Low Temperature Rate Coefficients for the Reaction CN + HC3N - The

Article pubs.acs.org/JPCA

Low Temperature Rate Coefficients for the Reaction CN + HC3N Sidaty Cheikh Sid Ely,† Sébastien B. Morales,† Jean-Claude Guillemin,‡ Stephen J. Klippenstein,§ and Ian R. Sims*,† †

Institut de Physique de Rennes, UMR CNRS-UR1 6251, Université de Rennes 1, 263 Avenue du Général Leclerc, 35042 Rennes Cedex, France ‡ Ecole Nationale Supérieure de Chimie de Rennes, CNRS UMR 6226, 11 Allée de Beaulieu, CS 50837, 35708 Rennes Cedex 7, France § Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States ABSTRACT: The reaction of CN radicals with HC3N is of interest for interstellar and circumstellar chemistry as well as for the chemistry of Titan’s atmosphere, as part of a general scheme for cyanopolyyne synthesis within these low temperature environments. Here, we present the first experimental measurements of its rate coefficient below room temperature down to 22 K, employing the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme or Reaction Kinetics in Uniform Supersonic Flow) technique coupled with pulsed laser photolysis−laser-induced fluorescence. A novel pulsed version of the CRESU technique employing a new spinning disk valve was used for some of the kinetics measurements. The measurements were in excellent agreement with the only previous determination at room temperature and show a marked increase in the rate coefficient as the temperature is lowered, with the results being well represented by the equation k(T) = 1.79 × 10−11(T/300 K)−0.67 cm3 molecule−1 s−1, with a root-mean-square (statistical) error of 0.61 × 10−11 cm3 molecule−1 s−1, to which should be added 10% estimated likely systematic error. High accuracy ab initio quantum chemical calculations coupled with variational two-transition state theory calculations were also performed and demonstrate excellent agreement within the combined experimental and predicted theoretical uncertainties. The theoretical rate coefficients, adjusted within expected uncertainties, can be accurately reproduced over the 5 to 400 K temperature range by the expression [(1.97 × 10−8) T −1.51 exp(−3.24/T) + (4.85 × 10−13) T 0.563 exp (17.6/T)] cm3 molecule−1 s−1, where T is in K. The new measurements are likely to be of interest to astrochemical and planetary atmospheric modelers.

1. INTRODUCTION Cyanopolyynes constitute a series of linear molecules with alternating carbon−carbon single and triple bonds, of generic formula H(CC)nCN. They have been detected in a wide variety of astrophysical environments, ranging from the cold environments of dense interstellar clouds and planetary atmospheres to warmer regions such as hot cores or circumstellar shells. The longest-chain interstellar molecule detected to date is HC11N, a member of this series. It was definitively detected in 1997 by Bell et al.1 in the TMC-1 cold molecular cloud, following laboratory spectroscopic experiments by Travers et al.2 Cyanopolyynes have also been observed in the photochemically active cold atmosphere of Titan, including HC3N and HC5N by the INMS (Ion Neutral Mass Spectrometer) on board the Cassini orbiter.3 The routes to the formation of these rather exotic species under low temperature conditions have been the subject of some debate over the years (see below), but it is now generally accepted that the most important synthetic route is via successive polymerization-type reactions involving additions of C2H and CN radicals to acetylenic chains, followed by elimination of H, for example, reactions P1 to P3 as proposed by Smith and Sims4 in 1992: © 2013 American Chemical Society

C2H + H(C≡C)n H → H(C≡C)n + 1H + H

(P1)

CN + H(C≡C)n H → H(C≡C)n CN + H

(P2)

C2H + H(C≡C)n CN → H(C≡C)n + 1CN + H

(P3)

CN + H(C≡C)n CN → NC(C≡C)n CN + H

(P4)

Reactions of type P1 involving the addition of the ethynyl radical to polyynes act as chain lengthening propagation reactions, while reaction type P2 produces the cyanopolyyne species that can continue to grow via further C2H additions of type P3. However, reactions of type P4, where the CN radical reacts with cyanopolyynes to generate the dicyanopolyyne, will act as chain termination reactions, as the dicyanopolyyne is unlikely to be reactive toward further attack by CN and C2H radicals. Existing experimental kinetics data on these reaction classes are rather sparse, especially at the low temperatures prevailing Special Issue: Curt Wittig Festschrift Received: July 11, 2013 Revised: September 17, 2013 Published: September 18, 2013 12155

dx.doi.org/10.1021/jp406842q | J. Phys. Chem. A 2013, 117, 12155−12164

The Journal of Physical Chemistry A

Article

2. EXPERIMENTAL METHODS 2.1. Generation of Cold Gas Flows. The CRESU technique used here for the generation of extremely cold supersonic gas flows suitable for the study of gas phase collisional processes by pulsed laser methods has been described in detail in previous publications.14,15 Briefly, isentropic expansion of a buffer gas through a Laval nozzle is used to generate a cold supersonic flow of buffer gas (He, Ar, or N2). Each nozzle is designed to achieve a particular temperature with precise flow conditions and a given buffer gas. Because of the relatively high density of the supersonic flow (10161017 cm −3 ), molecular collisions are frequent and thermal equilibrium is maintained for several tens of centimeters, corresponding to some hundreds of microseconds, downstream of the nozzle exit. Each Laval nozzle is mounted on a movable reservoir kept at room temperature inside a vacuum chamber. In particular, the CRESU technique has been previously employed to study the reactions of CN radicals with a number of stable molecular coreagents, such as O2, NH3,15,16 or various saturated and unsaturated hydrocarbons,8,17−19 using the pulsed laser-photolysis−pulsed laser-induced fluorescence method. All of these coreagents were available commercially, and the relatively rapid reactions observed, especially at low temperatures, necessitated flows of the order of 100 sccm (standard cm3 min−1) to make the measurements in the relatively short temporal window defined by the hydrodynamic flow time of the particular Laval nozzle used. A typical measurement campaign might require many hours of continuous operation, resulting in the consumption of molar quantities of reagent gases. While this does not pose any real problem for most commercially available reagents, unstable reagents that must be synthesized to order or isotopically labeled species are typically not obtainable in such quantities, at least at reasonable prices. HC3N is a good example; it is somewhat unstable and not commercially available, and while its synthesis is relatively straightforward,20 it is also rather laborious, and consequently, it is difficult to envisage its use in the large quantities potentially necessary for the study of a reaction with a rate coefficient an order of magnitude lower at room temperature compared with many other CN + hydrocarbon reactions.10 In order to allow studies such as this to be performed we have recently constructed a pulsed version of the CRESU apparatus,21 based around the use of a new kind of spinning disk valve.22 A previous pulsed version of the CRESU technique designed by M. A. Smith and co-workers used pulsed valves venting into a very small reservoir leading directly to the Laval nozzle23 and has been adopted by a number of groups.24−27 While this had the advantage of using existing pulsed valve technology, a small reservoir volume was necessary to enable a sufficiently rapid build-up to the design reservoir pressure, which is critical for the establishment of uniform supersonic flow for a given nozzle. This small volume is, however, disadvantageous, as Laval nozzles are designed to function with quasi-static gas upstream. The cross-sectional area of the reservoir is of the same order as the throat diameter of some of the Laval nozzles used, implying that the gas is already moving rapidly (and possibly turbulently) in the reservoir. This limits both the lowest obtainable temperatures (ca. 50 K to date) as well as the quality of the uniform supersonic flow. The new design conserves the large reservoir volume (22.5 dm3) of the continuous flow CRESU along with a large

in dense interstellar clouds (1020 K or even below in the case of cold cores5), circumstellar shells (∼30 K in the so-called photochemical shell6), and Titan’s atmosphere (70180 K through the troposphere and stratosphere7). Reaction type P2 has been found to be rapid down to 25 K for n = 1 (CN + C2H2) in the early 1990s in the first CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme or Reaction Kinetics in Uniform Supersonic Flow) measurements on radical + closed-shell molecule reactions by Sims et al.,8 and reaction type P2 was also found to be fast down to 15 K for n = 1 (C2H + C2H2) a few years later by Chastaing et al.9 No low temperature absolute kinetics measurements on these reaction types are available for n > 1 or for reaction types P3 and P4 for any n. This is in great measure due to the fact that the necessary coreagents are relatively unstable, are not generally commercially available, and have to be synthesized. As the CRESU technique uses rather large quantities of reagents, at least in its standard continuous flow configuration, this has hitherto precluded such measurements. In this and subsequent articles, we describe a number of adaptations of the technique that have enabled us to extend the range of measurements of low temperature rate coefficients to reactions covering either n > 1 (for reactions P1 and P2) or n = 1 for P3 and P4. In this article, we report on the first low temperature rate coefficient measurements for the first member of the chain termination reaction series P4, CN + HC3N. The only previous measurement of the rate coefficient for the reaction of cyano radicals (CN) with cyanoacetylene (HC3N) was performed by Halpern et al.10 using pulsed 193 nm ArF excimer laser photolysis of HC3N to generate ground state CN(X2Σ+), and pulsed laser-induced fluorescence at a wavelength of around 388 nm in the CN violet system for detection. The experiments were performed at room temperature and yielded a value for the rate coefficient of (1.70 ± 0.08) × 10−11 cm3 molecule−1 s−1. Observing that this is about 10 times slower than the rate coefficients of reactions of CN with unsaturated hydrocarbons, Halpern et al. propose a small activation barrier of 1.5 kcal mol−1. Apart from the recommendation of Halpern et al. the only prior theoretical prediction of the temperature dependence of this rate coefficient was made by Faure et al. in 2009, using a semiempirical model, which is based upon knowledge of the rate coefficient at room temperature, combined with calculations of the capture theory rate coefficient at two arbitrary temperatures between 5 and 50 K (here, 10 and 30 K were used). A fit of these three values (two capture theory values at 10 and 30 K and one experimental value at 300 K) to a Kooij11 temperature dependence yielded the predicted rate coefficient k = 1.85 × 10 −11 (T/300 K) −1.93 exp(−34.5 K/T) cm 3 molecule−1 s−1. As Faure et al. point out, an experimental determination of the rate coefficient down to low temperatures would enable these two predicted temperature dependences to be distinguished. Wakelam et al. in their 2010 review of rate coefficients for interstellar chemical modeling recommend, based on the semiempirical arguments advanced by Smith et al.12 and the absence of a barrier to reaction on the potential energy surface calculated by Petrie and Osamura,13 a rate coefficient for the CN + HC3N reaction of 3.5 × 10−10 cm3 molecule−1 s−1 at 10 K, very close to the value predicted by Faure et al. at that temperature. 12156



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downstream chamber volume (ca. 0.5 m3) but interrupts the flow with a slotted rotating disk a few mm downstream of the Laval nozzle throat. Gas flow is established with optimal upstream and downstream pressure conditions in just the time taken for the slot to pass across the Laval nozzle throat, resulting in the immediate establishment of optimal uniform supersonic flow. The technique has been demonstrated to work efficiently for a flow temperature of 22 K, returning kinetics results identical to those obtained with the continuous flow CRESU technique.21 The pulsed CRESU operated at one temperature, 22 K, and other low temperature experiments were performed using the continuous flow CRESU technique with a variety of Laval nozzles (see results). Room temperature measurements were accomplished by throttling the pumps and increasing the pressure in the main chamber up to that of the reservoir (ca. 10 mbar) thereby generating a subsonic flow at the same temperature as the reservoir. 2.2. Synthesis of HC3N and Gas Handling. HC3N was prepared in molar quantities following a two-stage synthesis based on the work of Moureu and Bongrand.20 Propiolamide (HCC−CONH2) was first prepared by the reaction of methyl propiolate (HCC−COOCH3, Sigma Aldrich 99%) with liquid ammonia (Air Liquide, 99.96%) under an inert (nitrogen) atmosphere at −60 °C, with a typical yield of 96%. This solid product was then mixed with sea sand and phosphorus pentoxide (P4 O10, Alpha Aesar 98%) and dehydrated under vacuum by heating to 180 °C. The HC3N product was collected in a liquid nitrogen trap as white crystals after passage through a trap held at −25 °C. The yield of this second stage was typically around 63%, with a final purity in excess of 98%. Particular care was taken to characterize the purity of the synthesized HC3N. Initial analysis by 1H NMR showed the presence of CH3CN (0.6%), C2H2 (0.3%), and CH3OH (0.2%) impurities, indicating an overall purity of ca. 99%: however, the method of transfer of the gas-phase sample could result in the loss of more volatile impurities (or, indeed, an overestimation of the level of less volatile substances). 13C NMR showed only the presence of cyanoacetylene. The infrared spectrum of a gasphase sample of HC3N enabled a more quantitative estimation of the purity. A precisely calibrated mixture of ca. 1% HC3N in helium was prepared and the infrared absorption spectrum measured over the range 10003500 cm−1 using a Fourier transform infrared spectrometer (Bruker IFS120HR). The integrated absorbances for the ν1 (C−H stretch) and 2ν5 (C− H bend) bands at 3327 and 1314 cm−1, respectively, were compared with the values calculated using the partial pressure of HC3N and integrated band intensities from the work of Jolly et al.28 This yielded an estimated purity of 99.6+0.4 ‑3.6 %, the principal source of uncertainty arising from the published errors in the integrated band intensities of Jolly et al. The synthesized HC3N was conserved in its solid form in a low temperature freezer. HC3N is found to be relatively unstable toward polymerization in the gas phase at high partial pressures and reactive toward air. In order to maintain its purity, a 13.5 dm3 stainless steel cylinder was constructed with a closure flange crossed by two stainless steel tubes. The cylinder, flange, and tubes were all fluorocarbon coated on their interior surfaces, and fluorocarbon flexible tubes, pressure couplings, and valves were used such that once the valves were closed, the gas could not come into contact with any metal surface that might enhance its decomposition by polymerization. Before each series of experimental runs, a mixture of approximately

300 mbar HC3N diluted in 3 bar of He (Air Liquide, 99.995% purity) was prepared using a high precision capacitance manometer (MKS 627D53MBC1B), and left for 24 h to allow for diffusive mixing. Carrier gases (He, Ar, or N2, Air Liquide 99.995%) were taken directly from the cylinders through stainless steel lines and fluorocarbon tubes. All flows were regulated and measured using mass flow controllers (various manufacturers). These flow controllers were calibrated by standard pressure rise/drop techniques using an independently calibrated volume. In order to correct principally for varying specific heat capacities of the different gases, so-called gas correcting factors provided by the flow controller manufacturers were used. However, for the case of the reagent HC3N/He mixtures, this information was not easily available. Standard empirical formulas enabled a preliminary estimation of this factor, but in order to ensure the highest possible accuracy in the kinetics measurements, the reagent flow was absolutely calibrated in real time by monitoring the pressure drop of the HC3N/He mixture as a function of time in the gas cylinder, the volume of which had been measured independently. In this way, each kinetics measurement was independently calibrated. During the kinetics measurements, both the chamber and stagnation pressure in the reservoir were measured by capacitance manometers (Edwards Barocel). Knowledge of the total gas density along the flow, achieved by means of impact pressure measurements using a Pitot tube, and of each gas flow enabled the calculation of the absolute concentration of the reactant in the supersonic expansion. 2.3. Generation and Detection of CN X2Σ+ Radicals. Cyano radicals in their X2Σ+ ground electronic state were generated as in Carty et al.17 by the photolysis of cyanogen iodide (ICN; Acros Organics, 98%) at 266 nm using the fourth harmonic output of a Nd:YAG laser (Spectra Physics GCR 190) at a fluence in the reaction zone of ∼35 mJ cm−2. A small flow (a few standard cm3 min−1) of argon was passed over crystals of ICN before this flow of gas entered the gas reservoir upstream of the Laval nozzle. Photodissociation of ICN at this wavelength produces CN radicals that are overwhelmingly in the v = 0 level of the X2Σ+ ground vibronic state, with less than 2% in the v = 1 level, but over a wide range of rotational levels.29 Rapid rotational relaxation is assured by collisions with the cold, dense buffer gas. Cyano radicals were detected by laser-induced fluorescence (LIF) with excitation in the (0,0) band of the CN (A2Σ+X2Σ+) system at ∼388 nm using the output of a tunable dye laser (Continuum ND6000) operating with Exciton Exalite 389 dye, pumped by the tripled output of another Nd:YAG laser (Spectra Physics GCR 230). The photolysis and probe lasers, after combination on a dichroic mirror, entered the CRESU chamber and gas reservoir via two quartz Brewster angle windows and passed through the throat of the Laval nozzle and along the axis of the gas flow. Fluorescence in the (0,1) band at ∼420 nm was collected at a certain distance from the Laval nozzle (10−30 cm), depending on the specific Laval nozzle, using a combination of an UVenhanced mirror and fused silica lenses onto the photocathode of a UV-sensitive photomultiplier tube (Thorn EMI 6723) through a narrow band interference filter centered at 420 nm with a 10 nm full-width at half maximum (fwhm) bandwidth (Ealing Optics). Tests were carried out to ensure that the signal was not saturated. 2.4. Kinetics Measurements. Pseudo-first-order decays were observed by recording the variation in the laser-induced 12157



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Table 1. Rate Coefficients for the Reaction of CN Radicals with HC3N Measured at Different Temperatures, with Associated Experimental Parameters T (K)

buffer gas

total density (1016 molecules cm−3)

22 22

He He

16.40 16.40

24 24

He He

36 36

range of [HC3N] (1013 molecules cm−3)

No. of experimental points

rate coefficient, k (10−11 cm3 molec−1 s−1)

0−4.93 0−1.95

14 11

18.30 18.30

0.14−2.48 0.25−2.43

9 8

He He

5.28 5.28

0−4.94 0−3.14

9 11

83 83

N2 N2

4.88 4.88

0.3−5.06 0.4−4.06

11 10

145 145

N2 N2

9.23 9.23

0.93−9.28 1.21−11.85

10 7

291 295 296

N2 N2 N2

35.40 24.50 5.70

0.19−241.17 5.19−78.38 0−30.46

13 10 10

11.71 ± 1.55a 9.27 ± 1.12 9.95 ± 1.13b 10.04 ± 1.48 8.64 ± 1.46 9.40 ± 1.23 7.17 ± 1.86 7.33 ± 0.88 7.32 ± 0.87 4.56 ± 0.57 3.62 ± 0.45 3.98 ± 0.45 3.18 ± 0.43 2.85 ± 0.56 3.10 ± 0.40 2.06 ± 0.28 1.81 ± 0.19 1.77 ± 0.21 1.82 ± 0.19

a

Quoted uncertainty (here and throughout the table) is calculated using the standard error evaluated from the second order plot, multiplied by the appropriate Student’s t factor for 95% confidence, and then combined with an estimated systematic error of 10%. bMean value of rate coefficients at each temperature is calculated using statistical uncertainties only, and the resulting uncertainty is then combined with an estimated systematic error of 10%.

fluorescence (LIF) signal as a function of the time delay between the pulses from the photolysis and probe lasers, for 200 different time delays, averaged typically 10 times. A baseline measurement was also recorded at negative time delays (probe before photolysis pulse) to establish a pretrigger baseline. These traces of LIF signal versus time delay were fitted to single exponential functions, the fit being started at time delays sufficient to allow for rotational relaxation. This procedure yielded pseudo-first-order rate coefficients related to the rate of loss of CN radicals. These were recorded for a range of different HC3N concentrations, specified in Table 1, enabling the construction of second-order plots and the determination of the bimolecular rate coefficient at each temperature. The absorption cross-section of ICN at 266 nm is ca. 3 × 10−19 cm2,30 and it was present at an average density of 1012 cm−3 in the gas flow. At the laser fluence used, only 1.4% of the precursor concentration is photodissociated, yielding an estimated maximum CN(X2Σ+) concentration of 1.40 × 1010 cm−3 (assuming a quantum yield of 1). This is 102 times less than the minimum HC3N concentration used (see Table 1) and 103105 times less than the typical value of the HC3N concentration, ensuring that pseudo-first-order conditions were respected at all times ([CN] ≪ [HC3N]). The absorption cross-section of HC3N at 266 nm is less than 6.7 × 10−21 cm2,31 ensuring that at most 0.03% of the HC3N would be photodissociated (assuming a quantum yield for photodissociation of 1 at that wavelength). This proportion is too small to interfere with the kinetics measurements.

on the potential energy surface for addition to each of the carbon atoms as well as to the nitrogen atom. High accuracy predictions for these saddle point energies were obtained from a combination of (i) basis set extrapolated CCSD(T)/CBS evaluations, (ii) core−valence corrections, (iii) CCSDT(Q) corrections, (iv) relativistic corrections, and (v) CCSD(T)/ccpVTZ zero-point energies. These predictions are expected to yield results that are only modestly less accurate than those obtained with the HEAT32 and W433,34 computational methods, for example. Note that this methodology is closely related to other high level methods such as W4 and so might be expected to have similar 2 sigma uncertainties of only a few tenths of a kcal/mol.34 The Dunning correlation consistent basis sets35,36 were employed throughout the analysis. The CCSD(T)/CBS results were obtained from explicit evaluations for the aug′-cc-pVQZ and aug′-cc-pV5Z basis sets, where the prime indicates that diffuse functions are included for only the s and p orbitals in C and N and the s function in H. An extrapolation coefficient of 0.93 was employed on the basis of a simple two point 1/(l + 1)4 extrapolation.37 The cc-pVDZ basis set was employed in the evaluations of the CCSDT(Q) correction. The core−valence corrections were evaluated from the difference between CCSD(T)/CBS predictions for calculations with and without frozen core orbitals. The latter basis set extrapolation was obtained from explicit calculations for the cc-pCVTZ and ccpCVQZ basis sets with an extrapolation coefficient of 0.69 again based on a 1/(l + 1)4 extrapolation. Scalar relativistic corrections were evaluated for CI/aug-cc-pCVTZ wave functions. Each of these corrections were obtained at the CCSD(T)/cc-pVTZ geometry. The quantum chemistry software package MOLPRO38 was used for all these evaluations, with the Kallay MRCC module used to perform the CCSDT(Q) calculation.39,40

3. THEORETICAL METHODS 3.1. Electronic Structure Methodology. The rovibrational properties of the stationary points for the addition reaction were determined at the CCSD(T)/cc-pVTZ level of theory. These calculations indicated that there are saddle points 12158



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Table 2. Theoretical Barrier Heights in Units of kcal mol−1 for the Addition of CN to HC3N addition site HC1C2C3N 1

C C2 C3 N

HLa

CCSD(T)/cc-pVTZb

CBSc

CCSDT(Q)/cc-pVDZd

core−valencee

rel.f

−0.42 1.59 4.81 2.10

−0.21 1.72 4.83 2.68

−0.46 −0.63 −0.51 −1.04

0.18 0.38 0.35 0.45

0.03 0.08 0.10 −0.05

0.03 0.04 0.04 0.07

a

High-level saddle point energies, which are a composite of the CCSD(T)/cc-pVTZ energy including zero-point energy and the remaining corrections. bCCSD(T)/cc-pVTZ energy including zero-point energy. cBasis set correction based on CBS extrapolation. dCCSDT(Q)/cc-pVDZ correction. eCore−valence correction. fRelativistic correction.

Figure 1. Typical kinetics plots at three temperatures: A, 291 K in a subsonic flow; B, 83 K in a continuous CRESU flow; and C, 22 K in a pulsed CRESU flow. See Table 1 for further details of the conditions. The upper panels shows the decay of CN (B2Σ+−X2Σ+) LIF signals at different concentrations corresponding to the points indicated in the lower panels, fitted to single exponential decays as described in the text. The lower panels show second order plots where the pseudo-first-order decay constants are plotted as a function of HC3N concentration and fitted to linear plots, which yield the rate coefficients shown in Table 1

atoms to a set of alkenes demonstrated the utility of this method.42 For the long-range/outer transition state, we evaluated the flux with a direct sampling of the intermolecular interaction energies at the CI+QC/CBS level using our variable-reaction coordinate transition state theory methodology. The CBS extrapolation is obtained from explicit cc-pVDZ and cc-pVTZ evaluations. The calculated long-range addition rate coefficient differs by 10% or less for the cc-pVDZ and cc-pVTZ basis sets and so should be reasonably well converged with respect to the basis set. The CBS extrapolation, which is admittedly rather approximate due to the small size of the basis sets, contributes an additional difference of 5% or less. Related calculations with the RMP2 method agree to within 15%. The reaction coordinate is taken to be the separation between the CN and HC3N centers-of-mass. Values ranging from 20 to 6 Å are considered in these long-range TS evaluations. Larger separations are beyond the outer transition state for the temperatures of relevance here, while the van der Waals complex is to some extent already formed at shorter separations. For the inner transition state, we have implemented variational TST employing the CC distance as a distinguished

These high level predictions for the zero-point energy (ZPE) corrected saddle point energies are summarized in Table 2 along with the components that lead to them. The carbon atoms are labeled from left to right in HC3N; i.e., HC1C2C3N. The saddle point for addition to the terminal carbon atom, C1, is submerged below the reactant energy, while all other saddle points are significantly positive. The difference of 2 kcal mol−1 or more between the saddle points, coupled with the lower entropy for the higher barriers, implies that only the addition to the C1 site makes a meaningful contribution to the addition kinetics at temperatures of 300 K and lower. Thus, the present transition state theory (TST) calculations focus on only this channel. 3.2. Kinetics Methodology. The submerged barrier for the addition to C1 also implies that there are two transition states involved in the addition at this site. A loose outer transition state provides a bottleneck to the formation of a CN···HC3N van der Waals complex from the CN and HC3N reactants. A tight inner transition state describes the transformation of the CN···HC3N van der Waals complex into a chemically bound NCCHCCN complex. Here, we use a two transition state model41 to predict the overall addition kinetics. Our prior comparison of theory and experiment for the addition of O(3P) 12159



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estimated probable systematic error of 10% due to uncertainties in the calibration of mass flow controllers and total density or pressure measurements to yield the final uncertainties, which are quoted along with the results in Table 1. The measured rate coefficients follow very closely a power law temperature dependence over the entire temperature range, and a nonlinear least-squares (unweighted) fit to the entire data set yields the following temperature dependence: k(T) = 1.79 × 10−11(T/300 K)−0.67 cm3 molecule−1 s−1, with a root-meansquare (statistical) error of 0.61 × 10−11 cm3 molecule−1 s−1, to which should be added 10% estimated likely systematic error. The theoretical predictions are displayed in Figure 2.

reaction coordinate. The reaction path energies, structures, and vibrational frequencies were evaluated at the CCSD(T)/ccpVTZ level for CC separations ranging from 2.2 Å to the saddle point separation of 2.52 Å. The good agreement between the ZPE-corrected CCSD(T)/cc-pVTZ saddle point energy of −0.22 kcal mol−1 and the higher level value of −0.42 kcal mol−1 suggests that the CCSD(T)/cc-pVTZ method should be appropriate for this mapping. Rigid rotor harmonic oscillator (RRHO) assumptions were employed in the evaluation of the number of states. Limited direct sampling of CCSD(T)/ccpVDZ energies indicates that the anharmonic effects at the inner transition state lower the inner transition state partition function by a nearly constant factor of ∼0.8, at least for the temperatures where it affects the kinetics. This correction factor is included in our final analysis, as is a dynamical correction factor of 0.85 for the overall rate coefficient. The latter correction factor is based on our direct trajectory simulations for methyl + methyl recombination.43

4. RESULTS Typical LIF decay traces and second order plots are shown in Figure 1 for three representative temperatures: 291, 83, and 22 K, the latter using the new pulsed CRESU. Two points are worthy of note. The use of a synthesized reagent places a strong constraint on the maximum reagent flow and hence density that is possible, and at the very lowest temperature (where in principle the use of the pulsed CRESU might enable the use of higher reagent densities) the maximum value is also limited by the onset of clustering, which is seen at higher densities by a clear departure from linearity in the second order plot.15 The time available to monitor the kinetics is limited by the duration of the uniform supersonic flow, and as a consequence, it was not possible to monitor the decays for two or more half-lives as would normally be the case. However, we were able to establish very precisely the baseline level by recording points at negative delays (i.e., the probe laser firing before the photolysis laser), and the use of these points to fix the baseline level enabled the nonlinear least-squares fitting program to determine the firstorder decay constants very precisely even over decay times of the order of one-half-life or less, as can be seen in Figures 1B,C. The constraint on the maximum total reagent concentration also meant that the intercept on the second order plots was often significant compared to the total variation in pseudo-firstorder rate coefficient achieved. This intercept is due to a combination of different loss processes for the CN radical, including diffusion out of the detection volume, and reaction with the precursor and any impurities present. However, all of these factors were kept constant during each run, and points on the second order plot were determined by alternating between high and low concentrations to avoid any possibility of influence on the gradient which yields the bimolecular rate coefficient. Errors were very carefully determined by performing an unweighted statistical analysis of the second order plots, yielding the gradient with its associated standard error. This standard error was then multiplied by the appropriate value of the two-sided Student’s t-distribution for 95% confidence limits, taking into account the number of degrees of freedom (equal to the number of points on the second-order plot minus two). This yielded an estimate of the statistical uncertainty, which was used to generate the weighted mean values when more than one measurement was performed at any single temperature. Subsequently, the statistical error was combined with an

Figure 2. Plot of the ab initio TST predictions for the CN + HC3N addition rate coefficient. For the (black) dotted line, only the outer TS is considered; for the (red) dashed line, only the fixed inner TS at its saddlepoint is considered; for the (blue) continuous line, a variational inner TS is considered; and for the (magenta) double-dash line, the full 2 TS model is implemented.

5. DISCUSSION Excellent agreement is obtained between the pulsed CRESU measurements at 22 K and the complementary continuous flow CRESU measurements at 24 K, providing confirmation of the quality and validity of the pulsed CRESU flow technique. Figure 3 shows the results of this study as a function of temperature. The new results are in excellent agreement with the room temperature rate coefficient of Halpern et al.10 (k = (1.70 ± 0.08) × 10−11 cm3 molecule−1 s−1) also shown in Figure 3 along with their predicted Arrhenius temperature dependence. It is clear, however, that the reaction does not possess a positive activation energy. Faure et al.’s44 semiempirical prediction for the temperature dependence of this rate coefficient is also shown in Figure 3. The prediction is based on a Kooij three-parameter fit to a simple capture theory calculation at two arbitrary (low) temperatures plus the measured room temperature value of Halpern et al. As can be seen, this prediction overestimates the rate coefficient at low temperatures by up to a factor of 6 (at ca. 20 K). This discrepancy, essentially due to the real rate coefficient falling significantly short of the capture theory calculation even at the lowest temperatures reached in this study (22 K), may be understood in terms of the new calculations we have performed. 12160



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Figure 3. Rate coefficients for the reaction of CN(X2Σ+) radicals with HC3N displayed on a log−log scale as a function of temperature. The filled (blue) circles show the experimental rate coefficients from this study with their associated uncertainties (see text for details). The solid (blue) line is a fit to these data yielding k(T) = 1.79 × 10−11(T/ 300 K)−0.67. The filled (black) square shows the room temperature rate coefficient of Halpern et al.10 with its quoted uncertainty, and the dashed (black) line shows their proposed Arrhenius temperature dependence employing an activation energy of 1.5 kcal mol−1. The dashed-dotted (dark red) line shows the semiempirical prediction of Faure et al.44

Figure 4. Comparison of the ab initio and adjusted TST predictions with experimental data for the CN + HC3N rate coefficient. As in Figure 3, the filled (blue) circles show the experimental rate coefficients from this study with their associated uncertainties. The (magenta) double-dash line shows, as in Figure 2, the fully ab initio 2 TS model predictions, while for the (green) solid line the inner saddle point is reduced by 0.15 kcal mol−1 and the lowest three frequencies are decreased by a factor of 1.15. The (green) dashed line shows the fit to the adjusted 2 TS model described in the text and valid over the temperature range 5400 K.

accurate predictions for such low frequencies, and a deviation of 15% for each is not unreasonable. Indeed, these 3 frequencies decrease by an average of 14% in changing from the cc-pVDZ to the cc-pVTZ basis, within our CCSD(T) rovibrational analyses, and a similar decrease might be expected for a further increase in the basis set size. Unfortunately, a CCSD(T)/ccpVQZ vibrational analysis was not feasible. If one instead chose to assign the full error in the theoretical calculations to the saddle point energy, one could obtain a roughly equivalent fit by simply decreasing the barrier by 0.3 kcal mol−1, which is also just within the range of uncertainties in the present barrier height analysis. The current experimental and theoretical study relates to the rate coefficient for the overall CN + HC3N reaction. No determination of the products of this reaction was possible in the current study. However, there is only one exothermic bimolecular channel,13 which is shown below, with the reaction enthalpy calculated from the appropriate enthalpies of formation:45−47

The present fully ab initio TST predictions for the high pressure addition rate coefficient are illustrated in Figure 2. The calculations considering only the inner or outer TSs indicate that the inner TS is dominant for the full range of temperatures considered here. Meanwhile, the variational effect for the inner TS is seen to be quite significant, yielding more than a factor of 2 reduction at 400 K. The minimum in the outer TS calculation is indicative of the change from a dominant dipole−dipole long-range interaction to a dominant dispersion and/or dipoleinduced dipole interaction as the temperature increases. As illustrated in Figure 4, the present two TS model predictions qualitatively reproduce the experimental observation of a rate constant that decreases with increasing temperature. However, the magnitude of the rate constant is underestimated, particularly near the intermediate temperature of 150 K, where the deviation between theory and experiment is a factor of 2−3. This deviation is within the combined uncertainty of theory and experiment. For example, reducing the high level prediction for the saddle point energy by 0.12 kcal mol−1 and at the same time decreasing the three transitional mode vibrational frequencies by a factor of 1.15 yields predicted rate coefficients that are essentially within the error bars of the experimental data, as illustrated with the adjusted line also shown in Figure 4. These adjusted theoretical rate constants can be accurately reproduced over the 5 to 400 K temperature range with the following sum of two modified Arrhenius expressions

CN + HC3N → C4 N2 + H

Δr H ⊖ = − 10.0 kcal mol−1 (R1)

The lack of pressure dependence to the rate constants as measured at room temperature (see Table 1) when the pressure was varied by a factor of almost 6 provides evidence that the reaction is likely proceeding to bimolecular products. While we cannot rule out the possibility that, under our experimental conditions, we are measuring an addition reaction in its high pressure limit, this appears most unlikely given the barrierless addition of CN to the terminal C1 carbon of HC1C2C3N (see Table 2) and the exothermic nature of the product channel involving H-elimination from that same site. Reaction R1 is included in models of the atmosphere of Titan by Wilson and Atreya, 48 Lavvas et al., 49 and Krasnopolsky,50 with a temperature-independent rate coef-

[(1.97 × 10−8)T −1.51 exp( −3.24/T ) + (4.85 × 10−13) T 0.563 exp(17.6/T )] cm 3 molecule−1 s−1

where T is in K. The three lowest inner transition state vibrational frequencies are 35, 53, and 72 cm−1. It is particularly difficult to obtain 12161



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ficient equal to the value measured at room temperature by Halpern et al.10 (1.7 × 10−11 cm3 s−1). C4N2 has been observed in the condensed phase in Titan’s atmosphere near the North Pole by its 478 cm−1 ν8 band infrared emission detected by the Voyager 1 mission.51−53 Various models for the formation of C4N2 in Titan’s atmosphere have been proposed. Yung in his 1987 update54 of his 1984 model55 suggests that C4N2 may be formed either by reaction R1 (using an estimated rate coefficient of 1 × 10−11 cm3 s−1) or by the disproportionation reaction

positive barriers, which would result in their rate coefficients falling to negligibly small values at the temperature of dense interstellar clouds. Reaction R1 can therefore be considered within the general polymerization-type scheme of reactions P1 to P4 as a chain termination reaction, which reduces somewhat the overall efficiency of the scheme for cyanopolyyne synthesis and growth.

6. SUMMARY AND CONCLUSIONS We have shown experimentally that the reaction of CN radicals with HC3N is barrierless and possesses a rate coefficient that increases rapidly below room temperature. A fully ab initio implementation of a two transition state model, employing variational TST predictions for each of the bottlenecks, yields predictions for the absolute value and temperature dependence of the rate coefficients that are in satisfactory agreement with the experimental measurements over the entire temperature range from 22296 K. The kinetics measurements were performed using the CRESU technique both in its traditional continuous flow version and for the first time using a new, pulsed version. The excellent agreement between these two measurements demonstrates the utility and performance of the new pulsed CRESU.

CHCN + CHCN → C4N2 + H 2 Δr H ⊖ = −102.0 kcal mol−1

(R2)

where the enthalpy of reaction is as quoted by Yung. Wilson and Atreya48 state that reaction R2 in combination with N2 photolysis to yield N(2D) and subsequent reaction of N(2D) with C2H2 is responsible for 98% of C4N2 production in Titan’s atmosphere. Lavvas et al.49 incorporate also the possibility of C4N2 generation by the reaction R3 (following Osamura and Petrie56): C3N + HCN → C4 N2 + H 2

(R3)

■

but state that both reactions R3 and R1 have only a minor contribution to the overall dicyanoacetylene production based on their calculations. However, Osamura and Petrie’s ab initio quantum chemical calculations56 indicate that reaction R2 is very unlikely to play a significant role in C4N2 production in Titan’s atmosphere owing to the high reactivity of the CHCN radical with abundant radicals such as CH3 via barrierless reactions. In addition, our new measurements indicate, for example, that at a temperature of 100 K corresponding to Titan’s lower stratosphere7 the rate coefficient for reaction R1 is more than twice the value used in the models. It would appear likely, therefore, that reaction R1 plays a more important role in C4N2 production than previously thought. The role of reaction R3 and the analogous reaction involving HNC (which has also recently been detected in Titan’s atmosphere57) remains unclear as no kinetics studies on the reactivity of the C3N radical exist in the literature to date. We have recently embarked on an investigation of C3N kinetics at low temperatures. Reaction R1 is also likely to be of importance for interstellar and circumstellar chemistry. HC3N is widely observed in both galactic58 and extragalactic59 sources. At the low temperatures of dense interstellar clouds (∼10 K), the fit to our measurements predicts a rate coefficient of (1.75 ± 0.19) × 10−10 cm3 molecule−1 s−1. This can be compared to the recommendation of Wakelam et al.60 of 3.5 × 10−10 cm3 molecule−1 s−1 for interstellar chemical modeling. While somewhat less rapid, these new measurements confirm the rapidity of this reaction at very low temperatures and its importance for interstellar chemistry. C4N2 is no doubt present in interstellar and circumstellar environments as a product of this fast neutral−neutral reaction but is difficult to detect as it possesses no dipole moment. Further reaction of C4N2 with C2H or CN is unlikely: Seki et al.61 measured a relatively slow rate coefficient of (5.4 ± 0.2) × 10−13 cm3 molecule−1 s−1 for the CN + C4N2 reaction at room temperature, and we have performed preliminary quantum chemical calculations at the same level as those performed for CN + HC3N, which indicate that both reactions possess

AUTHOR INFORMATION

Corresponding Author

*(I.R.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We are grateful to Daniel Travers, Jonathan Courbe, Ewen Gallou, and Jacques Sorieux for technical support. We acknowledge support from the French Centre National de la Recherche Scientifique (CNRS) via the Institut National des Sciences de l’Univers (INSU) Programme National de Physique et Chimie du Milieu Interstellaire and the Programme National de Planétologie. We are also grateful to the Centre National d’Etudes Spatiales (CNES) for support. This project received a grant from the European University of Brittany (UEB) and was partially supported with funds from the European Regional Development Fund. The work at Argonne was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under DOE Contract Number DEAC02-06CH11357.

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Low Temperature Rate Coefficients for the Reaction CN + HC3N - The

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