Kinetics of the Reaction of the Cyclopentadienyl Radical with Nitrogen

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Kinetics of the Reaction of the Cyclopentadienyl Radical with Nitrogen Dioxide Vadim D. Knyazev J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b05854 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 10, 2018

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The Journal of Physical Chemistry

Kinetics of the Reaction of the Cyclopentadienyl Radical with Nitrogen Dioxide

Vadim D. Knyazev

Research Center for Chemical Kinetics Department of Chemistry The Catholic University of America Washington, DC 20064 [email protected]

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Abstract The kinetics of the reaction of the cyclopentadienyl radical (c-C5H5) with nitrogen dioxide (NO2) was studied by Laser Photolysis / Photoionization Mass Spectroscopy. Overall rate constants were obtained in direct real-time experiments in the temperature region 305 – 800 K and at bath gas densities of (3.00 – 12.0)1016 molecule cm-3. The overall rate constant is independent of temperature between 300 and 400 K but decreases by a factor of approximately 7 above 400 K, without any discernible pressure dependence. A potential energy surface study of the reaction was performed, and an RRKM / Master Equation model was created. The reaction proceeds via initial addition to one of the two types of atoms of the NO2 molecule (nitrogen or oxygen). The N-bonded adduct can isomerize and decompose back to the reactants; this channel is significantly affected by falloff above 400 K and, although dominant at room temperature, becomes negligible at 600 K and above. The O-bonded adduct undergoes chemically activated isomerizations and decomposition, with a minor contribution from stabilization at low temperatures; this channel dominates at high temperatures and is effectively pressure-independent. The model provides a quantitative explanation for the observed temperature dependence of the rate constant.


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1. Introduction Reactions of delocalized polyatomic radicals are widely considered among major chemical pathways leading to the formation of polyaromatics and soot in combustion environments (e.g., ref 1. Among delocalized radicals, the cyclopentadienyl radical (c-C5H5) generated significant interest due to its role in molecular mass and aromatics growth (refs 2-6 and references cited therein). Although the reactions of the cyclopentadienyl radical are generally recognized as important in combustion systems, experimental data on the kinetics of gas-phase elementary reactions of c-C5H5 are sparse. The only two experimental studies available in the literature are those of Roy et al.,7,8 (a shock tube study of the reaction of addition of the hydrogen atom to c-C5H5), and the study of c-C5H5 self-reaction in ref 9. In the current work, the kinetics of the reaction of cyclopentadienyl radical with another open-shell molecule, NO2, was studied. c-C5H5 + NO2  Products

(1)

Reaction 1 was investigated using a Laser Photolysis / Photoionization Mass Spectrometry (LP/PIMS) apparatus in direct real-time experiments. Overall rate constants of reaction 1 were determined at temperatures between 305 and 800 K and at bath gas (helium) densities in the (3.0 - 12.0)×1016 molecule cm-3 range. The next section (2) of this article describes the experimental method and results. Section 3 reports the results of a computational study of the mechanism of reaction 1, including potential energy surface (PES) and master equation modeling. A discussion is provided in section 4.

2. Experimental The Laser Photolysis / Photoionization Mass Spectrometry (LP/PIMS) technique was used to study reaction 1; the experimental conditions were T = 305 – 800 K and bath gas densities [He] = (3 – 12)1016 molecule cm-3. Details of the experimental apparatus10 and the technique of c-C5H5 generation9 have been described previously. Cyclopentadienyl radicals were created in pulsed 248nm laser photolysis of cyclopentadiene and their kinetics were monitored in real time by photoionization mass spectrometry. The only other product of cyclopentadiene photolysis, H atom, decays on the surface of the boron oxide11 coated reactor within a fraction of a millisecond.9 The laser fluence of 2 – 10 mJ pulse-1 cm-2 was used with the firing frequency of 4 Hz. The flow rate 3 ACS Paragon Plus Environment


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of ~4 m s-1 was used for the gas mixture containing the bath gas (helium) and the radical precursor (cyclopentadiene). The photolyzed gas mixture was completely replaced with fresh reactants between laser pulses. Temporal ion signal profiles were recorded from 20 – 30 ms before the laser pulse and up to 15 - 30 ms after the pulse by a multichannel scaler. Data from, typically, 1000 to 5000 repetitions of the experiment were accumulated before being analyzed. The sources of the photoionization radiation were chlorine (8.9-9.1 eV, CaF2 window, used to detect c-C5H5 and c-C5H6) and hydrogen (10.2 eV, MgF2 window, used to detect C5H5O, C5H4O, NO, and to search for other potential products) resonance lamps. Experiments were conducted under pseudo-first-order conditions with the concentrations of NO2 ((0.04 – 3.4)1013 molecule cm-3) in large excess over cyclopentadienyl ([c-C5H5]0  (0.5 – 2.6)1011 molecule cm-3). Low initial concentrations of cyclopentadienyl radicals were used to ensure that the rates of radical-radical reactions were negligible compared to that of the reaction under study, that of C5H5 with NO2. The self-reaction of NO2 forming dinitrogen tetroxide is near the low-pressure limit under the experimental conditions12 and the effective second-order rate constant at the maximum bath gas concentration of 1.21017 molecule cm-3 is less than 210-16 cm3 molecule-1 s-1.13 Therefore, the NO2 self-reaction is negligible for the experimental [NO2] < 41013 molecule cm-3. The observed exponential decay of the c-C5H5 radical was attributed to a combination of reaction 1 and heterogeneous loss: c-C5H5 

heterogeneous loss

(2)

In each experiment to determine k1, the kinetics of the decay of c-C5H5 radicals was recorded at several different concentrations of nitrogen dioxide; the k2 values were determined in the absence of NO2. Values of k1 were obtained from the slopes of the linear k' (pseudo-first-order rate constant) vs. [NO2] dependences (k' = k1[NO2] + k2) (Figure 1 and Figures S1 – S7 in Supporting Information). Experiments were performed to verify independence of the decay constants of the photolyzing laser intensity or the initial c-C5H5 concentration. Potential pressure dependence was investigated at 400 K by varying the helium bath gas density within the (3.00 – 12.0)1016 molecule cm-3 range. The results did not reveal any pressure dependence within the experimental ranges of uncertainties. The results of the experimental study are presented in Table 1 and in Figure 2. The rate constant of reaction 1 exhibits a negative temperature dependence, which can be parameterized with the following modified Arrhenius expression: 4 ACS Paragon Plus Environment

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k1 = 2.751017 T-5.77 exp(-1661 K/T) cm3 molecule-1 s-1

(I)

Formation of potential reaction products was studied at two temperatures, 400 K and 800 K. Signals of C5H5O (m/z = 81) and NO (m/z = 30) were observed (Figure 1, inset b). The profile of the C5H5O signal demonstrated the behavior expected of a free radical: growth followed by a decay, indicating that C5H5O is likely a primary product of reaction 1. The sensitivity to NO was not of the quality sufficient to analyze its temporal profile (the lower trace in Figure 1, inset b). The signal, within its envelope of noise, can be that of a primary product of reaction 1, as well as of a subsequent reaction, such as, e.g., that of the C5H5O product with NO2, or a combination of both. Signals of both C5H5O and NO were noticeably stronger at 800 K compared to 400 K; however, no quantitative measurements of concentrations or branching fractions were attempted. Other potential primary or secondary products of reaction 1 were searched for using the hydrogen photoionizing lamp: HNO, C5H5NO2, C5H5NO, C5H4NO, C5H4O, and C5H5NO3. None of these products were observed except for a trace signal at m/z = 80, which can potentially be attributed to C5H4O, observed only at 800 K. Absence of detectable signals does not necessarily indicate that the corresponding species are not produced in the reactive system under study, as sensitivities of the equipment and, for most of these, ionizations potentials, are not known.

3. Potential Energy Surface (PES) and Mechanism of Reaction 1 Molecular structures were optimized and vibrational frequencies were calculated for all stationary points of the PES using the B3LYP method14-16 and single-point energy calculations were performed using the CCSD(T) method;17,18 the aug-cc-pvdz basis set19 was used in calculations using both of these methods. In addition, CBS-QB320,21 and G422 calculations were performed for all stationary points previously found in B3LYP calculations. The Gaussian 09 program23 was used for all potential energy surface calculations. Calculations performed at the CCSD(T)/B3LYP, CBS-QB3, and G4 levels are in qualitative agreement in the sense that the same reactive channels can be categorized as either important or unimportant based on the results of either method. The electronic plus ZPE energies, however, differ by as much as 24 kJ mol-1 between CCSD(T)/B3LYP and CBS-QB3 and up to 11 kJ mol-1 between CBS-QB3 and G4. CBS-QB3 energies (including ZPE) relative to the c-C5H5 + NO2 reactants are used in all discussions henceforth, unless specified otherwise, as well as in master equation calculations. The



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results of PES exploration with molecular structures, vibrational frequencies, and energies are presented in Supporting Information (Table S1). Addition of c-C5H5 to NO2 is possible at two sites (N and O atoms), resulting in the c-C5H5-NO2 and the c-C5H5-ONO adducts, respectively. Figures 3 and 4 present the corresponding potential energy surfaces. Only species and transition states for the most important channels (selected based on energy barrier heights, as well as RRKM and master equation calculations, see below) are shown to avoid congestion of the graphs; several negligible channels are not included. Addition to the nitrogen atom of NO2 can be followed by a migration of the H atom from the addition site to the second and then the third position in the ring (Figure 3, energy barriers of -58.5 and -78.6 kJ mol-1). H migration to the second position can also be followed by a transfer to an oxygen atom of the -NO2 group (to form C5H4-N(O)OH), but with a higher energy barrier (-17.9 kJ mol-1). Isomerization to c-C5H5-ONO requires a barrier that is 6.7 kJ mol-1 (9.4 at the G4 level) above the reactants. Any possible channels of decomposition of the three C5H5-NO2 isomers and C5H4-N(O)OH other than back to the c-C5H5 + NO2 reactants require high energy barriers, which makes them non-competitive. The kinetics of this channel of initial addition, therefore, is expected to mostly form the three C5H5-NO2 isomers, with high-pressure-limit behavior at low temperatures and high pressures and falloff at higher temperatures and lower pressures; the only chemical activation pathway to form c-C5H5-ONO is likely to be minor. The latter conclusion is supported by master equation calculations for the conditions of the current experimental study (see below). c-C5H5 + NO2

 

C5H5NO2 (4 adducts)

(1a)

Initial addition to one of the oxygen atoms of NO2 forms the c-C5H5-ONO adduct that can undergo several isomerizations, some of which result in chemically activated decomposition to products. The PES of these processes is shown in Figure 4. The initial adduct (cyclopenta-2,4dien-1-yl nitrite) is labeled 2,4-C5H5-ONO, to distinguish it from other c-C5H5-ONO isomers. Decomposition of 2,4-C5H5-ONO to 2,4-C5H5-O + NO via the rupture of the O-NO bond requires 16.7 kJ mol-1 relative to the reactants, which makes this channel negligible. Isomerization to c-C5H5-NO2 has a barrier of 6.7 kJ mol-1, which also prevents this channel from competing with other pathways. Two further reactions of the 2,4-C5H5-ONO adduct have energy barriers below the c-C5H5 + NO2 reactants: decomposition to c-C5H4O + HNO (-17.5 kJ mol-1) and hydrogen atom shift from the first to the second position relative to the C-O bond (-51.6 kJ mol-1), to form the 1,3-C5H5-ONO isomer (cyclopenta-1,3-dien-1-yl nitrite). Due to the lower barrier, H-atom 6 ACS Paragon Plus Environment

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shift has significantly greater probability than the decomposition reaction (comparison of the k(E) dependences is presented in Figure S8 in the Supporting Information). Subsequent reactions of 1,3-C5H5-ONO include, in the order of decreasing energy barriers and increasing importance, another H-shift to form 1,4-C5H5-ONO (cyclopenta-1,4-dien-1-yl nitrite, -61.5 kJ mol-1 barrier), O-N bond scission to form C5H5(O) (cyclopent-2-ene-1-one-4-yl radical) and NO (-106.6 kJ mol-1 barrier), and isomerization via nitrogen addition to the carbon atom adjacent to the C-O bond to form 2-NO-3-C5H5(O) (2-nitrosocyclopent-3-en-1-one, -136.2 kJ mol-1 barrier). The latter pathway has a very low barrier relative to 1,3-C5H5-ONO (38.2 kJ mol-1) compared to the excess rovibrational energy of greater than 174 kJ mol-1; therefore, it can be expected to be dominant under all practical conditions. Formation of 2-NO-3-C5H5(O) is followed by decomposition to C5H5(O) + NO or isomerization to 4-NO-2-C5H5(O) C5H5(O) (4-nitrosocyclopent-2-en-1-one) and decomposition to the same product. A transition state for a pathway leading from 1,3-C5H5-ONO to C5H4O + HNO products was searched for and not found. The overall result of the addition of cyclopentadienyl radical to one of the O atoms of NO2 is chemically activated decomposition to C5H5(O) + NO with a possible minor contribution of the C5H4O + HNO pathway. c-C5H5 + NO2

 

C5H5-ONO → C5H5(O) + NO

(1b)

c-C5H5 + NO2

 

C5H5-ONO → C5H4O + HNO

(1c)

Collisional stabilization of the initial C5H5-ONO addict is also possible, particularly at low temperatures and higher pressures: c-C5H5 + NO2 →

C5H5-ONO

(1d)

Models of reactions 1a (addition to the nitrogen atom) and 1b – 1d (addition to an oxygen atom) were created using the results of the quantum chemical study of the PES. Molecular structures, vibrational frequencies, and barriers for internal rotations were those obtained in B3LYP/aug-cc-pvdz calculations. The model of cyclopentadienyl radical included a pseudorotation degree of freedom24,25 with the effective rotational constant of 230 cm-1,25 as in the model of Sharma and Green.26 Energy-dependent rate constants k(E) for reaction steps involving a PES saddle point barrier (tight27 transition states) were calculated using the RRKM method (e.g., ref 28). Tunneling was included for hydrogen transfer channels using the barrier-width based Eckart tunneling correction.29,30 k(E) dependences for barrierless processes (without well-defined saddle points, loose27 transition states) were obtained using Inverse Laplace Transform31 (ILT) of the 7 ACS Paragon Plus Environment


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corresponding high-pressure-limit Arrhenius expressions. The latter were obtained from highpressure-limit k(T) dependences for the reverse association reactions (see below) and equilibrium constants calculated based on the PES study. The Chemrate program32 was used for k(E) calculations. Master equation calculations were then performed for reaction channels 1a, 1b, 1c, and 1d for the conditions of the current experimental study, i.e., T = 300 – 800 K and [He] = (3.0 – 12.0)1016 molecule cm-3. The MultiWell program33,34 was used in these master equation simulations. Lennard-Jones parameters for nitrobenzene35 were used for all C5H5NO2 species; helium parameters were taken from ref 36. Exponential-down model of collisional energy transfer with the fixed value of down = 300 cm-1 was used in all calculations. Collisional stabilization of all isomers resulting from the initial formation of C5H5-NO2 was included explicitly. For the transformations following the initial formation of C5H5-ONO, stabilization of all isomers other than 2,4-C5H5-ONO was not included because of the efficient chemically activated decomposition of 1,3-C5H5-ONO and other isomerization products to C5H5(O) + NO. Uncertainties in the rate constants for the barrierless association reactions appear to have the greatest effect on the overall results of modeling. These rate constants are needed for ILT calculations and especially for transforming the channels-specific branching fractions obtained from master equation simulations into rate constants for channels 1a – 1d of the overall c-C5H5 + NO2 reaction. The rate constant for the C5H5O + NO reaction was taken as equal to that of CH3O + NO addition:37 3.610-11 (T/298 K)-0.60 cm3 molecule-1 s-1. The overall rate constant of reaction 1 is not sensitive to this expression because of the low importance of the corresponding channel of 2,4-C5H5-ONO decomposition to C5H5O and NO due to the high energy threshold. The cyclopentadienoxy C5H5O radical product of this decomposition channel is thermally unstable and rapidly isomerizes to C5H5(O) (cyclopent-2-ene-1-one-4-yl radical),38 which is also produced in the main channel (1b) of the oxygen-site-addition initiated pathway of reaction 1. Thus, production of C5H5(O) is also not sensitive to the estimated rate constant of the C5H5O + NO reaction. High-pressure-limit rate constants for the two channels of the initial addition of c-C5H5 to NO2 directly affect the results of master equation modeling: calculated branching fractions must be multiplied by these values to obtain rate constants of reaction channels 1a – 1d under specific conditions. In addition, ILT-derived k(E) dependences of the corresponding dissociation processes affect the degree of falloff from the high-pressure limit, especially in the case of c-C5H5 addition to the N atom of NO2. No experimental of theoretical information is available on these high8 ACS Paragon Plus Environment

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pressure-limit rate constants. The only two cognate reactions studied experimentally are those of NO2 with the allyl (C3H5)39,40 and the propargyl (C3H3)41 delocalized radicals. In both cases, reactions were studied at low temperatures (201 – 363 K and 220 – 336 K, respectively) and low pressures (0.5 – 6 Torr). Both reactions exhibit negative temperature dependences of the rate constants and absence of a pressure dependence at the room temperature. Experimental data of these studies do not allow to distinguish the channels of addition of the respective radicals to the N or one of the O sites of NO2; therefore, the only analogy one can derive from refs 39-41 is that the overall radical + NO2 reaction rate constant can be expected to have negative temperature dependence. In the absence of any channel-specific data, the following expressions were selected for the high-pressure-limit rate constants of the addition of cyclopentadienyl radical to the two sites of NO2: k3 = 3.510-11 cm3 molecule-1 s-1

(II)

k4 = 2.610-10 (T/300 K)2.7 exp(-800 K/T) cm3 molecule-1 s-1

(III)

Here, reaction numbers 3 and 4 are assigned to addition to the N and the O sites of NO2 to form initial adducts, to avoid any confusion with the notations used for reactions 1a – 1d, which refer to the more complex processes of addition, stabilization, and chemically activated isomerization and decomposition: c-C5H5 + NO2  C5H5-NO2 (initial adduct)

(3)

c-C5H5 + NO2  C5H5-ONO (initial adduct)

(4)

The parameters of expressions II and III were chosen in a rather arbitrary manner, however, with the constraint that the resultant calculated overall k1(T) dependence provides a good match to the experimental one. In that sense, these parameters are the result of a fit of the model to experiment, albeit not a unique one. The calculated k1(T) dependences are shown in Figure 2 along with the experimental data, with three solid lines representing three different bath gas densities used in the experimental work.

4. Discussion The calculated k1(T) dependences shown in Figure 2 in both the Arrhenius and the linear sets of coordinates display a reasonable agreement with the experimental data, as can be expected 9 ACS Paragon Plus Environment


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from a model fit. The dashed lines in Figure 2 represent contributions from the initial addition to the N atom of NO2 (reaction 1a, long dashes) and to one of the O atoms (reaction channels 1b, 1c, and 1d, short dashes). At the lower temperature end of the experimental range, the overall reaction is dominated by the initial C5H5-NO2 formation, which is close to the high-pressure limit at the experimental pressures. This explains the independence of the overall rate constant of pressure observed at 400 K. The calculated k1(T) at 400 K and at 300 K differ very little, as expected from equations II and III. At higher temperatures, the addition channel forming C5H5-NO2 is affected by the falloff (the long-dashed line shows a pronounced decrease with the temperature), but the overall reaction rate constant displays only a very limited pressure dependence because at T > 500 K the channels stemming from the initial formation of C5H5-ONO dominate. These latter channels mostly produce the chemically activated decomposition products of channel 1b (C5H5(O) + NO). Reaction channel 1c is less than 0.5 %, and stabilization (channel 1d) is 4% or less at 300 K and 1.5% or less at 400 K; hence no discernible pressure dependence. The reverse dissociation to c-C5H5 + NO2 accounts for only 9% of the initially formed adducts at 800 K and less than 4% at 600 K and below. The predicted crossover between the two parts of the PES corresponding to the initial formation of two different adducts is negligible (0.01% or less). The numerical values of the branching fractions of the individual channels are presented in Table S2 in the Supporting Information. The results of the modeling explain the unusual, at first glance, shape of the experimental temperature dependence of the rate constant of reaction 1. In particular, the strong decrease in k1 between 400 K and 800 K, by a factor of ca. 7, corresponds to an effective large negative activation energy of -13 kJ mol-1, much larger than -3.4 and -2.4 kJ mol-1 for the reactions of the C3H5 and C3H3 delocalized radicals with NO2, respectively.40,41 The model explains this dramatic decrease in k1 via the switch from the fast addition mostly to the N site of NO2 at low temperatures (1a) to the slower addition to the O sites at higher temperatures (resulting in channels 1b – 1d), where channel 1a is unimportant because of the falloff. In a reversible reaction of addition, under certain conditions, one can generally expect to see a non-exponential kinetics of reactants decay corresponding to relaxation to equilibrium. This occurs at the temperatures where the rate of the (thermal) reverse decomposition of the adduct becomes comparable with the inverse of the characteristic time of the experimental measurements. For the experimental setup of the current work, this would correspond to the thermal adduct 10 ACS Paragon Plus Environment

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decomposition rate of ca. 50 – 500 s-1. The model of reaction 1 described above predicts the rate constants of the thermal decomposition of the C5H5-NO2 adduct of 920 s-1 at 800 K and 0.77 s-1 at 600 K for the experimental bath gas density of [He] = 6.01016 molecule cm-3. This means that below 600 K the decomposition reaction is too slow for the relaxation to equilibrium to be observable; at the same time, between 600 K and 800 K, the contribution of the reaction channel potentially affected by the reverse thermal decomposition (1a) is negligible compared to those of the channels resulting from the initial addition to an O atom, where reverse decomposition is negligible compared to the chemically activated decomposition to products (channels 1b and 1c). This explains the absence of the non-exponential kinetic behavior associated with relaxation to equilibrium. It is worth emphasizing here that the model of reaction 1 created in this work represents a quantum chemistry assisted, non-unique fit to the experimental data. The number of unknown parameters, such as those of the temperature dependences of the high-pressure limit rate constants of the addition reaction steps 3 and 4 (potentially six quantities of two modified Arrhenius dependences) exceeds the number of phenomenological parameters that can be derived from the experiment (three parameters of eq. I). Even with the additional constraint on the model imposed by the absence of a pronounced pressure dependence at 400 K, the amount of experimental data is insufficient to define all the properties of the model. The model, nevertheless, serves to explain experimental observations. In an earlier experimental study of cyclopentadienyl kinetics, an unusually strong negative temperature dependence of the rate constant of the self-reaction of c-C5H5 has been observed.9 It appears tempting, upon regarding the k1(T) dependence obtained in the current study, to generalize that rates of reactions of the cyclopentadienyl radical with open-shell species have strong negative temperature dependences. Yet, as the model described above demonstrates, such a generalization is not justified as the experimental results obtained here can be explained through conventional means. In the model, two channels of initial addition (3 and 4) have high-pressure-limit rate constants with either no temperature dependence (eq. II) or only a weak one (eq. III). Yet the overall temperature dependence at low pressures is rather strong, due to the combination of the falloff effects in channel 3 and the switch, with rising temperature, of the dominant role from falloff-affected channel 3 to channel 4, the rate constant of which is not sensitive to pressure because of the efficient forward reaction of the nascent adduct. 11 ACS Paragon Plus Environment


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Supporting Information Plots of the experimental k’ (pseudo-first-order rate constant) vs. [NO2] dependences, detailed results of the PES study, k(E) plots for two channels of forward reactions of the 2,4-C5H5-ONO adduct, calculated branching fractions of the individual channels of reaction 1, and complete lists of authors of refs 23 and 34 (22 pages). This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgement This research was supported by U.S. National Science Foundation, Combustion, Fire, and Plasma Systems Program under Grant No CBET-0853706.


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References 1. Richter, H.; Howard, J. B. Formation of polycyclic aromatic hydrocarbons and their growth to soot - a review of chemical reaction pathways. Prog. Energy Combust. Sci. 2000, 26, 565608. 2. Cavallotti, C.; Polino, D. On the kinetics of the C5H5 + C5H5 reaction. Proc. Combust. Inst. 2013, 34, 557-564. 3. Kislov, V. V.; Mebel, A. M. The formation of naphthalene, azulene, and fulvalene from cyclic C5 species in combustion: an ab initio/RRKM Study of 9-H-fulvalenyl (C5H5-C5H4) radical rearrangements. J. Phys. Chem. A 2007, 111, 9532-9543. 4. Mebel, A. M.; Kislov, V. V. Can the C5H5 + C5H5 → C10H10 → C10H9 + H/C10H8 + H2 reaction produce naphthalene? An ab initio/RRKM Study. J. Phys. Chem. A 2009, 113, 9825-9833. 5. Hansen, N.; Klippenstein, S.; Miller, J.; Wang, J.; Cool, T.; Law, M.; Westmoreland, P.; Kasper, T.; Kohse-Hoinghaus, K. Identification of C5Hx isomers in fuel-rich flames by photoionization mass spectrometry and electronic structure calculations. J. Phys. Chem. A 2006, 110, 4376-4388. 6. Robinson, R. K.; Lindstedt, R. P. On the chemical kinetics of cyclopentadiene oxidation. Combust. Flame 2011, 158, 666-686. 7. Roy, K.; Braun-Unkhoff, M.; Frank, P.; Just, T. Kinetics of cyclopentadiene decay and the recombination of cyclopentadienyl radicals with H atoms: Enthalpy of formation of the cyclopentadienyl radical. Int. J. Chem. Kinet. 2001, 33, 821-833. 8. Roy, K.; Braun-Unkhoff, M.; Frank, P.; Just, T. Kinetics of the cyclopentadiene decay and the recombination of cyclopentadienyl radicals with H-atoms: Enthalpy of formation of the cyclopentadienyl radical (vol 33, pg 821, 2001). Int. J. Chem. Kinet. 2002, 34, CP2-833. 9. Knyazev, V. D.; Popov, K. V. Kinetics of the self reaction of cyclopentadienyl radicals. J. Phys. Chem. A 2015, 119, 7418-7429. 10. Slagle, I. R.; Park, J. -.; Gutman, D. Experimental investigation of the kinetics and mechanism of the reaction of n-propyl radicals with molecular oxygen from 297 to 635 K. Proc.Combust.Inst. 1985, 20, 733. 11. Niiranen, J. T.; Gutman, D.; Krasnoperov, L. N. Kinetics and thermochemistry of the CH3CO radical: Study of the CH3CO + HBr -> CH3CHO + Br reaction. J. Phys. Chem. 1992, 96, 5881-5886. 12. Borrell, P.; Cobos, C. J.; Luther, K. Falloff curve and specific rate constants for the reaction NO2 + NO2 = N2O4. J. Phys. Chem. 1988, 92, 4377-4384. 13 ACS Paragon Plus Environment


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13. Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.; Hampson, R. F.; Hynes, R. G.; Jenkin, M. E.; Rossi, M. J.; Troe, J. Evaluated kinetic and photochemical data for atmospheric chemistry: Volume I - gas phase reactions of Ox, HOx, NOx and SOx species. Atmos. Chem. Phys. 2004, 4, 1461-1738. 14. Lee, C. T.; Yang, W. T.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density. Phys.Rev.B 1988, 37, 785-789. 15. Becke, A. D. A new mixing of Hartree-Fock and local density-functional theories. J. Chem. Phys. 1993, 98, 1372-1377. 16. Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab-initio calculation of vibrational absorption and circular-dichroism spectra using density-functional force-fields. J. Phys. Chem. 1994, 98, 11623-11627. 17. Cizek, J. Use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules. Advan. Chem. Phys. 1969, 14, 35-89. 18. Purvis, G. D. I.; Bartlett, R. J. A full coupled-cluster singles and doubles model: the inclusion of disconnected triples. J. Chem. Phys. 1982, 76, 1910-1918. 19. Kendall, R. A.; Dunning, T. H.,Jr; Harrison, R. J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796-6806. 20. Montgomery, J.; Frisch, M.; Ochterski, J.; Petersson, G. A complete basis set model chemistry. VI. Use of density functional geometries and frequencies. J. Chem. Phys. 1999, 110, 2822-2827. 21. Montgomery, J.; Frisch, M.; Ochterski, J.; Petersson, G. A complete basis set model chemistry. VII. Use of the minimum population localization method. J. Chem. Phys. 2000, 112, 6532-6542. 22. Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 theory. J. Chem. Phys. 2007, 126, 084108. 23. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H. et al. Gaussian 09. Gaussian, Inc. 2016, Revision A.02. 24. Kiefer, J. H.; Tranter, R. S.; Wang, H.; Wagner, A. F. Thermodynamic functions for the cyclopentadienyl radical: The effect of Jan-Teller distortion. Int J Chem Kinet 2001, 33, 834-845. 25. Katzer, G.; Sax, A. F. Numerical determination of pseudorotation constants. J. Chem. Phys. 2002, 117, 8219-8278.


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26. Sharma, S.; Green, W. H. Computed rate coefficients and product yields for c-C5H5 + CH3  Products. J. Phys. Chem. A 2009, 113, 8871-8882. 27. Benson, S. W. Thermochemical Kinetics, 2nd Ed. John Wiley and Sons: New York, 1976; . 28. Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: New York, 1972; . 29. Knyazev, V. D.; Bencsura, A.; Stoliarov, S. I.; Slagle, I. R. Kinetics of the C2H3 + H2  H + C2H4 and CH3 + H2  H + CH4 Reactions. J. Phys. Chem. 1996, 100, 11346-11354. 30. Knyazev, V. D.; Slagle, I. R. Experimental and theoretical study of the C2H3 = H + C2H2 reaction. Tunneling and the shape of falloff curves. J. Phys. Chem. 1996, 100, 16899-16910. 31. Forst, W. Unimolecular rate theory test in thermal reactions. J. Phys. Chem. 1972, 76, 342348. 32. Mokrushin, V.; Bedanov, V.; Tsang, W.; Zachariah, M. R.; Knyazev, V. D.; McGivern, W. S. ChemRate. 2011, Version 1.5.8. National Institute of Standards and Technology, Gaithersburg, MD. 33. Barker, J. R. Multiple-well, multiple-path unimolecular reaction systems. I. MultiWell computer program suite. Int. J. Chem. Kinet. 2001, 33, 232-245. 34. Barker, J. R.; Nguyen, T. L.; Stanton, J. F.; Aieta, C.; Ceotto, M.; Gabas, F.; Kumar, T. J. D.; Li, C. G. L.; Lohr, L. L.; Maranzana, A. et al. MultiWell-2016 Software Suite and User Manual. 2016. 35. Xu, S.; Lin, M. C. Computational study on the kinetics and mechanism for the unimolecular decomposition of C6H5NO2 and the related C6H5 + NO2 and C6H5O + NO reactions. J. Phys. Chem. B 2005, 109, 8367-8373. 36. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977.. 37. Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson Jr., R. F.; Kerr, J. A.; Troe, J. Evaluated kinetic and photochemical data for atmospheric chemistry. Supplement IV, IUPAC subcommittee on gas kinetic data evaluation for atmospheric chemistry. J. Phys. Chem. Ref. Data 1992, 21, 1125-1568. 38. Ghildina, A. R.; Oleinikov, A. D.; Azyazov, V. N.; Mebel, A. M. Reaction mechanism, rate constants, and product yields for unimolecular and H-assisted decomposition of 2,4cyclopentadienone and oxidation of cyclopentadienyl with atomic oxygen. Combust. Flame 2017, 183, 181-193.



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39. Slagle, I. R.; Yamada, F.; Gutman, D. Kinetics of free radicals produced by infrared multiphoton-induced decompositions. I. Reactions of allyl radicals with nitrogen dioxide and bromine. J. Am. Chem. Soc. 1981, 103, 149-153. 40. Rissanen, M. P.; Amedro, D.; Krasnoperov, L.; Marshall, P.; Timonen, R. S. Gas phase kinetics and equilibrium of allyl radical reactions with NO and NO2. J. Phys. Chem. A 2013, 117, 793-805. 41. Geppert, W. D.; Eskola, A. J.; Timonen, R. S.; Halonen, L. Kinetics of the reactions of vinyl (C2H3) and propargyl (C3H3) radicals with NO2 in the temperature range 220-340 K. J. Phys. Chem. A 2004, 108, 4232-4238.


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Table 1. Conditions and results of experiments to determine k1 T / K [He] a [c-C5H6] b [c-C5H5]0 c

[NO2] b

Id

k2 / s-1

k1 e

305

12.0

0.42

0.47

0.13 – 0.49

6.5

18.1

4.96 ± 0.68

400

3.0

0.27

0.78

0.044 – 0.42

10

23.0

4.35 ± 0.44

400

6.0

0.28

0.57

0.091 – 0.40

10

33.8

4.63 ± 0.68

400

12.0

0.26

0.47

0.096 – 0.35

10

26.4

4.39 ± 0.41

500

3.0

0.91

1.49

0.45 – 1.52

6.5

102.8

2.22 ± 0.38

600

6.0

0.28

0.56

0.20 – 1.40

7.8

45.2

1.45 ± 0.20

800

6.0

2.0

2.6

0.47 – 3.36

5.2

23.0

0.595 ± 0.052

800

6.0

2.0

1.1

0.47 – 3.36

2.2

19.4

0.641 ± 0.073

a

Concentration of the helium bath gas in units of 1016 molecule cm-3.

b

In units of 1013 molecule cm-3.

c

In units of 1011 molecule cm-3.

d

Laser intensity in mJ pulse-1 cm-2.

e

In units of 10-11 cm3 molecule-1 s-1. Error limits represent the sum of statistical (twice the

standard error) and estimated systematic uncertainty.


a)

-10

C5H5

0

10

20

Page 18 of 21

+

30

40

signal / arb. units

200

k' / s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

signal / arb. units


b)

t / msec

100

C5H5O+ +

NO

-10

0

10

20



0 0

1 2 3 13 -3 [NO2] / 10 molecule cm

Figure 1. Pseudo-first-order c-C5H5 decay rate k' vs. [NO2]. T = 800 K, [He] = 6.01016 molecule cm-3. The insets show the recorded profiles of (a) c-C5H5 and (b) C5H5O and NO for the conditions of the open circle: [NO2] = 1.201013 molecule cm-3, [c-C5H5] = 2.61011 molecule cm-3, k' = 101.4  2.8 s-1.


Page 19 of 21

1000 K / T 1.0

1.5

2.0

2.5

3.0

3.5

a)

-1

cm molecule s

-1

8

overall reaction

4

C5H5-NO2

3

2

k1 / 10

-11

C5H5-ONO 1

0.5 6 -1

b)

-1

cm molecule s

overall reaction

4 C5H5-NO2

3 -11

k1 / 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 C5H5-ONO 0 300

400

500

600

700

800

T/K

Figure 2. Temperature dependence of the rate constant of reaction 1 presented in Arrhenius (a) and linear (b) coordinates. Diamonds, circles, and squares: experimental results obtained at three 16 16 16 -3 bath gas (helium) densities: 3.010 , 6.010 , and 12.010 molecule cm , respectively. Lines represent the results of master equation modeling. Solid lines: overall rate constant at the same three experimental bath gas densities (lowest, central, and upper lines correspond to the lowest, central, and upper densities, respectively). Dashed lines: the rate constant of the reaction pathways proceeding through the initial formation of c-C5H5-NO2 (long dashes) and c-C5H5-ONO (short 16 dashes) at [He] = 6.010 .



C5H5 + NO2

6.7

O

E / kJ mol-1

0

-17.9

N O

C5H5-ONO

-58.5

O

-78.6

N

-100

OH

C5H4-N(O)OH

-156.8

-162.7

-158.2 -185.8

C5H5-NO2 -200

-180.6

C5H5-3-NO2

C5H5-2-NO2

O N

O O

O N

N

O

O

Reaction Coordinate

Figure 3. The potential energy surface (PES) of the pathway of reaction 1 proceeding through the initial formation of c-C5H5-NO2. Only species and transition states for non-negligible channels are shown to avoid graph congestion.

C5H5O + NO 6.7

0

16.7

C5H5 + NO2 0.0

-17.5

E / kJ mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 21

C5H4O + HNO O

-61.5

N

1,4-C5H5-ONO

-100

-106.6

-51.6 -131.9

C5H5-NO2 O N

-175.2

-156.8

2,4-C5H5-ONO

-165.7

-174.4

1,3-C5H5-ONO

-168.4

C5H5(O) + NO -233.9

O

O O

O

-136.2

-162.7

-200

O

N O

O

N

2-NO-3-C5H5(O)

-255.3

4-NO-2-C5H5(O)

O

-300

N

O

O N O

Reaction Coordinate

Figure 4. The PES of the pathway of reaction 1 proceeding through the initial formation of c-C5H5-ONO. Only species and transition states for non-negligible channels are shown to avoid graph congestion. 20 ACS Paragon Plus Environment

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TOC Graphic


Kinetics of the Reaction of the Cyclopentadienyl Radical with Nitrogen

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