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Kinetics of the CN + CS2 and CN + SO2 Reactions Wenhui Feng and John F. Hershberger* Department of Chemistry and Biochemistry, Department 2735, P.O. Box 6050, North Dakota State UniVersity, Fargo, North Dakota 58108-6050, United States ReceiVed: September 23, 2010; ReVised Manuscript ReceiVed: December 2, 2010
Diode infrared laser absorption spectroscopy was used to measure the rate constant (k1) of the CN + CS2 reaction for the first time. k1 was determined to be substantially pressure dependent with a value k1 ) (7.1 ( 0.2 to 41.9 ( 2.9) × 10-12 cm3 molecule-1 s-1 over 2-40 Torr at 298 K. The potential energy surface (PES) of the reaction was calculated using an ab initio method at B3LYP/6-311++G(d, p)//CCSD(T)/6-311++G(d, p) level of theory. Both experimental and computational results suggest that collision stabilization of the adduct NCSCS may dominate the reaction. The rate constant of the CN + SO2 reaction was measured to be very slow with an upper limit of k2 e 3.1 × 10-14 cm3 molecule-1 s-1, in disagreement with an earlier reported measurement. The PES of this reaction reveals an entrance barrier against formation of the low energy adduct NCOSO, in agreement with the experimental result. 1. Introduction The chemical kinetics of the CN radical are of substantial importance because of the role this species plays in combustion chemistry. For example, CN radicals are intermediates in the oxidation of HCN by OH radicals, an important part of NOx formation mechanisms in both fuel-rich hydrocarbon flames (the prompt-NO mechanism) and flames containing fuel nitrogen.1,2 While the literature database of rate constants for CN reactions is quite extensive,3-16 there is little information in the literature regarding the kinetics of CN reactions with sulfur-containing compounds, which may be of interest in combustion chemistry due to the presence of sulfur in some fuels.17 For example, no studies of the kinetics of CN + CS2 have been reported, and there is only one previous study of the CN + SO2 reaction, by Titarchuk et al., using laser induced fluorescence (LIF), in which a rate constant of 4.40 × 10-12 cm3 molecule-1 s-1 at 298 K was reported.18 In this paper, we report kinetic studies of the CN + CS2 and CS + SO2 reactions, using IR laser absorption spectroscopy
CN + CS2 f products CN + SO2 f products
(1) (2)
We also report ab initio calculations of the potential energy surfaces of these two reactions. 2. Experimental Section CN radicals were produced by photolysis of ICN using the fourth harmonic of an Nd:YAG laser at 266 nm:
ICN + hυ(266 nm) f CN + I
(3)
CN radicals were detected by time-resolved infrared laser absorption spectroscopy using lead salt diode lasers (Laser Components), as described in previous publications.19,20 One * Corresponding author.
of the CN (V ) 1 r V ) 0) transitions was located and identified at 2071.41 cm-1; this corresponds to the R(8) line.21 IR and UV light were made collinear and passed through a single-pass 143-cm absorption cell, and the transmitted infrared light was detected by a 1-mm diameter InSb detector (Cincinnati Electronics, ∼1 µs response time) and signal averaged on a digital oscilloscope. To account for probe laser thermal deflection affects, signals were collected with the diode laser slightly detuned off the spectroscopic absorption lines, and such transients were subtracted from the on-resonant transients. Typical experimental conditions were P(ICN) ) 0.1 Torr, P(CS2) ) 0-1 Torr, P(SF6) ) 1.0 Torr and Nd:YAG laser pulse energies of ∼4 mJ. SF6 buffer gas was used in order to relax any nascent vibrationally excited CN radicals to a Boltzmann distribution. SF6 (Matheson) were purified by passing through an Ascarite II column in order to remove trace amount of CO2. SF6, CS2 (99.9%, Sigma), and SO2 (99.98%, Matheson) was purified by repeated freeze-pump-thaw cycles at 77 K to remove trace amount of O2. N2 (99.999%, Matheson) was used without further purification. 3. Results and Discussion 3.1. Kinetics of the CN + CS2 Reaction. Figure 1 shows typical CN transient infrared absorption signals as a function of time. In the absence of CS2 reagent, a ∼1.2 × 104 s-1 decay rate over the time range 400 µs is observed. This decay is attributed to removal of CN radicals by pathways other than the title reaction, including CN + CN, I + CN reactions as well as diffusion out of the probed region of the reaction cell. (Reaction with trace O2 present in the absorption cell may contribute as well). Upon the addition of 0.1 Torr of CS2, a significant increase in CN decay rate is observed. Using the typical conditions described above, we estimate an initial CN radical density of about ∼1.6 × 1013 molecules cm-3, based on a 266 nm absorption coefficient of 0.009 cm-1 Torr-1 and a quantum yield of unity.22 Under these conditions, if the CS2 concentration is greater than 1.6 × 1015 molecules cm-3 ≈ 50 mTorr, pseudofirst-order kinetics are expected, and thus the time-dependent CN concentration has the form
10.1021/jp109107t 2011 American Chemical Society Published on Web 12/17/2010
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Figure 1. Infrared absorption signal of CN at 2071.41 cm-1 as a function of time. Reaction conditions: P(CS2) ) 0.0 Torr (upper trace); P(CS2) ) 0.10 Torr (middle trace). Both traces: P(ICN) ) 0.10 Torr, P(SF6) ) 1.0 Torr; 266 nm laser pulse energy ≈ 4 mJ. Bottom trace shows the residual of an exponential fit of the middle trace.
[CN]t ) [CN]0 exp(-k′t)
(4)
k′ ) k1[CS2] + k0
(5)
where k′ is the observed pseudofirst-order CN signal decay rate, k1 is the desired bimolecular rate constant for the CN + CS2 reaction, and k0 represents other loss mechanisms as described above. The transient signals were fit to the above function to determine the decay rate k′. Good fits were obtained for all signals except those with zero CN pressure, where radical-radical reactions dominate and pseudofirst-order conditions are therefore not expected. Figure 2 shows the resulting decay rates as a function of CS2 pressures. Linear dependences are observed, as is expected under the pseudofirst order kinetics conditions, in which [CS2] . [CN]. As per a standard kinetic treatment, the slope of this plot is the desired bimolecular rate constant k1. At the total pressure of 2.1 Torr, we measured the rate constant to be
k1 ) (7.1 ( 0.2) × 10-12 cm3 molecule-1 s-1 where the error bar represents one standard deviation of the uncertainty in the slope of Figure 2. Figure 3 shows the rate constant as a function of total pressure. In these experiments, typical conditions where 0.1 Torr of ICN, 0-0.1 Torr of CS2, 1.0 Torr of SF6, and N2 was included in order to reach the desired total pressure. Over the pressure range used of 2.1-40 Torr, k1 (298 K) varies over the range (7.1 ( 0.2 - 41.9 ( 2.9) × 10-12 cm3 molecule-1 s-1. (Error bars represent one standard deviation). We are not aware of any previously reported study on the kinetics of this reaction. 3.2. Kinetics of CN + SO2. Figure 4 shows that the CN decay rates as a function of SO2 pressures. Only very small changes in the CN decay rates were observed upon adding SO2 reagent. Even including 2.0 Torr SO2 in the reactants mixture, the CN decay rates only change by 2300 s-1 relative to the original value without SO2. Following the standard kinetic treatment, we obtain
k2 ) 3.1 × 10-14cm3 molecule-1 s-1
at 298 K
Figure 2. Pseudofirst-order decay rate constants of the CN radical as a function of CS2 pressures. P(ICN) ) 0.10 Torr, P(CS2) ) variable, P(SF6) ) 1.0 Torr; 266 nm laser pulse energy ≈ 4 mJ.
Figure 3. Rate constant (298 K) of CN + CS2 reaction as a function of total pressure (P). The error bars represents one standard deviation.
Such a small rate constant, however, is subject to significant errors from possible secondary chemistry. For example, it is possible that a trace oxygen impurity in the reagents leads to the following reactions:
CN + O2 f NCO + O
(7)
CN + O f CO + N
(8)
Both reactions are fast, with k7 ) 2.3 × 10-11 cm3 molecule-1 s , and k8 ) 1.83 × 10-11 cm3 molecule-1 s-1.24 These reactions would result in an increase in the measured CN decay rate. Also, SO2 has a modest absorption at 266 nm of 0.014 Torr-1 cm-1,25 but the photolysis wavelength is above the threshold for SO2 dissociation, so this does not represent a route to additional O atoms. An O2 impurity in the ICN or buffer gas reagents would primarily contribute to the intercept of Figure 4, but an O2 impurity in the SO2 sample would lead to a slight increase in the slope of Figure 4, leading to an overestimate of the rate constant. In fact, only a 0.1% impurity would be required to essentially produce all of the slope in Figure 4. We therefore -1 23
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Feng and Hershberger TABLE 1: Total Energies (hartrees), Zero-Point Energies (ZPE, hartrees), and Relative Energies (∆E, kcal/mol) for Species on the Doublet Potential Energy Surface Relevant to the CS2 + CN Reaction Obtained at DFT and CCSD(T) Levels of Theory geometry optimization species
B3LYP/ 6-311++G(d, p)
ZPE
CCSD(T)/ 6-311++G(d, p)
∆Ea
CS2 + CN NCS + CS M1 M1b M2 T1/1b TR/2
-927.303208 -927.277259 -927.315369 -927.314106 -927.345429 -927.296753 -927.277324
0.011779 0.010970 0.014020 0.014119 0.015552 0.013330 0.012299
-925.8933925 -925.8932814 -925.9296226 -925.9286268 -925.9508935 -925.9132144 -925.8885258
0 -0.4 -21.3 -20.6 -33.7 -11.5 3.4
a
Figure 4. Pseudo-first-order decay rate constants of the CN radical as a function of SO2 pressures. P(ICN) ) 0.10 Torr, P(SO2) ) variable, P(SF6) ) 1.0 Torr; 266 nm laser pulse energy ≈ 4 mJ.
conclude that our value for k2 must be considered an upper limit; the true value of k2 is possibly much smaller. Our upper limit for k2 is in major disagreement with the one previous study of the kinetics of CN + SO2, in which Titarchuk et al.18 reported k2 ) 4.40 × 10-12 cm3 molecule-1 s-1 at 298 K. We do not have an explanation for this discrepancy but note that there are many ways in which an experimentally measured rate constant may be erroneously high (such as contribution of secondary reactions as described above, and/or the contribution of oxygen impurities due to the very fast CN + O2 reaction); however, there are far fewer sources of error that would cause a measurement to be too low. The only way to get an anomalously low value for the rate constant would be if some fast secondary chemistry resulted in regeneration of CN radicals, leading to a decrease in the measured decay rates. One possible such reaction is
O + ICN f IO + CN
(9)
No direct measurement of k9 has been reported in the literature, but this reaction was proposed to have a rate constant of >1.6 × 10-14 cm3 molecule-1 s-1 in an early discharge study.26 Future work in this laboratory will include a measurement of k9, but the following experiment demonstrates that it is not a major source of error in the present study: a straightforward pseudofirst order kinetics measurement of the CN + O2 rate constant in our system (using ICN/O2/SF6 reagents) gives a value of ∼2.0 × 10-11 cm3 molecule-1 s-1 at 298 K, in good agreement with literature values for k7. If reaction 9 was a major factor in the CN + SO2 measurement due to oxygen atom production from trace O2 impurities or other O atom formation routes, it would be a much more major problem when O2 is included as a reagent, because reaction 7 produces O atoms as the major product channel. Alternatively, a measurement of the CN + NO rate constant using ICN/NO/SF6 mixtures gives ∼2 × 10-13 cm3 molecule-1 s-1 at low pressures, also in good agreement with literature data. In summary, the ICN precursor gives reasonable CN radical decay rates for known literature reactions. There is nothing special about the CN + SO2 system that would alter this conclusion, except for the possibility of two-photon dissociation of SO2 to give oxygen atoms. While we cannot completely rule out some contribution, we note that
single-point energy
Relative to the reactants, after correction for ZPE.
TABLE 2: Total Energies (hartrees), Zero-Point Energies (ZPE, hartrees), and Relative Energies (∆E, kcal/mol) for Species on the Doublet Potential Energy Surface Relevant to the SO2 + CN Reaction Obtained at DFT and CCSD(T) Levels of Theory geometry optimization species
B3LYP/ 6-311++G(d, p)
SO2 + CN NCO + SO M3 M4 M5 TR/3 T3/4 T3/5
-641.392126 -641.403608 -641.473543 -641.472667 -641.427277 -641.390565 -641.471928 -641.391119
a
singlepoint energy
ZPE
CCSD(T)/ 6-311++G(d, p)
∆Ea
0.011599 0.012521 0.015204 0.015173 0.015222 0.011967 0.015045 0.013180
-640.3229128 -640.3241452 -640.3915810 -640.3906085 -640.3503151 -640.3098510 -640.3906181 -640.3085508
0 -0.2 -40.8 -40.2 -14.9 8.4 -40.3 10.0
Relative to the reactants, after correction for ZPE.
the photolysis laser pulse energies (∼4 mJ) are quite low, minimizing such effects. 3.3. Potential Energy Surface. The Gaussian-03 set of programs27 were used to characterize the potential energy surfaces of the CN + CS2 and CN + SO2 reactions. Optimization at the DFT-B3LYP/6-311++G(d, p) level was used to obtain geometries of reactants, products, intermediates and transition states. Vibrational analysis was used to identify intermediates and transition states according to the number of imaginary frequencies. Intrinsic reaction coordinate (IRC) calculations were used to link each transition state structure with corresponding intermediate geometries to develop an energy profile. Following geometry optimization, single point energies were computed at the CCSD(T)/6-311++G(d, p) level of theory. Values from these calculations were combined with zero point energy (ZPE) corrections, determined using force constants calculated at the DFT-B3LYP/6-311++G(d, p) level, to give a total energy. These values were compared to the total energy of the reactants, (CN + CS2 or CN + SO2) to give the relative energies, shown in Tables 1 and 2. The optimized geometries are shown in Figure 5. Figure 6a shows the potential energy surface of the CN + CS2 reaction. As shown, CN can attack the S atom of CS2 to form the first intermediate M1 directly. No transition state was found for the process. In addition to a normal transition state search, we calculated the energy of M1 as a function of the enlarged C-S bond length (i.e., back toward reactants), again finding no energy barrier for the association step. M1 lies at 21.3 kcal/mol below the reactants, so it is considerably energized after formation and can easily transform to M1b by an out-of
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Figure 5. DFT-B3LYP/6-311++G(d, p) optimized geometries of the intermediates and the transition states on the doublet state potential energy surfaces of the CN + CS2 and CN + SO2 reactions. Bond lengths are given in Å and bond angles in degrees.
Figure 6. Doublet potential energy surfaces of the (a) CN + CS2 and (b) CN + SO2 reactions. Relative energies are taken from the CCSD(T)/ 6-311++G(d, p) values, on the basis of optimized geometries and zero-point energy corrections calculated at the B3LYP/6-311++G(d, p) level.
plane rotation of a C-S bond via the transition state T1/2, which is 11.5 kcal/mol below the reactants. The two intermediates are found to have similar structures and of energy. M1b may directly dissociate into NCS + CS. An additional route involves CN attack onto the C atom of CS2 to form intermediate M2 via the saddle point TR/2, which is 3.4 kcal/mol above the reactants. Because of the energy barrier related to TR/2, this route is probably unfavorable at moderate temperatures. At the B3LYP/6-311++G(d, p)//CCSD(T)/6-311++G(d, p) level, formation of NCS +CS is slightly exoergic by 0.4 kcal/ mol, compared to the reactants. In an attempt to further refine this value, we reoptimized the geometries of the CN + CS2 reactants and the CS + NCS products at higher levels of theory. At the CCSD(T)/6-31G(d,p) level (for both geometries and energy), using B3LYP zero-point energy corrections, the products are 2.5 kcal/mol higher than the reactants. At the highest level of theory we employed, CCSD(T)/6-311++G(d,p)
(geometries and energies), with B3LYP zero-point energies, the reaction returns to being slightly exoergic by 0.4 kcal/mol. We conclude that this reaction is approximately thermoneutral, and that the level of theory is not sufficiently converged to permit unambiguous determination of the sign of ∆rE. It is useful to compare our theoretical values with experimentally available thermo-chemical data. Based on an upper limit for the heat of formation of NCS, ∆fH° e 72.7 kcal/mol,28 as well as other thermochemical data from NIST-JANAF standard tables,29 we determine an enthalpy of reaction of ∆rH° e 6.8 kcal/mol. This is in agreement with our calculations, but still leaves the sign undetermined. In summary, the likely reaction mechanism for the CN + CS2 reaction is formation of M1 and/or M1b, followed by collisional stabilization and/or possible formation of NCS + CS products. Our experimental observation of a highly pressure
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dependent rate constant suggests the collisional stabilization dominates this reaction at room temperature. Figure 6b shows the potential energy surface of CN + SO2 reaction. Formation of NCO + SO products is roughly energetically neutral; however, there is a significant entrance barrier (TR/3, 8.4 kcal/mol) toward the formation of the initial adduct M3. This barrier is sufficiently high to make the rate constant very small at moderate temperatures, in agreement with our experimental measurement. 4. Conclusion Diode IR laser absorption spectroscopy was used to measure the rate constants of the reactions of CN with CS2 and SO2. The rate constant of CN + CS2 reaction at 298 K is determined to be (7.1 ( 0.2 - 41.9 ( 2.9) × 10-12 cm3 molecule-1 s-1 over the pressure range 2-40 Torr, showing substantial pressure dependence. The potential energy surface of the reaction, calculated at the B3LYP/6-311++G(d, p)//CCSD(T)/6-311++ G(d, p) level of theory, revealed two isomers of a low energy NCSCS adduct, which may be collisionally stabilized. The CN + SO2 reaction is very slow, with an upper limit to the rate constant of 3.1 × 10-14 cm3 molecule-1 s-1 at 298 K. Acknowledgment. This work was supported by Division of Chemical Sciences, Office of Basic Energy Sciences of the Department of Energy, Grant DE-FG03-96ER14645. References and Notes (1) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287. (2) Miller, J. A.; Bowman, C. T. Int. J. Chem. Kinet. 1991, 23, 289. (3) Atakan, B.; Jacobs, A.; Wahl, M.; Weller, R.; Wolfrum, J. Chem. Phys. Lett. 1989, 154, 449. (4) Sun, Q.; Yang, D. L.; Wang, N. S.; Bowman, J. M.; Lin, M. C. J. Chem. Phys. 1990, 93, 4730. (5) Durant, J. L., Jr.; Tully, F. P. Chem. Phys. Lett. 1989, 154, 568. (6) Balla, R. J.; Castleton, K. H.; Adams, J. S.; Pasternack, L. J. Phys. Chem. 1991, 95, 8694. (7) Yang, D. L.; Yu, T.; Wang, N. S.; Lin, M. C. Chem. Phys. 1992, 160, 307. (8) Yang, D. L.; Yu, T.; Wang, N. S.; Lin, M. C. Chem. Phys. 1992, 160, 317.
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