kinetic absorption spectroscopy and determined the rate constant of the reaction R1 in the temperature range of 305410 K as k1 = 6.31 109 L mol1 s1 exp(2.5 kJ mol1/(RT)).1115 They claimed that the absence of S2 absorption in their study means that routes R2 and R3 must be at least 2 orders of magnitude slower than route R1. This research group also performed classical trajectory calculations on a modified LEPS potential energy surface by confining the trajectories to collinear motions.12 Although on a r 2011 American Chemical Society
close examination of the trajectories some important conclusions could be reached, the computed CS vibrational energy was much less than that found experimentally. The kinetics of reaction R1 was investigated in a fast flow reactor with ESR detection over the temperature range 227538 K by Westenberg and deHass, and the Arrhenius equation was reported as k1 = 1.20 1010 L mol1 s1 exp(2.5 kJ mol1/(RT)).16 Valuable results for the reaction R1 have been obtained using crossed molecular beams. Having measured the angular distribution and velocity of SO reactively scattered from crossed molecular beams of oxygen atoms and CS2, Geddes et al. observed the SO is strongly forward scattered, indicating a stripping reaction.17 They showed that most of the energy is released into rotational degrees of freedom of products and the reaction proceeds via highly bent intermediate configurations. No OCS signal was detectable in their experiments consistent with the much smaller rate constant of the reaction channel R2. In another similar study, reactive scattering measurements at two initial translational energies 13 and 38 kJ mol1, using a supersonic beam of oxygen and crosscorrelation time-of-flight analysis of SO product velocities have revealed that the reaction R1 proceeds by a stripping mechanism unaffected by initial translational energy.18 Slagle et al. reported three open channels for the O þ CS2 reaction by studying this reaction in high-intensity undiscriminated crossed molecular beams using photoionization mass spectrometry to detect the products.19 Then, using a fast-flow reactor, they measured the overall rate constant at 302 K as k = 2.41 109 L mol1 s1 and the branching ratio k2/k = 0.093. Fast flow studies of the reaction R1 using ESR detection, have led to an Arrhenius rate constant Received: January 8, 2011 Revised: March 15, 2011 Published: April 06, 2011 4263
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The Journal of Physical Chemistry A expression of k1 =1.66 1010 L mol1 s1 exp(5.35 kJ mol1/(RT)) over the temperature range of 218293 K.20 Hudgens and co-workers studied the infrared chemiluminescence from the reaction O þ CS2.21 Although emissions from the products CS, SO, and CO were observed, no emission from OCS product was detected, indicating that this product channel is almost inactive with respect to energy partitioning into stretching modes of OCS. Graham and Gutman found that the overall rate constant increases with temperature in a non-Arrhenius manner increasing from 1.75 109 L mol1 s1 at 249 K to 6.75 109 L mol1 s1 at 500 K.22 The fraction of the reaction proceeding by route R2 decreases with increasing temperature from 0.098 to 0.081 over the same temperature range. Cooper and Hershberger have used time-resolved diode laser spectroscopy to directly detect CO and OCS products and estimated the branching ratios k2/k and k3/k to be 0.085 and 0.030 at 296 K, respectively.23 To date, there is an overall agreement that the major route is the reaction channel R1 and consistent values for its rate constant are reported by several research groups. However, the existing data are contradictory regarding the branching ratios of the reaction channels R2 and R3. A few theoretical calculations are reported to explain the mechanism of the formation of OCS.24,25 However, no detailed theoretical ab initio study is performed on the kinetics and mechanism of this reaction and the role of the reaction channels R2 and R3 has remained obscure. In the present study, the potential energy surface of the title reaction is explored by various high-level quantum mechanical methods. Then, statistical rate theories are employed to compute the rate constants and branching ratios of the three main channels of the title reaction. The calculated results are compared with the available experimental data.
’ COMPUTATIONAL DETAILS Electronic-Structure Calculations. Various high-level quantum chemical calculations were employed to evaluate the accurate geometries, energies, and rovibrational properties of all stationary points, that is, minimum energy structures and saddle points. Special attempts were made to use suitable and welltested methods for reaction dynamics studies. First, all geometries were fully optimized at the BB1K28 and MPWB1K methods29 along with the 6-31þG(d,p) and MG3S basis sets.30 These hybrid meta density functional methods (HMDFT), developed by Truhlar et al., are optimized against a representative database of very high level calculations of saddle point geometries and energies. These two methods mix a pure DFT functional with some nonlocal exchange with kinetic energy density which depends on density as well as the gradient of density and give remarkably accurate barrier heights with slight deterioration of reaction energetics. It is shown that among 29 DFT methods, BB1K and MPWB1K are the two most accurate methods for calculating the barrier heights of heavy atom transfer reactions.31 These methods have also led to reasonable results for a combination of thermochemical kinetics and nonbonded interactions.32 Conventional KohnSham methods are only parametrized against a data set for thermochemistry, and they significantly underestimate reaction barriers.33 For example, the popular B3LYP method has shown a mean unsigned error four times larger than that of BB1K in calculations of barrier heights.31 These functionals do not also account successfully for dispersion interactions.34 Both unrestricted second-order MøllerPlesset perturbation (uMP2) theory35 and unrestricted Becke-3 LeeYangParr
ARTICLE
(uB3LYP) density functional36,37 were also used to locate the stationary point. The standard basis sets 6-311þþG(2df,2p) and 6-311þG(3df,2p) were used with the uMP2 and uB3LYP methods, respectively. All electrons were included in the correlation calculations at the uMP2 level and the spin contaminations were annihilated by single point calculations at the PMP2/6311þþG(2df,2p) level of theory. The highest-level geometry optimizations performed here involve unrestricted quadratic configuration interaction with single and double excitations (uQCISD),38 employing the standard 6-311þG(2d,2p) basis set. Energies at all of the stationary points were then recalculated with the unrestricted coupled cluster method with single, double, and noniterative triple excitations uCCSD(T)39 and the unrestricted quadratic configuration interaction with single, double, and noniterative triple excitations uQCISD(T) in combination with the augmented correlationconsistent polarized triple-ζ basis set AUG-cc-pVTZ.40 All electrons were included in the correlation calculations. To compute very accurate energies, G3//B3LYP theory was also employed.41 This theory is a variation of Gaussian 03 (G3) theory in which the geometries and zero-point energies are obtained from B3LYP method instead of geometries from MP2 method and zero-point energies from HartreeFock method. It is shown that G3//B3LYP theory gives significantly improved results for several cases in which the MP2 theory is deficient for optimized geometries. Vibrational frequencies were computed at the B3LYP/6-311þG(3df,2p), BB1K/6-31þG(d,p), and CCD/6-311þG(2d,2p) levels of theory. All of the quantum chemical calculations were performed with the Gaussian 03 package of programs.42 Dynamical Calculations. As indicated before, the reaction between CS2 and O(3P) can proceed via three different pathways. On the basis of the information obtained from the potential energy surface, that is, energies, vibrational frequencies, and moments of inertia, the rate constants for the reaction channels R1, R2, and R3 were calculated. The rate constant for the reaction R1 was calculated by means of conventional transition state theory (CTST)4349 in the temperature range from 200 to 2000 K, thereby: kB T Q 6¼ðTÞ V MEP exp kðTÞ ¼ kw ðTÞ ð1Þ h Q A Q B ðTÞ kB T where kB and h are Boltzmann’s and Plank’s constants, respectively, T is the temperature, the Qs represent the products of electronic, rotational, vibrational, and translational partition functions for the transition state (numerator) and reactants (denominator) and VMEP is the potential energy corrected for zero-point energy at the generalized transition state location at zero degree. κw(T) is the corresponding Wigner tunneling correction50 at temperature T: 1 hυ 2 Γ ¼ 1þ ð2Þ 24 kB T where υ* is the imaginary frequency of the activated complex at the top of the barrier and other parameters are the same as ones in eq 1. All vibrational modes are treated as harmonic oscillators, except the lowest vibrational frequency. The lowest vibrational mode is considered as a hindered internal rotation and its corresponding partition function is calculated by using the method of ‘‘ single conformer’’ (SC) approximation.51 According to the SC 4264
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approximation, the hindered rotation partition function can be expressed as HO I Q HR ¼ QSC tanhðQ FR =QSC Þ
ð3Þ
FR I Here, QHO SC , Q , and QSC are the harmonic oscillator, the free rotor approximation, and the high-temperature limit of the harmonic oscillator partition functions defined as
Q HO SC ¼
epω1 =ð2kB TÞ 1 epω1 =ðkB TÞ
ð4Þ
ð2πIkTÞ1=2 pσ
ð5Þ
Q FR ¼
Q ISC ¼ kB T=pω1
ð6Þ
where ω1 is the harmonic frequency (in the units of radians per unit time), I is the moment of inertia for the internal rotation, and kB, T, and p are well-known physical quantities. This method is used to obtain the hindered rotation partition function, in such a way that free rotational partition function (QFR) in the limit of kBT , W and vibrational partition function (QHO SC ) in the limit of kBT , p are obtained. W is a symmetric approximation to the barrier to internal rotation away from the minimum. The first three electronic levels of O(3P) were used to calculate the electronic contribution to total partition function of O(3P).52 As it is shown in Figure 1 and will be discussed in detail in the next section, the reaction can also proceed via the saddle points TS2 and TS3, leading to a common chemically activated intermediate (INT2). The products OCS þ S and CO þ S2 originate from the unimolecular decomposition of this intermediate. In this research, RRKM theory is used to compute the rate constants for decomposition of this vibrationally excited adduct to different products.53,54 According to the RRKM theory, the energyspecific rate constant for unimolecular reaction is given by kðEÞ ¼ Lq
þ Qþ 1 GðEvr Þ Q 1 hFðEÞ
ð7Þ
where G(Eþvr) is the sum of active vibrational and rotational states for the transition state, F(E) is the density of active quantum states for reactant, and Q1þ and Q1 are the partition functions for the adiabatic rotations in the transition state and reactant. In the WhittenRabinovitch approximation,55 the following expression is used for the vibrational sum of state. GðEþ Þ ¼
ðEþ þ aEzÞ s Q s! hνi
ð8Þ
i¼1
Figure 1. The geometries of reactant, transition states, intermediates, and products arising from the O(3P) þ CS2 reaction. The values from top to bottom are calculated at the MP2/6-311þþG(2df,2p), B3LYP/ 6-311þG(3df,2p), MPWB1K/6-31þG(d,p), BB1K/6-31þG(d,p), and QCISD/6-311þG(2d,2p).
inorganic molecules calculated by direct count, Whitten and Rabinovitch obtained the following expression for w. w ¼ ð5:00ε þ 2:73ε0:5 þ 3:51Þ1
0:1 < ε < 1:0 ð11aÞ
Here E is the vibrational internal energy, Ez is the zero-point energy, s is the number of the vibrational degrees of freedom, and νi is the frequency of the ith vibrational mode. The parameter a is calculated via the equations
Here, ε is the internal energy scaled with the zero-point energy.
w ¼ ð1 aÞ=β
ð9Þ
ε ¼ E=Ez
ð10Þ
The expression for the density of state is obtained from the derivative of the eq 8 as follows. ðE þ aEZ Þs 1 dw Q 1β FðEÞ ¼ ð13Þ dε ðs 1Þ! hνi
with s 1Æν2 æ w¼ sÆvæ2
By comparing with the state sums for various organic and
w ¼ expð 2:4191ε0:25 Þ
4265
1:0 e ε
ð11bÞ ð12Þ
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Transition state theory with the application of RRKM theory to the unimolecular decomposition of the chemically activated INT2 intermediate, was used to compute the rate constant for the reaction channels R2 and R3. If the decomposition barrier to regenerate reactants is significantly greater than the decomposition barrier to products, then D2/D3, the ratio of yields of OCS þ S to CO þ S2, is given by53 Z ¥ k4 ðEÞgðEÞ dE ðk 4 ðEÞ þ k5 ðEÞÞ E ð14Þ D2=D3 ¼ Z 0¥ k5 ðEÞgðEÞ dE E0 ðk4 ðEÞ þ k5 ðEÞÞ where k4(E) and k5(E) are the energy-specific rate constants for unimolecular decomposition of INT2 to OCS þ S and CO þ S2, respectively; g(E) dE is given by gðEÞ dE ¼ Z
ka ðEÞFðEÞ expðE=kB TÞ dE ¥
ka ðEÞFðEÞ expðE=kB TÞ dE
ð15Þ
0
Here ka(E) is the rate for dissociation of INT2 to form products. In this research, the values of k(E), F(E), and G(Evrþ) were calculated by using the RRKM program from Zhu and Hase.56
Figure 2. Relative energies of the stationary points located on the triplet ground-state potential energy surface. The energy values are given in kJ mol1 and are calculated using CCSD(T)/Aug-cc-pVTZ.
’ RESULTS AND DISCUSSION The geometries of reactant, transition states, and products of the title reaction optimized at various levels of theory are shown in Figure 1. The relative energies of the stationary points located on the triplet ground-state potential energy surface calculated by uCCSD(T)/Aug-cc-pVTZ are shown in Figure 2. The relative energies of the stationary points computed at various levels of theory are listed in Table 1. Table 2 provides a comparison of the vibrational frequencies obtained with two levels of theory. The vibrational frequencies of transition states were examined using molecular visualization to verify that the imaginary frequency corresponds to the reaction coordinate. Intrinsic reaction coordinate (IRC) calculations57 were performed to explore the minimum energy path from transition states to the corresponding local minima. In this study, the results obtained for individual channels have been first presented and then overall rate constant and branching ratios are discussed. Reaction Channel R1. The first way, reaction R1, proceeds through a critical configuration corresponding to a transition state structure, TS1, leading to an OS...CS intermediate denoted as INT1. The intermediate INT1 decomposes to yield OS þ CS. As can be seen from Figure 1, the angle — OSC is about 108 indicating a highly bent structure and the angle SCS is about 177. Having measured the angular distribution and velocity of SO reactively scattered from the crossed molecular beam of O (3P) and CS2, Geddes et al. concluded that the angle — OSC must be close to 90 together with some departure of the SCS angle from linearity.17 Our calculated geometries are in close agreement with this interpretation of the experimental observations. Smith performed classical trajectory calculations on a modified LEPS potential energy surface to simulate the reaction dynamics in a model in which the oxygen atom attack occur along the CS2 molecular axis.12 This model channeled most of the energy into SO vibration rather than translation, incompatible with the experimental observation of high SO rotational excitation. The computed activation energies for the reaction R1 by several methods are provided in Table 1. The results show that the activation energies are very sensitive to effects of electron correlation and basis set. It is well-known that the B3LYP and MP2 methods fail in the calculation of barrier heights for heavy atom transfer reactions.31 In this research, the barrier heights computed at the BB1K, G3B3, QCISD(T), and CCSD(T) levels were used to calculate the rate constant of the reaction R1 in the temperature range from 200 to 2000 K. As shown in Table 1,
Table 1. The Relative Energies of the Stationary Points Computed at Various Levels of Theory in kJ mol1. All Values Are Corrected for Zero Point Energies T.S.1
T.S.2
T.S.3
T.S.4
T.S.5
INT1
INT2
CS þ SO
OCS þ S
CO þ S2
0.0
23.07
20.43
201.02
94.00
125.53
225.22
68.87
232.20
343.37
MP2/6-311þþG(2df,2p) PMP2/6-311þþG(2df,2p)
39.18 29.19
96.79 67.20
96.97 74.47
183.54 189.19
101.30 115.48
63.70 85.10
198.82 217.34
56.88 68.58
243.35 242.39
336.43 343.85
BB1K/6-31þG(d,p)
12.50
52.56
52.22
164.86
129.14
60.31
193.57
14.47
210.53
305.29
4.20
51.37
47.94
172.81
137.52
100.92
201.51
37.99
211.90
324.87 304.62
B3LYP/6-311þg(3df,2p)
BB1K/MG3S
10.75
50.70
50.26
167.21
131.21
62.54
196.00
13.08
210.73
3.79
49.57
45.95
175.38
139.57
104.30
204.16
36.84
212.21
325.33
CCSD(full)/Aug-cc-pVTZ
14.84
57.33
53.51
171.54
74.75
76.15
183.78
54.44
239.29
343.46
MPWB1K/6-31þG(d,p) MPWB1K/MG3S QCISD(full)/Aug-cc-pVTZ
12.89
63.55
47.16
174.92
79.90
78.33
185.67
58.28
240.42
343.84
CCSD(T)/ Aug-cc-pVTZ QCISD(T)/ Aug-cc-pVTZ
5.41 5.00
45.34 56.04
32.04 27.90
180.12 182.81
97.36 100.39
85.25 87.50
200.23 204.34
60.02 61.81
233.17 233.63
339.53 339.52
G3B3
8.87
44.45
37.50
187.36
95.02
105.75
208.66
71.94
266.90
334.12
4266
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Table 2. Vibrational Wave Numbers and Moments of Inertia Ii for the Reactants, Transition States, and Products of the Reaction O(3P) þ CS2 Calculated with CCD/6-311þG(2d,2p), BB1K/6-31þG(d,p)a (Values in Parentheses) vibrational frequencies (cm1)
a
principle moments of inertia (amu Å2)
CS2
397.2, 397.2, 676.5, 1547.3 (406.9, 406.9, 680.4, 1554.2)
154.42, 154.42 (151.28, 151.28)
TS1 TS2
568.5i, 135.7, 364.3, 373.0, 690.3, 1565.5(319.1i, 107.8, 359.6, 384.7, 655.9, 1511.8) 539.5i, 255.8, 331.5, 398.0, 639.0, 1417.6(547.6i, 257.1, 332.8, 399.4, 641.7, 1421.8)
32.21, 226.89, 259.11(36.96, 229.70, 266.66) 53.05, 160.07, 213.12 (52.87, 160.48, 213.35)
TS3
674.1i, 230.7, 305.0, 378.6, 633.6, 1375.7(669.6i, 233.5, 309.5, 389.6, 639.4, 1394.7)
53.21, 155.77, 208.98(51.90, 153.60, 205.50)
INT2
298.3, 399.6, 508.4, 540.5, 637.1, 1814.2 (229.3, 400.9, 510.0, 542.2, 639.0,1819.7)
53.05, 160.07, 213.12 (78.72, 102.54, 181.26)
TS4
281.1i, 258.2, 444.4, 518.0, 613.5, 1929.3(352.3i, 220.2, 397.5, 493.3, 763.8, 2003.1)
84.14, 118.8, 202.9(82.76, 124.48, 207.24)
TS5
105.2i, 112.3, 160.9, 222.3, 279.0, 1985.9(94.4i, 105.8, 167.7, 194.6, 296.8, 2124.5)
34.03, 327.9, 380.49(35.14, 330.04, 365.14)
These values are scaled by 0.9561 (ref 28).
Table 3. The Energy-Specific Rate Coefficients for the Decomposition of the Energy-Rich Intermediate INT2 to the Reactants and the Products
Figure 3. The thermal rate coefficients for the reaction channel R1 computed at temperatures in the range of 2002000 K. Experimental data are given for the purpose of comparison. Solid line is calculated from CCSD(T) results, dashed-dot line from QCISD(T) results, dashed line from BB1K results, dotted line from G3B3 results; (Δ) from ref 13, (þ) from ref 16, (b) from ref 20, (9) from ref 22, (O) from ref 26.
high-level quantum chemical methods predict that the decomposition barrier to the reactants is much higher than the decomposition barrier to CS þ SO (3Σ). Therefore, this vibrationally excited species decomposes rapidly to CS þ SO (3Σ). The vibrational frequencies and the principle moments of inertia of the reactant, transition states, and chemically activated intermediates calculated by various methods are provided in Table 2. The data presented in Tables 1 and 2 were employed to calculate the molecular partition functions required for computing the rate constant of the reaction R1. The calculated rate constants are plotted in Figure 3 in comparison with the available experimental data. The rate coefficients computed by using QCISD(T) and CCSD(T) barrier heights are in good agreement with the experimental data. However, the rate coefficients have been slightly overestimated by BB1K method and underestimated by G3B3 method. In general, the rate coefficients computed by using all of these methods are in reasonable agreement with the available experimental data. By using the barrier height at the CCSD(T)/Aug-cc-pVTZ level, the non-Arrhenius expression for the reaction R1 was found to be k1 = 5.05 108 T0.54 exp(4.21 kJ mol1/(RT)) L mol1 s1. Reaction Channels R2 and R3. The potential energy surface (PES) was explored at several levels of theory to locate all of the stationary points involved in the reaction, resulting in the products
energy (kJ mol1)
k (INT2fCSþOS)
k (INT2fOCSþS)
k (INT2fCOþS2)
228.9
3.041 107
4.233 1013
2.647 1012
237.2
8
5.276 10
4.313 10
13
2.990 1012
245.6
9
2.260 10
4.390 10
13
3.344 1012
254.0
6.281 10
4.463 10
13
3.707 1012
262.3
1.378 10
4.533 10
13
4.075 1012
270.7 279.1
10
2.600 10 4.418 1010
13
4.600 10 4.663 1013
4.450 1012 4.828 1012
287.4
6.946 1010
4.724 1013
5.209 1012
295.8
1.029 10
4.783 10
13
5.592 1012
304.2
1.453 10
4.839 10
13
5.976 1012
9 10
11 11
OCS þ S(3P) and CO þ S2. As illustrated in Figure 2, the reaction proceeds via two saddle points, TS2 in Cs symmetry and TS3 in C2v symmetry, leading to a common activated intermediate denoted as INT2. The optimized geometries of all stationary points are depicted in Figure 1. Table 1 provides a comparison of the relative energies of several species involved in the reaction along the minimum energy path, calculated at several levels of theory. Although some electronic structure calculation methods predict comparable values for the energies of the saddle points TS2 and TS3, the higher levels of theory predict lower values for the energy of TS3. The relative energies of TS2, calculated at the G3B3, CCSD(T), and QCISD(T) levels of theory, are 44.45, 45.34, and 56.04 kJ mol1, respectively, while the corresponding values for TS3 are 37.50, 32.04, 27.09 kJ mol1. As can be seen from Figure 1 and Table 1, consistent geometries and energies are obtained for INT2 at various levels of theory. The average of the relative energies of INT2 calculated by several theoretical methods is 201.61 kJ mol1 with a standard deviation of 11.35 kJ mol1. The chemically activated molecular intermediate INT2 decomposes to form products through the saddle points TS4 and TS5. As shown in Table 1, the decomposition barriers of INT2 to the products COS þ S(3P) are between 201.02 and 164.86 kJ mol1. The decomposition barriers to CO þ S2 (3Σg) are between 139.57 and 74.75 kJ mol1. Transition state theory (eq 1) was used to calculate the overall rate coefficient for the formation of INT2 via transition states TS2 and TS3. On the basis of the barrier heights computed at the uCCSD(T)/AUG-cc-pVTZ, RRKM theory was used to calculate the energy-specific rate coefficients for the decomposition of the 4267
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Table 4. Experimental Branching Ratios for Reaction Channels R2 and R3 in Comparison with the Values Computed at the QCIST/Aug-cc-pVTZ Level (the Values in the Parentheses) temperature
OCS þ S (3P)
249
0.098 (
