On the mechanism of the HCCO + O2 reaction: Probing multiple pathways to a single product channel

We explore the mechanism of the HCCO + O2 reaction using time-resolved Fourier transform spectroscopy.

Utilizing an isotopically labeled reactant (18O2) and state-selective product detection, we determine the relative flux through different paths on the potential energy surface leading to a single asymptote: H + CO + CO2.

In the labeled reaction, the dominant isotopic products are C18O and 16OC18O. Combined with data from the corresponding reaction in natural isotopic abundance, these results show that at least 85% of the reactive flux passes through a four-membered OCCO ring intermediate.

An alternative reaction path through an energetically allowed three-membered COO ring intermediate represents less than 15% of the total reactive flux.

The average energy deposited in vibration of CO and CO2 is in reasonable agreement with a statistical model using the separate statistical ensembles method.


The measurement of total rate coefficients, product branching ratios, and product energy distributions are common methods in the elucidation of reaction mechanisms.

Typically, each product branching ratio is interpreted as a measurement of the flux through one exit channel of the reaction.

However, it is possible that two energetically feasible paths on the potential energy surface (PES) lead to a single product channel.

Measuring the contribution of each allowed reaction path toward a given exit channel tests our understanding of both the PES itself, and the calculations carried out on that surface to predict kinetics and dynamics.

In such cases it is usually quite difficult, if not impossible, to experimentally determine the contributions of these multiple reaction paths because they produce identical products.

It is sometimes possible to measure contributions from multiple pathways if energy partitioning in a product molecule depends strongly on the different pathways, but this method may only be viable for the simplest cases.1–3

Isotopic labeling of reactants combined with isotope-specific detection of products offers the possibility of probing contributions of individual reaction paths in addition to more commonly measured product branching ratios.

In this paper, we use this concept to interrogate reaction paths in the HCCO + O2 reaction.

The ketenyl radical (HCCO) is a key intermediate in acetylene oxidation chemistry and consequently an important species in combustion of all hydrocarbons.4–7

HCCO is formed primarily via the reaction of C2H2 + O C2H2 + O(3P) → HCCO + H ΔH0 = −19.6 kcal mol−1,8,9→CH2 + CO ΔH0 = −47.9 kcal mol−1.

Recent measurements of this reaction agree that HCCO + H is the dominant channel at room temperature.10–13

Experimental values of k1a/k1 range from .08510

(285 K), .08311

(290 K), .08013

(900–1200 K) to .06412

(1500–2000 K), while a theoretical calculation predicts a k1a/k1 ratio of 0.7,14 with little temperature or pressure dependence.

The value of this branching ratio is critical in determining the mechanism behind “prompt” CO2 formation in acetylene oxidation.

Prompt CO2, that is, the formation of CO2 with the same time constant as the partially oxidized species CO, was first observed in Kistiakowsky's group in the 1960s.15–18

Eberius et al. observed further evidence of prompt CO2 from measurements in lean C2H2/O2 flames.19

Modeling results from Miller et al20. successfully reproduced these experimental measurements under the assumption that CH2 + CO is the dominant product channel of reaction (1).

However, in light of newer experimental evidence that HCCO + H is the major product channel of reaction (1), Klippenstein, Miller, and Harding21 recently proposed a new model for prompt CO2 formation that centers on oxidation of HCCO HCCO + O2 → H + CO + CO2 ΔH0 = −110.4 kcal mol−1,→OCHCO + O ΔH0 = −1.3 kcal mol−1,→OH + CO + CO ΔH0 = −86.0 kcal mol−122.There are four measurements of the total rate coefficient for this reaction.23–26

Peeters et al11. have suggested that the title reaction occurs though channel (2), while Murray et al25. presented tentative evidence that channel (4) is the major product channel.

Using variational transition state theory master equation calculations and direct trajectory simulations, Klippenstein et al21. predicted that reaction (2) is the dominant product channel of the title reaction for a temperature range of 300–2500 K and pressures up to 100 atm.

Shortly thereafter, Osborn directly observed the HCCO reactant and the CO and CO2 products from the HCCO + O2 reaction using time-resolved Fourier transform emission spectroscopy.27

The emission spectra indicated that the nascent CO and CO2 products are highly internally excited.

No emission from the OH radical was observable, implying that reaction (4) is not a major product channel.

By comparison with a reference reaction that produces OH, the author concluded that the OH + CO + CO channel represents at most 10% of the reaction products27 at 293 K. These results are in agreement with the detailed calculations of Klippenstein et al., which predict that channels (3) and (4) are negligible at room temperature, but may make a small contribution at higher temperatures.

A diagram of the PES for this reaction is presented in Fig. 1.

It is important to distinguish between product channels (2)–(4) and reaction paths (A)–(F) on the PES.

There are three reaction paths (A, C, and D) that lead to H + CO + CO2 products.

These paths involve either a four-membered OCCO ring (III) or a three-membered OCO ring (II) as reaction intermediates.

Similarly, there are two reaction paths (B and F) leading to OH + CO + CO.

Measuring the relative flux on these reaction paths through these intermediates is the focus of this paper.

Isotopic labeling has been widely applied in various fields of chemistry to determine the properties of chemical compounds and their origins and evolutions in reactions.28

This technique can provide important insights into reaction mechanisms and dynamics,29–32 where the same products may arise from several different pathways, although such studies are still scarce.

In order to further elucidate the reaction mechanism of HCCO + O2, we have studied this reaction comparing 18O2 with 16O2 reactants using time-resolved Fourier transform spectroscopy (TR-FTS).

As shown in Fig. 1, products arising from three-membered or four-membered ring intermediates are isotopically distinguishable.

All the possible isotopic variants of CO and CO2 can be easily separated by rotationally-resolved infrared spectroscopy.

The emission spectra of the isotopically labeled products provide a direct measurement of the reactive flux through different reaction pathways.

The vibrational distributions of the products from the emission spectra allow additional insight into the reaction dynamics.


A detailed description of the experimental apparatus has been published previously.27,33

In short, helium is bubbled through a 273 K sample of ethyl ethynyl ether (HCCOC2H5) at 60 sccm.

This flow is combined with O2 (100 sccm) and delivered to a Teflon-lined stainless steel flow cell through a 1.5 cm diameter Pyrex tube.

Ethyl ethynyl ether is photolyzed at 193 nm to produce HCCO + C2H5 with near unit quantum yield.34

The 193 nm photons from an unfocused ArF excimer laser are introduced into the cell about 1 cm below the gas mixture entrance.

Typical laser pulsewidth is 20 ns with a fluence of 24–30 mJ cm−2 pulse−1 at a 50 Hz repetition rate.

Helium (100 sccm) is injected adjacent to the laser windows to minimize chemical deposition on the windows' surfaces.

The pressure of the cell is measured by a capacitance manometer, and maintained at 1.1 Torr through a closed-loop feedback valve throttling the pump.

In order to compare the 16O2 and 18O2 results without variations from long term laser power drift, back to back experiments are performed with either 16O2 or 18O2 flow under the same conditions.

The gas manifold is back filled with helium and pumped out several times to reduce cross contamination before changing O2 isotopes.

The absorption cross section of ethyl ethynyl ether is 7 × 10−18 cm2 molecule−1 at 193 nm.

From the flow rates of different gases, the total pressure of the cell and the absorption cross section of ethyl ethynyl ether at 193 nm, we estimate [HCCO]0 ≅ 8 × 1013 molecules cm−3.

The O2 concentration is fixed at 1.26 × 1016 molecules cm−3, ensuring pseudo-first-order reaction conditions and minimizing secondary reactions of HCCO.

Spectra taken without O2 present have an equal flow of helium substituted for O2 in order to maintain the same sample refreshing rate in the flow cell.

Time-resolved infrared emission is collected by Welsh collection optics,35 made from a pair of 10 cm diameter silver-coated spherical mirrors.

The emission is sent into an evacuated Fourier transform spectrometer (Bruker IFS 66v/S) through a KBr window and focused onto a liquid nitrogen cooled InSb photodiode.

The signal is amplified and digitized by a 16-bit 200 kS s−1 digitizer.

The Fourier spectrometer operates in step-scan mode.36

Time traces of the emission signal are collected and averaged over four laser shots at each mirror position (∼10 000 mirror positions for a 0.115 cm−1 resolution spectrum from 1800 to 2400 cm−1).

The time-resolved interferograms at 5 μs intervals are later extracted from these traces and Fourier transformed into time-resolved spectra.

Data collection begins 20–25 μs prior to the photolysis laser pulse to provide a background noise measurement and a clear reaction starting point (t = 0).

Helium (99.999% Matheson), 16O2 (99.995% Matheson, natural isotopic abundance assumed: 99.76% 16O2, 0.04% 17O2, 0.20% 18O2) and 18O2 (isotopic purity 99%, Isotek) gases are used without further purification.

Unfortunately, the high cost of 18O2 severely limited the amount of signal averaging possible in these experiments, resulting in lower signal-to-noise ratios than we would normally accept.

The limited supply of 18O2 also forced us to use a slower gas flow rate than previously utilized.27

The flow rate still ensures complete flushing of the laser interaction region between laser shots.

However, the cold gas filter effect (absorption of emission by ground state stable molecules) may perturb the populations slightly since the optical path of the Welch collection optics covers a large volume of the cell in addition to the laser interaction region.

Ethyl ethynyl ether is obtained from Aldrich as a 40% solution in hexane and used without further purification.

Hexane has a negligible absorption cross-section at 193 nm, and therefore does not affect the radical production method.

Note that the C2H5 cofragment produced by the photolysis laser will react with O2, but does not produce CO or CO2, and hence does not affect the present measurements37.

Results and analysis

HCCO radicals produced from ethyl ethynyl ether photodissociation at 193 nm are internally excited and emit strongly in the 1800–2040 cm−1 region.27

This emission arises from the Δυ2 = −1 asymmetric stretch bands of HCCO.38

Unfortunately, HCCO absorbs very strongly at the photolysis wavelength (193 nm), dissociating to produce CH and vibrationally excited CO.39

The infrared emission from HCCO and this photolytically-produced CO overlap with the emission produced by products of the HCCO + O2 reaction.

Fortunately, CO from HCCO photodissociation can be easily removed by subtracting spectra taken with and without O2 present.

We observe that excited HCCO radicals are quenched in less than 15 μs, and that the quenching rate of HCCO is independent of O2 and He concentration, indicating that the excited HCCO radicals are mainly quenched by hexane and/or ethyl ethynyl ether under the present experimental conditions.

Furthermore, vibrational relaxation of CO by O2 and He is very slow.

Therefore, the background subtraction procedure is expected to completely remove the emission from the excited HCCO and photolytically-produced CO without introducing any bias to the signals from the HCCO + O2 reaction.

All spectra are background subtracted using this method.

Because CH radicals are also produced in the photodissociation of HCCO, it is important to consider their effect on the system.

Although CH does react with O2, producing both CO and CO2 with branching ratios of 0.5 and 0.3 respectively,40 no evidence has been observed that the CH + O2 reaction plays a significant role in CO and CO2 production in the current experiments.27

Specifically, the rate coefficient for CH + O2 at 300 K is 4.7 × 10−11 cm3 molecule−1 s−1,41 corresponding to a rise time of ∼2 μs for products from this reaction at the O2 concentrations in this experiment.

No production of CO or CO2 is observed on this timescale.

Instead, it is likely that most CH radicals react with ethyl ethynyl ether and/or hexane.

The reactions of CH with large hydrocarbons are extremely rapidly (1–2 orders of magnitude faster than the CH + O2 reaction at room temperature)42 and these reactions are unlikely to produce CO or CO2.

In the HCCO + O2 reaction, CO and CO2 are formed with significant vibrational excitation, such that their spectra overlap.27

Efficient cooling of CO2, by vibrational energy transfer to the bath gas, causes its spectrum to blue shift until at t = 300 μs it no longer overlaps the CO transitions.

The HCCO + O2 reaction has a half-life time of ∼80 μs24–26 under the current experimental conditions.

Therefore, at t = 300 μs the reaction is essentially complete.

To simplify quantification of the different isotopic products, we analyze spectra at this long delay time.

Note that by observing both CO and CO2, we obtain two independent measurements of 18O positions in the reaction products.

Emission spectra of the CO product from the HCCO + 16O2 and HCCO + 18O2 reactions at t = 300 μs are shown in Figs. 2 and 3 respectively.

In both figures the upper panels show the experimental data along with a non-linear least squares fit33 and residuals of emission intensity.

The lower panels show a narrower wavelength region to clarify the spectroscopic differences between C16O and C18O and the agreement between the experimental data and the fits.

When we fit the emission spectra allowing contributions from both CO isotopes, we find the only detectable carbon monoxide products of HCCO + 16O2 and HCCO + 18O2 are C16O and C18O respectively.

An upper limit of the branching ratio of C16O in the HCCO + 18O2 reaction will be given later based on the signal-to-noise ratio of the data.

The validity of the background subtraction method is verified in the case of the HCCO + 18O2 reaction, where the entire C16O signal is removed upon background subtraction, implying that all C16O signals in the raw data arise from HCCO photodissociation.

The vibrational distributions of CO derived from the fitting are shown in Fig. 4.

The emission spectra of CO2 from the HCCO + 16O2 and HCCO + 18O2 reactions are shown in Figs. 5–7.

Fig. 5 shows spectra acquired early in the reaction (t = 25 μs) that do not show any resolved rotational lines, but provide a good picture of the nascent vibrational energy of the CO2 product.

The contributions from CO have been removed from Fig. 5 by a procedure described below.

At t = 300 μs, CO2 has cooled sufficiently that few vibrational bands are populated, and the emission bands are rotationally resolved, as shown in Figs. 6 and 7.

Rotational resolution is critical in determining the relative abundance of each CO2 isotope.

Only 16OC16O emission is seen in the natural abundance case, and only 16OC18O emission in the labeled reaction.

No emission from 18OC18O is observed.

Quantitative measurement of isotope ratios

The nonlinear least-squares fitting procedure for CO has been described in detail previously.33

Transition energies are calculated from the spectroscopic constants for both C16O and C18O.43

Initially we fit spectra at t = 300 μs, where CO2 emission does not overlap CO emission.

Rotational relaxation of CO is extremely fast and is expected to reach equilibrium in less than 1 μs under the current experimental conditions.44

At t ≥ 5 μs, the rotational distribution for each vibrational band does in fact fit a rotational Boltzmann distribution.

The population of each vibrational level is allowed to vary independently during the nonlinear least-squares fitting to obtain the best fit to each experimental spectrum.

Either a fixed rotational temperature of 330 K for all vibrational bands is used, or the rotational temperature for each individual vibrational state is allowed to vary during the fitting procedure.

The average fitted rotational temperature is 330 ± 50 K, and the quality of the fits is unchanged if the rotational temperature is fixed at this value.

This rotational temperature is slightly higher than the ambient room temperature, which is expected considering the energy deposited in the system by the laser and the heat of reaction.

Considering the enthalpy change (ΔH =  − D0(HCCO—C2H5) + |ΔH0(ch.

2)|) along with the heat capacities and mole fractions of the major species, we calculate a temperature increase of 25–35 K, depending on the value assumed for the heat capacity of HCCOC2H5.

This temperature change is in good agreement with the spectroscopic rotational temperature of CO derived from the fitting.

Because C16O is not observed in the HCCO + 18O2 reaction, we evaluate the upper limit of C16O formation with an analysis similar to the one used for OH yield estimation.27

The absorption intensities of the υ′ = 1 ← υ″ = 0 transition of C16O and C18O show that the two isotopes have essentially equal Einstein A coefficients.45

Therefore the emission intensity of the two CO isotopes should be proportional to the absolute number densities of the emitting species.

Because the vibrational distributions of C16O and C18O can be approximately described by Boltzmann distributions with similar vibrational temperatures, the emission intensities are expected to be proportional to the total CO number density, including the ground vibrational state.

In the present experiments, the product of vibrational state population with the Einstein A coefficient is largest for the υ′ = 2 band, making it the most sensitive transition for CO detection.

Beginning with the best-fit population distribution (which contains only C18O), we manually increase the population of C16O in the spectral simulation until several peaks originating in υ′ = 2 can be distinguished from the background.

This analysis provides an upper limit of [C16O]/[C18O] < 0.16 in the HCCO + 18O2 reaction.

While emission from CO is rotationally resolved at all reaction times, CO2 emission is rotationally resolved only at later times.

The fitting of CO2 emission spectra is more complicated because of the presence of three vibrational modes, vibrational angular momentum, and the effect of nuclear spin.

Given the 1800–2400 cm−1 spectral window observed in these experiments, only transitions in the antisymmetric stretch bands, i.e. (mnlp) → (mnlp − 1), need be considered.

The spectroscopic constants for C16O2, 16OC18O and 18OC18O are adopted from refs. 46 and 47.

The fitting of CO2 spectra at long delay times (e.g., 300 μs) indicates that only the lowest few vibrational states are populated.

The magnified regions in Figs. 6 and 7 clearly show that the different isotopes of CO2 can be resolved.

The only CO2 isotope observed in HCCO + 18O2 is 16OC18O. Our detection sensitivity for CO2 is lower than for CO because so many more initial states are populated in the case of the triatomic molecule.

Nevertheless, a similar analysis to that described above for CO indicates a limit of [18OC18O]/[16OC18O] < 0.30.

This value is likely significantly overestimated due to the poor signal-to-noise ratio of the CO2 emission spectra.

Nascent product state distributions

In order to estimate the nascent product vibrational state distributions, the overlapping emission of CO and CO2 at early times should ideally be separated.

However, a good approximation to the nascent CO product state distribution can be measured at t = 300 μs because CO cools very slowly due to collisions.

Using a process described below, we can also fit the CO distribution at early times when interference from CO2 is substantial.

The resulting CO vibrational distributions, shown in Fig. 4, can for simplicity be fit to a Boltzmann distribution, yielding temperatures of 8600 ± 900 K and 9500 ± 1000 K for C16O and C18O respectively.

The vibrational distributions of CO are similar for both C16O and C18O. The distributions on a Boltzmann plot are somewhat non-linear, with greater population in higher vibrational levels than a true vibrational temperature would allow.

Note that the early time C16O distribution in Fig. 4 appears quite linear, while the population of higher vibrational levels of C16O seems to increase by t = 300 μs.

Most of this variation can be attributed to the less than optimal signal-to-noise ratio of the data.

As discussed above, the high cost of 18O2 limited signal averaging in the present experiments.

To facilitate comparisons between isotopes, the reaction using 16O2 is executed with the same limited averaging times.

Earlier data on the HCCO + 16O2 reaction,27 utilizing more signal averaging, provide a more precise representation of the C16O vibrational distribution, and display curvature in the Boltzmann plot that is intermediate between all the data presented in Fig. 4.

While this distribution could be described as bimodal, we hesitate to draw conclusions based on bimodality without substantially more data collection over a range of total pressures.

It is important to note that curvature in the vibrational distribution has no impact on the isotope ratios discussed in section IIIA.

Since the Boltzmann vibrational temperatures for the two CO isotopes are within mutual uncertainty, we conclude that different oxygen isotopes have little effect on the vibrational distribution of CO. The derived vibrational temperatures are consistent with the previous result of 8500 ± 800 K.27

The much more rapid vibrational energy transfer from CO2 requires that its nascent distribution be measured at the earliest reaction time with sufficient signal (t = 25 μs in this case).

To meaningfully fit the broad CO2 emission at this early time requires both a robust method for removing the sharp features due to CO, and a spectroscopic model of highly excited CO2.

To remove the early-time CO spectral features, we first fit one CO spectrum at t = 300 μs, where CO2 does not interfere.

We then separate all time-resolved spectra into two regions by determining where CO could contribute to the total emission (i.e., near a known CO line) and where the emission must be solely due to CO2.

Explicitly, these “separated” experimental spectra can be represented by the following equations, where I(,t) is the emission intensity as a function of wavenumber and δ is the experimental root-mean-square (RMS) noise: Eqn. (6) retains all wavenumbers in the spectra where CO emission intensity is expected to be lower than the RMS noise.

Therefore, contains emission solely from CO2, while has contributions from both CO and CO2.

The small gaps in are bridged using linear interpolation to obtain a continuous CO2 emission spectrum for each delay time in the data sets.

This method is attractive because it does not require any a priori assumption as to the time-dependent shape of the broad CO2 emission.

Because only the accurately known rovibrational line positions of CO are involved in this treatment, we obtain the least biased separation of CO and CO2 emissions.

Because the CO2 emission spectrum at short delay times is not rotationally resolved, our spectroscopic model uses a resolution of 4 cm−1.

We assume a Boltzmann rotational distribution at 330 K and a Boltzmann vibrational distribution.

While the nascent CO2 vibrational state distribution may be far from statistical, fast internal vibrational redistribution (IVR) of CO2, due to Fermi resonances and high vibrational state density,48 is expected to redistribute the vibrational energy statistically among the three vibrational modes on a time scale less than our temporal resolution.

The fit has two parameters: vibrational temperature and total intensity.

The early spectra of CO2 indicate that vibrational states as high as υ3 ∼ 18 can contribute to the wavelength region where we observe emission.

Because of the anharmonicity and rotation-vibration interaction constants related to the υ3 mode, the population of υ1 and υ2 (symmetric stretch and bend modes) cannot be neglected.

The maximum quantum numbers for the υ1, υ2, and υ3 modes in the fit are 30, 65, and 25 respectively.

As in the rotationally resolved fitting, only (mnlp) → (mnlp − 1) transitions are included.

Emission spectra of CO2 at t = 25–185 μs are fit using the low-resolution model.

Fig. 5 shows representative experimental spectra and corresponding fits.

The residuals in Figs. 5–7 are generally comparable to the baseline noise away from spectral features.

The increased residuals in the lower panel of Fig. 5 may indicate that our spectroscopic model of hot CO2 is too simplistic, but we believe the data do not justify a more complex model.

The temporal evolution of CO2 vibrational temperature is well fit by a single exponential curve as shown in Fig. 8.

The vibrational temperatures obtained are 5900 ± 500 K and 6300 ± 500 K for nascent C16O2 and 16OC18O respectively by extrapolating the exponential fitting to t = 0.


Reaction paths and their isotopic signatures

The possible outcomes of the HCCO + 18O2 labeled reaction can be considered with reference to Fig. 1 and the work of Klippenstein et al.21

Kinetic isotope effects are expected to be negligible due to the small mass difference between the two oxygen isotopes, and the large exothermicity of the observed product channels.

In this case the isotopic labeling provides a means to distinguish different reaction paths without significantly affecting the reactivity of the system.

As O2 approaches HCCO, a barrier at saddle point 1 (sp1) arises because the addition of O2 breaks the resonance stabilization in HCCO.

The initial adduct (I) can dissociate along two different reaction coordinates to yield H(18O)CC16O + 18O (path E) or, with an energetically expensive H atom transfer, 18OH + C16O + C18O (path F).

Theoretical calculations indicate that these two pathways are of very minor importance at room temperature due to the high potential energy barriers sp2 and sp.321

In light of these calculations, we expect that only paths A–D, which yield product channels 2 and 4, have the possibility to contribute at room temperature.

The unpaired electron on oxygen in the initial adduct (I) may attack either carbon atom, forming a three-member (II) or resonantly stabilized four-member (III) ring intermediate.

The barrier to ring closing is higher for (II) than for (III), but the formation of a three-member ring involves less of an entropy penalty.

It is therefore not obvious which pathway will be more favorable.

The dissociation of the three-member ring intermediate (II) occurs through C–C bond cleavage along path D. HC18O2 (IV) is at most only marginally bound,49 and will dissociate giving the final products H + 18OC18O + C16O.

In comparison, decomposition of the four-member ring intermediate may proceed through three different paths (A–C).

In all cases, O–O bond fission occurs first over sp5, leading to an 18OCHC(18O)16O complex (the flat region near −94 kcal mol−1).

The barrier to C–C bond fission in this complex is essentially zero, and it may dissociate directly via path A to HC18O + 16OC18O. HC18O will almost certainly dissociate over sp8 due to the great exothermicity of this product channel, yielding finally H + C18O + 16OC18O. However, the direct dynamics classical trajectory calculations of ref. 21. provide evidence of two additional paths for decomposition of III.

Following O–O bond fission over sp5, the hydrogen atom may transfer to the unpaired electron on the 16O atom.

If the C–C bond lives long enough for internal rotation about this bond, the H atom could also transfer to the 18O atom in the CO2 moiety.

In either case, after the H transfer the ensuing C–C bond fission leads to HOCO + CO (V), with isotope labels shown in Fig. 1.

The HOCO radical will almost certainly dissociate because of the great exothermicity of the reaction.

This dissociation, and the corresponding reaction OH + CO, has been studied extensively.50,51

There are two possible dissociation channels of HOCO: OH + CO and H + CO2.

The OH + CO → HOCO reaction has a loose transition state, and may have a slight entrance barrier, while H + CO2 → HOCO has a tight transition state.

High level ab initio calculations have located saddle points on the HOCO → CO2 + H potential, which are 1.5 and 7.8 kcal mol−1 above the HO + CO asymptote for cis and trans HOCO respectively.52

Variational transition state theory rate coefficient calculations53 predict that these two dissociation channels are almost equally important with 1 kcal mol−1 energy above the OH + CO asymptote.

However, the OH + CO channel quickly becomes the dominant reaction channel and remains about an order of magnitude faster than H + CO2 as energy increases.

Since the reaction of HCCO + O2 is highly exothermic, we expect that H + CO2 would be a minor channel of HOCO dissociation.

Note, however, that path C cannot be distinguished from path A using the present isotopic labels.

Therefore, if we ignore the possibility of internal rotation about the C–C bond as (III) dissociates, the resulting isotopic intermediate is H16OC18O + C18O, which leads to 16OH + C18O + C18O. At the other limit, if rotation about the C–C bond were facile as (III) dissociates, the final products would be a mixture of 18OH + C16O + C18O and 16OH + C18O + C18O with a relative ratio of 1∶1, as indicated in Fig. 1.

Contributions of each reaction path

Given these possible paths on the potential energy surface, we now evaluate the constraints placed on the flux through these paths by the experimental data.

Assuming that paths C, E, and F are negligible, as discussed above, we can draw the following connections between the product rate coefficients and the path-specific rate coefficients for this reaction: k2 = kA + kD,k4 = kB,ktot = k2 + k4 = kA + kD + kB, where ktot is the total rate coefficient.

Note that k2, the rate coefficient for H + CO + CO2 production, may contain contributions from both the three- and four-member ring intermediates.

The data place three constraints on these equations: two isotope ratios measured in this work, [C16O]/[C18O] < 0.16 and [18OC18O]/[16OC18O] < 0.30, and the limit on total OH production (kB/ktot) < 0.10 from .ref. 27

The quantities we wish to obtain are the fractions of flux through the three- and four-member ring pathways: Φ3-mem = (kD/ktot) and Φ4-mem = 1 − Φ3-mem.

The CO2 isotopic ratio yields the most straightforward analysis.

Because only paths A and D produce CO2, we have [18OC18O]/[16OC18O] = kD/kA < 0.3, and therefore kD/(kA + kD) < 0.23.

In the limit that 100% of the reaction produces CO2 (i.e., (kB/ktot) = 0) we have simply Φ3-mem = kD/(kA + kD) < 0.23.

At the other limit, if 90% of the total reaction produces CO2 (i.e., (kB/ktot) = 0.1) the flux through the three-member ring becomes The conservative estimate based on the CO2 isotope ratio is therefore Φ3-mem < 0.23.

An evaluation based on the CO isotope ratios is somewhat more complicated because every possibility produces either one or two CO molecules.

If internal rotation of the CO2 moiety about the C–C bond as (III) dissociates is slow, the H atom can only transfer to the 16O atom along path B, and we have In the limit that k4 = kB = 0, we obtain Φ3-mem = (kD/ktot) < 0.14, while for (kB/ktot) = 0.1 the result increases slightly to Φ3-mem = (kD/ktot) < 0.15.

Finally, if internal rotation of the CO2 moiety about the C–C bond as (III) dissociates is fast, the H atom may transfer with equal probability to 16O or 18O along path B. In this case 25% of the CO produced along path B is C16O, and we have As before, in the limit that k4 = kB = 0, we obtain Φ3-mem = (kD/ktot) < 0.14, but in contrast, for (kB/ktot) = 0.1 the result decreases to Φ3-mem = (kD/ktot) < 0.10.

Overall, the conservative result from the CO spectra is Φ3-mem < 0.15, which is somewhat more restrictive than the result obtained from the CO2 spectra, as expected from their worse signal-to-noise ratio.

In summary, we find that at least 85% of the total reactive flux passes through the four-member ring intermediate.

Path A is the dominant reaction path, and H atom transfer during dissociation of (III) plays at most a minor role.

These results agree qualitatively with the rate constants and the 209 direct dynamic trajectories calculated by Klippenstein et al.21

Our reaction path analysis depends strongly on the signal-to-noise ratio of the data.

The accuracy of our derived limits could be improved with better quality data, which is limited primarily by the cost of 18O2.

Vibrational energies compared with a statistical model

The vibrational temperatures of CO and CO2 extracted from the data are 9050 (average of C16O and C18O) and 6100 K (average of 16OC18O and 16OC16O) respectively, which correspond to average vibrational energies of 15.7 and 43.6 kcal mol−1 for CO and CO2 respectively.

We have modeled the energy partitioning in this channel using the separate statistical ensembles (SSE) method.54

The SSE model is a refined phase space theory (PST), in which the vibrational branching is defined early in the dissociation, and the coupling between vibrations is assumed to be small for the remainder of the dissociation process.

The rotational distributions are then statistically distributed using PST within each vibrational reservoir.

The SSE model is usually applied to unimolecular photodissociation in which the products have no recombination barrier.

In the present reaction, while the barriers to decomposition of the four-membered ring intermediate are small, the overall reaction is exothermic, in contrast to unimolecular dissociation.

Nevertheless, we have applied this model to the HCCO + O2 reaction because it is straightforward to implement and provides a first assessment of the degree to which the system behaves statistically.

In the HCCO + O2 reaction, the four-membered ring intermediate dissociation along path A involves two bond cleavages.

According to Klippenstein et al.'s calculation,21 the step-wise dissociation occurs with O–O bond fission prior to C–C bond fission.

The barrier height for O–O bond breaking (sp5) is less than 4 kcal mol−1 while there is no barrier for the subsequent C–C bond breaking.

Furthermore, the barrier to formation of the four-member ring intermediate (sp4) is even smaller than sp5.

While there is a small exit barrier (sp8) to dissociation of HCO,55 this barrier is also small compared to the available energy.

It is worth noting that a modified statistical model was required to describe HCO dissociation at low and intermediate energies above the dissociation threshold56 because its low density of states leads to slow IVR.57

However, these nonstatistical effects are expected to be less important at high HCO internal energy.

Because the excess reaction energy is significantly larger than all these barrier heights on the PES of the HCCO + O2 reaction, the SSE method may still be applicable for the four-membered ring intermediate decomposition and subsequent HCO dissociation.

In order to evaluate the CO vibrational energy distribution, a two-step reaction mechanism was assumed for the four-membered ring intermediate: dissociation to HCO + CO2 (VI), followed by HCO → H + CO.

The available energy for the first step is the energy difference between the HCCO + O2 reactants and HCO + CO2, 126.0 kcal mol−1.

The available energy for the second step is the internal energy of HCO minus the H—CO bond enthalpy.

The small exit barrier of HCO dissociation (sp8) is ignored in the SSE calculation.

For each HCO vibrational level, the corresponding CO vibrational state distribution is calculated.

The population of each vibrational state of CO is summed over all the possible HCO vibrational energies to obtain the final CO vibrational state distribution.

The vibrational frequencies for HCO are adopted from .ref. 58

The SSE method is only performed for 16O isotopes in the current study.

Since the model is only sensitive to the final product vibrational frequencies, and this frequency difference is small for 16O and 18O isotopes, the results of 18O isotopes are expected to be very similar to 16O.

The predicted average vibrational energies from the SSE method are 48.2 kcal mol−1 for CO2, and 15.8 kcal mol−1 for CO, respectively, in reasonable agreement with the experimental values.

The CO vibrational state distribution obtained from the SSE model is shown in Fig. 4.

The predicted product state distribution is in qualitative, but not quantitative agreement with experimental results.

One interpretation of the highly excited CO2 and CO vibrational state distributions observed in this reaction is that the large geometry changes between the four-membered ring intermediate and the separated products lead to significant Franck–Condon excitation of product vibrational modes.

However, the reasonable agreement between experiment and the SSE model implies that a statistical description is sufficient to explain the experimental results, due to the large exothermicity of the reaction and strong coupling between vibrational degrees of freedom as the intermediate dissociates.


We have studied the reaction HCCO + 18O2 using time-resolved Fourier spectroscopy.

The observed C18O and 16OC18O emission spectra indicate that the reaction occurs primarily through a four-membered ring intermediate.

Spectral fits yield the limits Φ3-mem < 15% and Φ4-mem > 85% for the total reactive flux through the two possible ring intermediates.

Hydrogen transfer during decomposition of the four-membered ring intermediate is a minor process.

The CO and CO2 products are found to be highly vibrationally excited with vibrational temperatures of 9050 ± 1400 K and 6100 ± 700 K respectively.

The average vibrational energy deposited in CO and CO2 is reasonably well predicted by the separate statistical ensembles (SSE) method, implying that statistical rather than dynamical effects dominate this reaction mechanism.