Ethynyl Radical Hydrogen Abstraction Energetics and Kinetics Utilizing High-Level Theory

The ethynyl radical, C2H, is found in a variety of different environments ranging from interstellar space and planetary atmospheres to playing an important role in the combustion of various alkynes under fuel-rich conditions. Hydrogen-atom abstraction reactions are common for the ethynyl radical in these contrasting environments. In this study, the C2H + HX → C2H2 + X, where HX = HNCO, trans-HONO, cis-HONO, C2H4, and CH3OH, reactions have been investigated at rigorously high levels of theory, including CCSD(T)-F12a/cc-pVTZ-F12. For the stationary points thus located, much higher levels of theory have been used, with basis sets as large as aug-cc-pV5Z and methods up to CCSDT(Q), and core correlation was also included. These molecules were chosen because they can be found in either interstellar or combustion environments. Various additive energy corrections have been included to converge the relative enthalpies of the stationary points to subchemical accuracy (≤0.5 kcal mol–1). Barriers predicted here (2.19 kcal mol–1 for the HNCO reaction and 0.47 kcal mol–1 for C2H4) are significantly lower than previous predictions. Reliable kinetics were acquired over a wide range of temperatures (50–5000 K), which may be useful for future experimental studies of these reactions.


INTRODUCTION
The ethynyl radical, C 2 H ( 2 Σ + ), is known to be a key intermediate in a number of diverse environments.It has been observed in both combustion reactions 1,2 and planetary atmospheres. 3,4−13 It is also a reactive species in Titan's atmosphere where the temperature is altitude-dependent (70 K at the tropopause and 94 K at the surface).To better understand the importance of these reactions involving the ethynyl radical in these drastically different environments, there is a need to accurately model the reactions of C 2 H with a variety of reactants over an extremely broad range of temperatures.
−16 The sizable dissociation energy of acetylene's sp-hybridized C−H bond thermodynamically drives these hydrogen abstraction reactions.−19 Theoretical results corroborate this claim with moderate to low reported barrier heights for several hydrogen atom donors. 14,20At this time, most experimental and theoretical studies involving ethynyl radical hydrogen abstractions have focused on hydrocarbon hydrogen atom donors.−30 However, little work has been done on larger molecules.
Reactions involving nitrogen containing radicals and their kinetics in the gas phase are also of considerable interest due to the role these species play in the formation and removal of NO x pollutants in combustion processes. 31NCO plays a key intermediate in combustion, however, very little is known of the kinetics of the reactions of NCO with hydrocarbons. 19,32o previous experimental studies on C 2 H + HNCO have been reported, but a theoretical study in 2003 by Chen and Ho 31 addressed the reaction mechanisms for NCO and C 2 H 2 at the CCSD(T)/6-31++G**//B3LYP/6-31++G** level of theory and they were able to find a direct pathway for the NCO + C 2 H 2 → C 2 H + HNCO reaction.
Additionally, nitrous acid, HONO, has been detected in the interstellar medium, 33 and the reaction involving CN has been explored theoretically 34 with MP2 and CCSD(T); however, no study has been reported involving C 2 H. Furthermore, the kinetics of the pyrolysis and oxidation of methanol, CH 3 OH, which could be considered as an alternative, more environmentally friendly fuel or fuel additive to gasoline, have been of great interest in the last several years. 35Hydrogen abstraction reactions could happen at two different sites for CH 3 OH.The hydrogen could be abstracted off the hydroxyl, −OH, group (reaction R1), or the methyl, −CH 3 , group (reaction R2).
In 2011, a theoretical paper by  15 In the present study, a similar computational approach will be utilized to investigate the C 2 H + HX → C 2 H 2 + X reactions, where HX = HNCO, trans-HONO, cis-HONO, C 2 H 4 , and CH 3 OH.Our study will provide high-level ab initio characterization of hydrogen abstraction reactions of the ethynyl radical with various medium sized molecules including HNCO, trans-HONO, cis-HONO, C 2 H 4 , and CH 3 OH.A composite approach will be implemented to converge the energies within subchemical accuracy (≤0.5 kcal mol −1 ).These highly accurate energetics will be used to compute reliable rate constants with canonical transition state theory that can be used in future kinetic studies.

THEORETICAL METHODS
Full geometry optimizations and corresponding harmonic vibrational frequency computations were performed on each of the stationary points for the C 2 H + HX, where HX = HNCO, trans-HONO, C 2 H 4 , and CH 3 OH (reaction R1), reactive surfaces using the explicitly correlated CCSD(T)-F12a method 37 in conjuction with the cc-pVTZ-F12 basis set 38,39 as implemented in Molpro 2010. 40A restricted open-shell Hartree−Fock (ROHF) reference was used for all open-shell computations to avoid issues with spin contamination that are sometimes prevalent with the ethynyl radical.For the C 2 H + HX, where HX = cis-HONO and CH 3 OH (reaction R2), reactive surfaces, full geometry optimizations and corresponding harmonic vibrational frequency computations were performed on each of the stationary points at the MP2 41 / aug-cc-pVTZ 42 level of theory as implemented in Psi4. 43Single point energy computations were performed on the MP2/augcc-pVTZ geometries with CCSD(T)-F12a/cc-pVTZ-F12 in Molpro 2010.
The electronic energies of the CCSD(T)-F12a/cc-pVTZ-F12 stationary points were computed according to the focal point analysis (FPA) of Allen and co-workers. 44,45For the present study, methods that describe electron correlation up to CCSDT(Q) 46 and basis sets as large as aug-cc-pV5Z 47 were used.Single point energy computations were performed on the CCSD(T)-F12a/cc-pVTZ-F12 optimized geometries with CCSD(T) 48,49 /aug-cc-pVXZ (where X = D, T, Q, 5) 42 in Molpro 2010, and CCSDT 50 /aug-cc-pVDZ and CCSDT(Q)/ aug-cc-pVDZ as implemented in MRCC 2018. 51As shown in Table 1, there is excellent convergence to the complete basis set (CBS) limit.The CCSD(T)/CBS energies were obtained through extrapolation of the Hartree−Fock (HF) and correlation energies.The three-parameter exponential function by Feller is used to extrapolate to the HF/CBS limit. 52 The two-parameter cubic function of Helgaker et al. 53 is used to extrapolate the correlation energies (E corr ) to the CBS limit.
The focal point energies were obtained with the following formula: Additional corrections were made to account for approximations made during the focal point computations.To account for the core-correlation neglected under the frozencore approximation, the CCSD(T)/aug-cc-pCVQZ energy with all electrons correlated was computed and the difference between the energies with and without the core−electrons was determined (δ CORE ).A scalar relativistic correction (δ REL ) was obtained at the X2C−CCSD(T)/aug-cc-pCVTZ-X2C level of theory. 54The clamped-nuclei approximation was treated with the diagonal Born−Oppenheimer correction (δ DBOC ) 55,56 performed at the ROHF/aug-cc-pVTZ level of theory.Spin− orbit coupling constants (δ SO ) were included for the NCO and CH 3 O products in order to account for the splitting of the electronic ground state. 57,58Lastly, zero-point vibrational energies (δ ZPVE ) were obtained from the CCSD(T)-F12a/cc-pVTZ-F12 harmonic vibrational frequencies.All of these corrections were added together to obtain the relative enthalpies at 0 K using the following equation: a Additional focal point tables can be found in the Supporting Information.δ denotes the change in the relative energy with respect to the previous level of theory.The numbers in [ ] are obtained by the extrapolation schemes found in the Theoretical Methods section.
Using canonical transition state theory, 59,60 the rate constants were computed over a wide range of temperatures i k j j j j j y where Q TS (T) and Q R (T) are the partition functions of the transition state and reactants, respectively, and ΔH ⧧ is the reaction barrier height from eq 4. The transmission coefficient, κ(T), was determined with an asymmetric Eckart potential barrier using the relative enthalpies of the prereactive complex, transition state, and products for each reaction, and the imaginary harmonic vibrational frequency corresponding to the reaction mode of the transition state. 61owman and co-workers demonstrated that an Eckart tunneling model provides accurate kinetics in agreement with experimental results for hydrogen abstraction reactions involving the ethynyl radical; 15 therefore, Eckart tunneling was used here.−64 In this work, pressure dependence will not be taken into account.2 shows the reaction enthalpies at 0 K for the C 2 H hydrogen-abstractions involving HNCO, trans-HONO, C 2 H 4 , and CH 3 OH (reaction R1).The last column of Table 2 demonstrates excellent agreement between our computed reaction enthalpies and the reaction enthalpies reported in the Active Thermochemical Tables (ATcT) (Version 1.122r) of Ruscic and co-workers. 65,66The mean absolute error (MAE) between the two is 0.19 kcal mol −1 .The root-mean-square error (RMSE) is 0.25 kcal mol −1 .The largest deviation is found for the CH 3 OH + C 2 H → CH 3 O + C 2 H 2 reaction with a difference of 0.48 kcal mol −1 .

Energies and Geometries. Table
Figure 1 depicts the geometries of the hydrogen abstraction transition states found for each reaction studied in this research.Table 3 shows the reaction enthalpies of the CCSD(T)-F12a/cc-pVTZ-F12 transition states relative to their respective reactants.According to the results in Table 2, the energetics of the products are expected to be accurate within 0.48 kcal mol −1 ; however, the relative energetics of the transition states are highly dependent on the employed level of theory.Because of this, we expect the barrier heights to be reliable well within chemical accuracy (1 kcal mol −1 ).Of the corrections listed in Table 3, δ ZPVE is the largest suggesting that obtaining accurate barrier heights not only requires accurate electronic energies, but also reliable vibrational frequencies.Additionally, δ REL is small, but not negligible for these reactions which involve first and second row atoms.The diagonal Born−Oppenheimer corrections for the reaction enthalpies and transition state barriers were consistently small (≤0.2 kcal mol −1 ) for almost all of the reactions.However, for the CH 3 OH + C 2 H → CH 3 O + C 2 H 2 reaction where δ DBOC is computed as 0.47 kcal mol −1 .Bartlett and co-workers proposed that δ DBOC can be utilized as a diagnostic for the presence of a nearby conical intersection. 67Typically for most well-behaved systems without a nearby conical intersection, the δ DBOC is small, but this is not true in the proximity of a conical intersection.The E DBOC becomes nonintegrable over domains that include a conical intersection because the secondderivative of the T ̂n operator blows up, as shown by Meek and Levine. 68It is recommended that DBOC not be included when employing mixed quantum-classical methods and approximate quantum dynamical methods.Therefore, the δ DBOC was not included in determining the final reaction enthalpy and transition state barrier of the As shown in Table 3, the C 2 H + CH 3 OH reaction has a very slightly submerged transition state barrier of −0.27 kcal mol −1 , suggesting that this reaction will be rapid even at low temperatures.The C 2 H + HNCO and C 2 H + trans-HONO reactions have low barriers less than 5 kcal mol −1 , meaning   these reactions will likely proceed more slowly than the barrierless reaction.
Table 4 compares the reaction enthalpies (Δ r H), the barrier heights (ΔH ⧧ ), important transition state features (shown in Figure 2), and the imaginary mode frequency (ω ⧧ ) of the transition state of the C 2 H + HX, where HX = HNCO, trans-HONO, C 2 H 4 , and CH 3 OH (reaction R1), reactions.To better determine if these hydrogen abstraction reactions follow the Evans−Polanyi principle, the reactions have been listed in order of decreasing exothermicity (Δ r H).The Evans−Polanyi principle observes that the activation energy between two similar reactions is inversely proportional to the reaction exothermicity. 69,70The reactions studied here, in general, appear to follow the Evans−Polanyi principle; however, the C 2 H + trans-HONO reaction seems to be an exception.One might expect the abstraction of the hydrogen from trans-HONO to have a submerged barrier of around −2 kcal mol −1 .Instead, the barrier height for trans-HONO is 4.91 kcal mol −1 .The interaction between the nitrogen of trans-HONO and the terminal carbon of C 2 H could potentially be causing the unexpected ΔH ⧧ increase.
To better understand the relationship between the reaction rates and how closely the transition states match the isolated reactants, Hammond's postulate is assessed.The Hammond idea states that the geometry of the transition state resembles either the reactants or products depending on the exothermicity of the reaction, and this was also taken into consideration in this study.In order to determine how closely the transition state resembles the isolated reactants, the distance between the terminal carbon of the ethynyl radical and the hydrogen that is being abstracted in the transition state (R CH ), was considered.The percent change between the XH bond length in the donor bond and the transition state (ΔR XH ) was also taken into account.The transition state will more closely resemble the reactants than the products if the ΔR XH value is less than 50%.The reactions in this study do follow Hammond's postulate.For example, the ΔR XH value of the C 2 H + HNCO reaction is 9.1%, and the energy difference of the reactants and transition state is 2.2 kcal mol −1 while the energy difference of the transition state and products is 24.3 kcal mol −1 .Energetically, the transition state lies closer to the reactants than the products, which corresponds to the calculated ΔR XH value that is less than 50%.

C 2 H + HNCO.
A previous study by Chen and Ho investigated the C 2 H + HNCO → C 2 H 2 + NCO reaction at the CCSD(T)/6-311++G**//B3LYP/6-311++G** level of theory. 31They found that the reaction proceeded through a transition state barrier of 6.23 kcal mol −1 and ended with the products at −21.79 kcal mol −1 relative to the reactants.
As seen in Figure 3, the reaction pathway found in this study is qualitatively similar to that of Chen and Ho.As laid out in Table 5, our transition state barrier of 2.19 kcal mol −1 is 4.04 kcal mol −1 lower than that of Chen and Ho.However, the ending products of −22.05 kcal mol −1 relative to reactants    show less than a 0.3 kcal mol −1 difference.The bond lengths of the transition state geometry are also similar to that of Chen and Ho with the largest difference being 0.14 Å for the H−C bond between HNCO and C 2 H.However, there is an 11.5°d ifference for the CNH angle in HNCO.Chen and Ho did not report rate constants for this reaction.

C 2 H + HONO.
Both the trans and cis isomers of HONO were considered for this study; however, only the reaction pathway involving the trans isomer was characterized at the highest level of theory implemented in this study.The study that investigated the CN + HONO reaction found that the trans isomer is 0.45 kcal mol −1 lower in energy than the cis isomer with an isomerization barrier of 9.46 kcal mol −1 at the CCSD(T)/aug-cc-pVTZ//UMP2/6-311++G(d,p) level of theory. 34here have been no previously reported theoretical studies or experimental measurements involving the C 2 H + HONO → C 2 H 2 + NO 2 reaction.As shown in Figure 4, the reaction pathway involving the trans isomer found in this work at the CCSDT(Q)/CBS//CCSD(T)-F12a/cc-pVTZ-F12 level of theory proceeds through a transition state barrier of 4.91 kcal mol −1 .Due to the stabilities of the ethylene and nitrogen dioxide, the energy of the products is −53.69 kcal mol −1 relative to the reactants.In Figure 5, the reaction pathway involving the cis isomer found in this work at the CCSD(T)-F12a/cc-pVTZ-F12//MP2/aug-cc-pVTZ level of theory proceeds through a prereactive complex at −0.91 kcal mol −1 followed by a submerged transition state barrier of −3.62 kcal mol −1 and ends with the products at −56.17 kcal mol −1 relative to the reactants.As shown in Figure 6, the C 2 H + CH 3 OH → C 2 H 2 + CH 3 O reaction proceeds through a prereactive complex at −6.45 kcal mol −1 and then through a very slightly submerged transition barrier of −0.27 kcal mol −1 , and ends in the products at −28.25 kcal mol −1 relative to the reactants, which is qualitatively in agreement to that of Tri and Hue.The prereactive complex energy was determined at the CCSD(T)-F12a/cc-pVTZ-F12 level of theory with no additional corrections.

C 2 H + CH 3 OH. There have been no previously reported experimental measurements involving the
Additionally, the C 2 H + CH 3 OH → C 2 H 2 + CH 2 OH reaction was also investigated for this study; however, no direct transition state was found for CH 2 OH production at our highest-level of theory.The reported transition state geometry of Tri and Huêappears to be in C s symmetry (Figure 7a      This floppy dihedral angle made this transition state difficult to optimize and locate.As shown in Figure 8, the C 2 H + CH 3 OH → C 2 H 2 + CH 2 OH reaction pathway characterized at the CCSD(T)-F12a/cc-pVTZ-F12//MP2/aug-cc-pVTZ level of theory proceeds through a prereactive complex at −1.64 kcal mol −1 followed by a submerged transition state barrier of −2.58 kcal mol −1 and ends with the products at −37.63 kcal mol −1 relative to the reactants.MP2/aug-cc-pVTZ gives an imaginary mode of 32i for the prereactive complex, but we believe this mode is an artifact of the level of theory and will likely disappear at a more rigorous level of theory.In terms of chemical reactivity, it appears this reaction pathway where the hydrogen is abstracted from the methyl group will likely prevail because it has a lower barrier height compared to the hydrogen being abstracted from the hydroxyl group.However, Tri and Huêreport that the reaction pathway where the hydrogen is abstracted from the hydroxyl group has a lower transition state barrier; therefore, it would be beneficial to further study this reaction pathway in a future study.

C 2 H + C 2 H 4 .
A previous study by Temelso and coworkers studied the C 2 H + C 2 H 4 → C 2 H 2 + C 2 H 3 reaction with the B3LYP, BHLYP, MP2, and CCSD(T) methods in conjunction with the cc-pVXZ (where X = D, T, Q) basis sets. 71However, CCSD(T)/cc-pVDZ was the highest level of theory reported for the barrier height.They found that the reaction proceeds through a transition barrier of 1.7 kcal mol −1 , and ends in the products at −19.5 kcal mol −1 at the CCSD(T)/cc-pVDZ level of theory using an ROHF reference.They also calculated the ΔH(0 K) at the CCSD(T)/cc-pVTZ level of theory and determined it to be −22.6 kcal mol −1 , which is in excellent agreement with our results.
As shown in Figure 9, the reaction pathway characterized in this study is qualitatively similar to that of Temelso and coworkers.Our transition state barrier of 0.47 kcal mol −1 is 1.23 kcal mol −1 lower than that of Temelso and co-workers, but their ending product energy of −22.6 kcal mol −1 relative to reactants at the CCSD(T)/cc-pVTZ level of theory is in excellent agreement with our results.The transition state geometries are quite similar as shown in Table 6, with the largest difference being the CHC angle.Temelso and coworkers report a linear angle while we predict a 168.7 degree angle.Rate constants were not reported for this reaction by Temelso and co-workers.
Additionally, Dash and Rajakumar studied the C 2 H + C 2 H 4 → C 2 H 2 + C 2 H 3 reaction and computed the CCSD(T)/cc-pVTZ and G3(MP2) electronic energies at each stationary point.However, they employed the M06-2X/6-31+G(d,p) level of theory to optimize the geometries and determine the harmonic vibrational frequencies. 20The transition state barrier is quite different at each level of theory as seen in Table 6.The M06-2X/6-31+G(d,p) pathway is in good agreement with our results, but the CCSD(T)/cc-pVTZ//M06-2X/6-31+G(d,p) transition state barrier of 2.25 kcal mol −1 is 1.78 kcal mol −1 higher than our transition state barrier.The G3(MP2)//M06-2X/6-31+G(d,p) pathway predicts a submerged transition state barrier of −1.43 kcal mol −1 .The transition state geometries are quite similar and the largest difference is the CHC angle again.Rate constants were reported by Dash and Rajakumar and will be discussed in the Kinetics section.

Kinetics.
The rate constants computed in this study using the rigid-rotor harmonic oscillator approximation can be found in Table 7.The Theoretical Methods section contains     the methods used for obtaining these rate constants.The abstractions from cis-HONO and CH 3 OH (both reactions R1 and R2) have submerged barriers, and as such the rate constants for these reaction will likely be large at all temperatures.Because of this, we have only examined the rate constants for the abstractions from HNCO, trans-HONO, and C 2 H 4 .
Quantitatively accurate kinetic models require highly accurate barrier heights of reaction.This makes the rate constants highly dependent on the calculated barrier heights.Additionally, the reaction barriers are low, therefore, variational effects are likely to be important which could be beneficial to explore in a future study.d,p) and CCSD(T)/cc-pVTZ//M06-2X/6-31+G(d,p) levels of theory are given by the dashed purple line and dashed pink line, respectively.The rate constants for only the abstraction channel by Dash and Rajakumar at the CCSD(T)/cc-pVTZ// M06-2X/6-31+G(d,p) level of theory are given by the red dotted line.Our computed rate constants for the abstraction channel are in good agreement with theirs at the CCSD(T)/ cc-pVTZ//M06-2X/6-31+G(d,p) level of theory.Dash and Rajakumar observed a strong negative temperature dependence for their computed rate constants, and the hydrogen abstraction contribution to the total rate constant is negligible below 250 K. Above 1000 K, the abstraction and addition reactions are in competition with each other.However, this competition is outside of the scope of the present study but it could be beneficial to explore the effects in the future.A negative temperature dependence was also reported in earlier experimental studies, but not to the same degree as that of Dash and Rajakumar.The experiments were performed using supersonic expansion methods.Opansky and Leone used transient infrared laser absorption spectroscopy, 9 Chastaing et.al used CRESU (laval nozzle expansion), 72 and Vakhtin et al. used pulsed nozzle expansion methods. 73

CONCLUSION
The energetics of ethynyl radical hydrogen abstraction reactions involving HNCO, trans-HONO, cis-HONO, C 2 H 4 , and CH 3 OH have been determined using highly accurate ab initio methods.Subchemical accuracy was achieved through various additive energy corrections, and shows excellent agreement with the available Active Thermochemical Table values.Additionally, accurate transition state barriers have been determined for the reactions involving HNCO, trans-HONO, C 2 H 4 , and CH 3 OH (reaction R1) in this study.The reaction pathways involving cis-HONO and CH 3 OH (reaction R2) have been determined at the CCSD(T)-F12a/cc-pVTZ-F12// MP2/aug-cc-pVTZ level of theroy.The reactions with CH 3 OH (reactions R1 and R2) and cis-HONO have submerged barriers below the relative enthalpies of the reactants.Abstractions of trans-HONO, HNCO, and C 2 H 4 have barriers between 0.5 and 5.0 kcal mol −1 .The reactions appear to follow the Evans−Polanyi principle and a strong correlation between the barrier height and reaction enthalpy was seen.One exception to the Evans−Polanyi principle was found with the C 2 H + trans-HONO reaction, which is believed to be due to the interaction between the nitrogen in trans-HONO and the terminal carbon of the ethynyl radical.This interaction raises the barrier height of the transition state to almost 5 kcal mol −1 .
Reliable kinetics were obtained for a subset of the above reactions implementing an Eckart tunnelling model.The computed rate constants for the C 2 H + C 2 H 4 → C 2 H 2 + C 2 H 3 reaction are in good agreement with those computed by Dash and Rajakumar.However, there appears to be a potential  9,18,20,72,73 competition between the abstraction and addition channels of this reaction which could explain the disagreement between the computed rate constants and experiment.The kinetics of the reactions with trans-HONO and HNCO have not yet been explored, so the results presented in this study may aid in future experimental studies.
■ ASSOCIATED CONTENT

aδ
denotes various corrections.See the Theoretical Methods section for details.b CBS denotes the CCSD(T)/CBS relative energy.c Enthalpies obtained from the ATcT.65,66d  Absolute value of the difference between total and ATcT.e CH 3 OH + C 2 H → CH 3 O + C 2 H 2 .f DBOC correction not included in the final total.

Figure 2 .
Figure 2. General representation of the transition state geometrical features.
C 2 H + CH 3 OH → C 2 H 2 + CH 3 O/CH 2 OH reactions.One previous study by Tri and Huêinvestigated the C 2 H + CH 3 OH reaction mechanism theoretically and determined the potential energy surfaces of 12 different reaction pathways. 36They determined that the pathways that formed C 2 H 2 + CH 3 O and C 2 H 2 + CH 2 OH were the most favorable with submerged barrier heights of −4.01 and −0.14 kcal mol −1 , and ended with the products at −32.32 and −38.45 kcal mol −1 , respectively, at the B3LYP/6-311++G(3df,2p)//B3LYP/6-311++G(d,p) level of theory.For the C 2 H + CH 3 OH → C 2 H 2 + CH 3 O reaction, they were able to locate a prereactive complex at −4.06 kcal mol −1 , but they did not report a prereactive complex for the C 2 H + CH 3 OH → C 2 H 2 + CH 2 OH reaction.
) with a H a −O−C-H b dihedral angle of 180.0°.Calculations at the MP2/aug-cc-pVTZ level of theory determined a transition state with a H a −O−C-H b dihedral angle of 45.9°(Figure 7b).

Figure 7 .
Figure 7. Qualitative geometries of C 2 H + CH 3 OH methyl abstraction transition state.Bond distances are given in Å, and angles are given in degrees.

Table 1 .
Representative Incremental Focal Point Table for the Products of the C 2 H + HNCO → C 2 H 2 + NCO Reaction Relative to the Reactants (kcal mol −1 ) a

Table 3 .
Enthalpies at 0 K (ΔH 0 K in kcal mol −1 for Transition States Relative to Reactants (C 2 H + HX → C 2 H 2 + X) a See the Theoretical Methods section for details.b CBS denotes the CCSD(T)/CBS relative energy.c CH 3 OH + C 2 H → CH 3 O + C 2 H 2 .d DBOC correction not included in the final total.
a δ denotes various corrections.

Table 5 .
Comparison of the C 2 H + HNCO → C 2 H 2 + NCO Abstraction at Different Levels of Theory a

Table 6 .
Comparison of the C 2 H + C 2 H 4 → C 2 H 2 + C 2 H 3 Abstraction at Different Levels of Theory a 3.2.1.C 2 H + C 2 H 4 .The computed rate constants from this study for the C 2 H + C 2 H 4 hydrogen abstraction reaction are plotted in Figure 10 (solid red line).Additionally, the canonical variational transition state theory (CVT) theoretical rate constants of Dash and Rajakumar, as well as various experimental rate constants have been included.The rate constants of Dash and Rajakumar were obtained from the sum of the individual rate coefficients associated with abstraction (C 2 H + C 2 H 4 → C 2 H 2 + C 2 H 3 ) and addition (C 2 H + C 2 H 4 →