Research ArticleChemistry

Direct measurements of DOCO isomers in the kinetics of OD + CO

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Science Advances  12 Jan 2018:
Vol. 4, no. 1, eaao4777
DOI: 10.1126/sciadv.aao4777


Quantitative and mechanistically detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analog deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real time, the branching and isomerization kinetics and absolute yields of all species in the OD + CO reaction are quantified as a function of pressure and collision partner.


Fundamental understanding and control of bimolecular reactions have long been the primary motivations for the fields of chemical kinetics and dynamics. One approach has been to construct a detailed dynamical understanding from the bottom up, exemplified by the field of crossed molecular beam experiments, where reaction dynamics are dissected from single collision processes (1). For applications in combustion, atmospheric, and fundamental chemistry, a broader goal from these studies is the prediction of the rates and outcomes of reactions. This knowledge requires direct connection of reaction dynamics to molecular structure and detailed understanding on how the dynamics change during the chemical transformation from reactants to products. However, transitions from reactants to products in bimolecular reactions are often multistep because of the involvement of multiple reactive intermediates, transition states, and final product channels on a multidimensional potential energy surface (PES). These factors have limited experimental characterization of the underlying dynamics, and theoretical models are often required to assist with detailed mechanistic interpretation (24). It is thus of particular interest to develop new experimental approaches for the study of reaction kinetics and dynamics from real-time observation of individual elementary chemical reactions.

The reaction of hydroxyl (OH) with carbon monoxide (CO), Eq. 1, exemplifies such a system that has an intricate reaction mechanism governed by multiple bound states, both reactive and nonreactiveEmbedded Image(1)

The gas-phase kinetics of OH + CO has received considerable attention from both experimental and theoretical efforts due to its fundamental and practical importance in atmospheric and combustion chemistry (5). The observed rate coefficient, k1, displays strong pressure and non-Arrhenius temperature dependence, which is now understood to arise from the formation of the HOCO complex, with subsequent tunneling to the products H + CO2. Figure 1 shows the PES for the OH + CO reaction.

Fig. 1 The OH + CO reaction PES with energies in kilojoules per mole.

The colored PES in the background depicts the HOCO isomer potential energy wells along the H–O–C–O dihedral angle (parallel to page) and O–H bond length (perpendicular to page).

Over the past four decades, the HOCO formation mechanism had been derived from fits of the observed k1(P,T) to theoretical models (617). These studies led to the following proposed reaction mechanism for OH + CO, starting from the calculated asymptotic (stationary) states in Fig. 1Embedded Image(2)Embedded Image(3)Embedded Image(4)Embedded Image(5)

Reaction 1 initially produces energized HOCO*, which either back-reacts to OH + CO or proceeds to form H + CO2 (Eq. 2). In the presence of a buffer gas, M, HOCO* may be collisionally stabilized (Eq. 3). At low pressures, the overall reaction rate can be represented by an effective bimolecular rate coefficient, k1([M],T) = k1a([M],T) + k1b([M],T), where k1a and k1b describe the formation of stabilized HOCO and H + CO2, respectively.

HOCO exists as two geometrical isomers, trans-HOCO and cis-HOCO, with the latter being slightly less stable by 5 to 7 kJ mol−1 (18, 19). Current theory predicts that both isomers will be formed by stabilization upon associative recombination of OH + CO, with the trans-HOCO isomer favored. Calculations indicate that the barrier for isomerization (TS4; Fig. 1) is low, leading to rapid isomerization between the two isomers (Eq. 4). However, further reaction to products must proceed through the cis-HOCO isomer (Eq. 5), because the transition state to form H + CO2 products from trans-HOCO (TS3) is predicted to be much higher than that from cis-HOCO (TS2). The cis-isomer thus plays a critical role in the OH + CO reaction, and the isomerization dynamics determine product formation. Direct and simultaneous detection of reactant OH, intermediates cis-HOCO and trans-HOCO, and product H + CO2 and measurement of their time dependence in the same reaction environment would reveal the coupled dynamics of all participating species from beginning to end.

Recently, Bjork et al. (20) observed the deuterated analog trans-DOCO formed from the OD + CO reaction under thermal conditions, providing the first direct experimental confirmation of the HOCO mechanism; however, a full understanding of the reaction mechanism requires observing the cis-HOCO radical and the final products. Although the cis-HOCO radical has been detected using molecular or ion beams (19, 21, 22) and matrix (23, 24) techniques that can trap metastable species, it has not yet been observed in a thermal reaction environment as the product of OH + CO, leaving a substantial gap in our understanding of this reaction. Because experimental characterization of the OH + CO reaction kinetics is currently fragmented, the state of knowledge for the OH + CO mechanism continues to rely on theory (3, 6, 8, 18, 25).

We now report a direct observation and measurement of the deuterated analog cis-DOCO intermediate from the OD + CO reaction via time-resolved frequency comb spectroscopy, a technique for obtaining high-resolution, transient absorption spectra over a wide spectral range in the mid-infrared (IR) (λ = 3 to 5 μm) with microsecond time resolution (20, 2628). Using a room temperature flow cell, the OD + CO reaction is initiated at t = 0 by photodissociation of O3 in the presence of D2, CO, and N2 (total pressure range, 20 to 100 torr). From real-time measurements of the time-dependent populations of reactant OD, intermediates trans-DOCO and cis-DOCO, and product CO2 via their IR absorption spectral windows shown in Fig. 2, we disentangle the entire kinetic process by following this reaction step by step. We now have direct access to the reaction rate coefficients and branching yields of all chemically accessible product channels; to date, this provides the most comprehensive experimental observations of this multistep reaction.

Fig. 2 Spectroscopy of DOCO isomers.

(A) Full cis-DOCO spectrum (top). The data and simulation are given by positive and negative absorbances, respectively. The color codes are as follows: blue, cis-DO12CO; red, cis-DO13CO; green, OD; gray, D2O. For clarity, only the simulated cis-DO12CO and cis-DO13CO are shown for comparison with experimental results in the zoomed-in bottom panels, where the strongest Q branches are located. (B) Trans-DOCO spectrum (black). Simulated trans-DOCO (brown), OD (green), and D2O (gray) are shown as inverted absorbances. The detection spectral regions are 2400 to 2850 cm−1 (OD), 2450 to 2650 cm−1 (cis-DOCO) (A), 2640 to 2720 cm−1 (trans-DOCO) (B), and 2380 to 2445 cm−1 (CO2). Data in (A) and (B) were obtained by integrating from t = 0 to 200 μs at a 100-μs camera integration time.


Figure 2A shows the gas-phase spectrum of cis-DOCO in the OD stretch fundamental band, which has not been observed before this work. To confirm the identification of cis-DOCO, we performed additional experiments to obtain an isotopic substitution spectrum. The predominately b-type nature of the cis-DOCO OD stretch band gives rise to an observed progression of Q branches, each consisting of many unresolved individual rovibrational transitions, spaced approximately 7 cm−1 apart (table S1). By fitting the frequencies of these spectral features, the v = 1 band origin and A rotational constant for both 12C and 13C isotopologues of cis-DOCO are obtained. The predicted and measured spectroscopic constants for both 12C and 13C isotopologues of cis-DOCO are compiled in table S2. The measured isotopic shifts to these molecular constants are then compared to their respective ab initio values predicted using second-order vibrational perturbation theory (VPT2) at the CCSD(T)/ANO1 level (table S3). The agreement between the experimental and theoretical values provides conclusive evidence for the identification of cis-DOCO.

The time-dependent concentrations of OD, cis-DOCO, trans-DOCO (Fig. 2B), and CO2 are determined from the IR absorption signals; time traces at a single reaction condition are plotted in Fig. 3A. Although the reaction system is characterized by a complex set of primary and secondary reactions, as described in our earlier works (20, 28), we find that at early times (t < 200 μs), we can effectively model the time dependence including only formation, isomerization, and loss processes of DOCO isomers, represented by rate coefficients k1a,i([M],T), kiso,ij([M],T), and kloss,i (i,j = cis or trans), respectively, with the following rate equations (Eq. 6)Embedded Image(6)

Fig. 3 Time traces of reaction components and the formation rates for the sum of DOCO isomers.

(A) Time dependence of reactant OD (green circles), intermediates cis-DO12CO (blue squares) and trans-DOCO (brown diamonds), and product CO2 (purple triangles) obtained from fitting full experimental spectra for a sequence of time windows after the initiation of the reaction. Quantities in parenthesis are multiplicative factors used to scale the traces to fit on a single plot. The camera integration time is 20 μs for OD, cis-DOCO, and trans-DOCO and 50 μs for CO2. Each time point corresponds to ≈400 averaged spectra. The error bars are from uncertainties in the fit and the measured densities of the gases. The dashed and dotted lines are fits of eq. S4 for OD, Eq. 6 for trans- and cis-DOCO, and eq. S8 for CO2 using values measured from this work. (B) k1a,sum is plotted as a function of CO, whereas [N2] is held constant at 8.9 × 1017 molecules cm−3. (C) k1a,sum is plotted as a function of N2, whereas [CO] is held constant at 5.6 × 1017 molecules cm−3. In both plots, [D2] and [O3] are fixed at 1.4 × 1017 and 2 × 1015 molecules cm−3, respectively. The red dashed lines show the fits obtained from a multidimensional linear regression procedure described in the main text. Data in (B) and (C) were obtained at a 50-μs camera integration time. The error bars in (B) and (C) represent uncertainties from fits to Eqs. 8 and 9 and the measured densities of the gases.

The subscript t denotes time. The time-dependent [cis-DOCO]t and [trans-DOCO]t are denoted by [cis]t and [trans]t, respectively. kiso,ct([M],T) and kiso,tc([M],T) are the pressure-dependent effective isomerization rate coefficients for cistrans and transcis, respectively. kloss describes the decay of DOCO from a reaction with one or more species X, and [OD]t is the time-dependent concentration of OD in the ground vibrational state. We have previously characterized vibrationally excited OD populations and lifetimes at our experimental conditions; nonequilibrium effects introduce no more than a 10% error in our current measurements (20). We assume that the dissociation/tunneling of thermalized cis-DOCO to D + CO2, which proceeds over a high barrier (TS2), cannot compete with the other channels at these time scales.

Considering the possibility of substantial isomerization rates that may compete with the formation rate, we set out to perform experiments to disentangle their relative effects by varying the buffer gas species and its pressure. We sought to distinguish formation from isomerization by first determining the effective bimolecular formation and loss rate coefficients for the sum of DOCO isomers, k1a,sum([M],T) ≡ k1a,cis([M],T) + k1a,trans([M],T), and a similar expression for kloss,sum (Eq. 7)Embedded Image(7)where [DOCOsum] ≡ [trans] + [cis]. Using the total DOCO concentration eliminates the need to model isomerization in Eq. 6 (derived in section S2). In the low-pressure limit studied here, the DOCO formation rate obeys a termolecular rate law, in which M represents the buffer gas species (a third-body collider). In this reaction, M comprises all the high-density species present (N2, CO, D2, and O3).

The solution to Eq. 7 is a convolution of the DOCO loss term with [OD]t, given by the integral in Eq. 8 (u is a dummy variable). [CO] is in large excess and remains effectively constant throughout the reactionEmbedded Image(8)

The effective bimolecular rate coefficient k1a,sum([M],T) can be decomposed into three terms dependent on N2, CO, and D2 concentrationsEmbedded Image(9)where k1a,sum(CO), k1a,sum(N2), and k1a,sum(D2) are the termolecular rate coefficient dependence on M = CO, N2, and D2, respectively. k1a,sum(0) is an offset term that accounts for additional background species. O3 is not included in Eq. 9 because its concentration is smaller by a factor greater than 102 compared to the other buffer gas species. Its main contribution is to DOCO loss.

By simultaneously fitting [DOCOsum]t and [OD]t from data in Fig. 3A across varying [CO], [N2], and [D2], the effective bimolecular rate coefficients for the DOCOsum formation, k1a,sum, are obtained as follows. [OD]t are fit using empirically derived analytical functions (eq. S4). This spline interpolation procedure provides an analytical expression for [OD]t without making any assumptions about its formation or decay mechanisms. The observed [DOCOsum]t is then fit to Eq. 8, integrating the fitted [OD]t function over the time window of −25 μs (convoluted with the finite response time of the camera) to 200 μs. The fitted parameters in Eq. 8 are k1a,sum and rloss,sum; the latter is an effective first-order rate for the loss of DOCOsum.

DOCO must be lost by reaction with one or more species, which we define as X; then, rloss,sum = kloss,sum[X], where kloss,sum is a bimolecular rate coefficient. We hypothesized that X = O3, because O3 is the highest concentration candidate that is reactive with DOCO. To test this, rloss,sum is determined independently by measuring [cis]t and [trans]t while varying the density of O3; the results are shown in fig. S1. The observed loss rate is proportional to O3 and is invariant to [CO], [N2], and [D2], leading to an empirical bimolecular rate coefficient for DOCO loss to O3, kloss,sum = 2.5(6) × 10−11 cm3 molecules−1 s−1, from a global fit across all CO, N2, and D2 data sets. We conclude that X is predominantly O3. One possible outcome from the reaction of DOCO with O3 is to recycle OD, which, together with the reaction of D + O3 → OD + D, would lead to the quasi–steady state observed in [OD]t at long delay times (Fig. 3A). The direct measurement of [OD]t eliminates the need to explicitly treat the recycling in our analysis. Finally, because there is some O2 present in the O3 flow, some of the loss is due to reaction with O2, which will also appear to vary linearly with O3. Any contribution to rloss,sum from the reaction with O2 is likely to be minor, because [O2] << [O3], and in addition, the rate coefficient for DOCO + O2 is an order of magnitude lower than that for kloss,sum.

After establishing that rloss,sum is due to reaction with O3, we next determine the effective bimolecular rate coefficients, k1a,sum, to form DOCO from Eq. 8 for each buffer gas ([CO], [N2], and [D2]). The results from experiments varying each gas concentration independently while fixing [O3] = 2 × 1015 molecules cm−3 (rloss,sum = 5 × 104 s−1) are displayed as data points in Fig. 3 (B and C) and fig. S2, respectively.

Fits of k1a,sum reveal that, under our conditions, CO and N2 contribute to DOCO stabilization; there is no observable dependence on D2 over the limited pressure range studied. To account for all three species present in each experiment, we perform a multidimensional linear regression of the data in Fig. 3 (B and C) and fig. S2 (fitted bimolecular rate coefficients) to Eq. 9 to determine the termolecular rate coefficients k1a,sum(CO), k1a,sum(N2), and k1a,sum(D2), respectively. The linear fits are given as red dashed lines. In the varying CO experiment (Fig. 3B), a clear linear dependence is observed, indicating a termolecular dependence of k1a,sum on CO or k1a,sum(CO). The offset in the linear fit comes from the N2 termolecular dependence of k1a,sum or k1a,sum(N2). A similar linear dependence is seen for varying N2 (Fig. 3C), with the offset being the k1a(CO) component. The results obtained from the multidimensional linear regression are k1a,sum(CO) = Embedded Image cm6 molecules−2 s−1, k1a,sum(N2) = Embedded Image cm6 molecules−2 s−1, and k1a,sum(D2) = Embedded Image cm6 molecules−2 s−1. We observe an additional offset in the effective bimolecular rate constant, k1a,sum(0) = Embedded Image cm3 molecules−1 s−1. More than 80% of the offset term, k1a,sum(0), can be accounted for by a combination of the upper bound of k1a,sum(D2) and competition from DOCO loss processes (rloss,sum). The D2 concentrations are too low (<10% of total gas) to determine k1a,sum(D2) accurately. Discussions of all statistical and systematic error sources for k1a,sum are found in table S4.

Up to this point, we have considered only the formation kinetics of the two DOCO isomers together and thus could neglect cis/trans isomerization. To resolve the dynamical coupling of the isomer-specific formation and isomerization kinetics, we measure the time dependence of the [trans]/[cis] ratio at nine different partial pressures of CO. Figure 4A shows five representative experimental time traces of this ratio, which are offset vertically for reasons of clarity. The observed time evolution of the [trans]/[cis] ratio to a steady-state value for each trace indicates a transition between two distinct time regimes: the early-time DOCO formation (k1a) and subsequent relaxation by trans/cis isomerization (kiso).

Fig. 4 DOCO formation and isomerization kinetics.

(A) Ratio of [trans-DOCO] to [cis-DOCO] as a function of time for different CO concentrations. The CO concentrations are 5.6 × 1017, 6.0 × 1017, 6.4 × 1017, 6.7 × 1017, and 7.1 × 1017 molecules cm−3 for blue squares, red circles, black diamonds, cyan hexagons, and green triangles, respectively. For these experiments, [N2], [D2], and [O3] were fixed to 8.9 × 1017, 1.4 × 1017, and 2 × 1015 molecules cm−3, respectively. The arbitrary y-axis offsets of −5, −2.5, 0, +2.5, and +5, respectively, are added for ease of viewing. At high [CO] (>6.4 × 1017 molecules cm−3), all curves reach the same asymptotic value within experimental uncertainties. The dashed lines are fits of the rate equation model to the data. Data were obtained at a 20-μs camera integration time. The error bars represent uncertainties from the spectral fit and measured densities of gases. (B) Fitted isomerization rate coefficients for cistrans (Embedded Image; blue squares) and transcis (Embedded Image; red circles). The ratio of Embedded Image as a function of [CO] is given in the inset. (C) Fitted effective bimolecular formation rate coefficients (k1a) for trans-DOCO (k1a,trans; black diamonds) and cis-DOCO (k1a,cis; green squares). The ratio of the formation rate coefficients k1a,trans/k1a,cis as a function of [CO] is given in the inset. The error bars in (B) and (C) represent uncertainties from the individual parameter variance and covariance between k1a,sum and kiso.

We hypothesize that the observed time dependence of the [trans]/[cis] ratios can be described by a simple kinetic model given by eqs. S9 to S17 and qualitatively understood as follows. The nascent [trans]/[cis] ratio extrapolated to t ≈ 0 μs (before any thermal, canonical isomerization) is determined only by the ratio of the formation rate coefficients for the two isomers (k1a,trans/k1a,cis). This initial ratio then rises/decays to a steady-state value. The rate of the exponential rise/decay increases with the sum of kiso,tc and kiso,ct and is an indication of how fast the trans to cis populations approach this steady state. During this time (t < 50 μs), formation and isomerization compete. At t > 50 μs, the isomerization reaction dominates and establishes steady-state populations of trans and cis isomers that persist at long times. If the formation and loss processes for DOCO are slow relative to isomerization, the trans and cis isomers are in equilibrium. The [trans]/[cis] ratio then becomes independent of [CO] and [trans]/[cis] = kiso,ct/kiso,tc = Kiso, the equilibrium constant (Kiso) for DOCO isomerization.

To quantify the isomerization and isomer-specific formation rate coefficients, we fit time-dependent [trans]/[cis] ratios by extending Eq. 6 to include the rate equation for OD formation and decay (eq. S7). The dashed lines (Embedded Image ≈ 0.9 to 1.7) in Fig. 4A are results obtained from fitting the formation rate coefficients, k1a,cis and k1a,trans, and isomerization coefficients, kiso,tc and kiso,ct, to all nine experimental data sets (differing in CO pressures) simultaneously. Here, k1a,sum = k1a,cis + k1a,trans is fixed to the value measured previously for the sum of isomers (in Fig. 3B). We also assume that the loss rate is isomer-independent and fix kloss to the fitted value in Eq. 8.

The CO dependence of the fitted isomer-specific Embedded Image and k1a is given in Fig. 4, B and C, respectively, and compiled in table S5. Both the formation and thermalized isomerization rate constants are observed to be linear with pressure and hence in the low-pressure limit. For the termolecular formation rate coefficients, we find that k1a,trans(CO) = 1.4(4) × 10−32 cm6 molecules−2 s−1 and k1a,cis(CO) = 6(2) × 10−33 cm6 molecules−2 s−1 from fitting the data in Fig. 4C. The ratio of the fitted isomerization rate coefficients (Fig. 4B, inset), however, varies with CO concentration and only becomes constant at higher [CO]. This ratio should be a constant and independent of [CO]; this variation, which reflects different values of the steady-state [trans]/[cis] ratio, indicates the existence of competition between DOCO isomerization, bimolecular formation, and reactive loss. The fitted isomerization rates are thus empirical, and we designate them as apparent isomerization rate coefficients kiso,tcfit and kiso,ctfit.

Figure 4A shows that with increasing [CO], the transition from decay to rise behavior in the [trans]/[cis] ratio occurs at approximately [CO] = 6.5 × 1017 molecules cm−3. This trend can now be explained by comparing the Embedded Image and k1a,trans/k1a,cis ratios given in the insets of Fig. 4, B and C, respectively. This transition is also the intersection point of the decreasing Embedded Image and increasing k1a,trans/k1a,cis. At the lowest CO pressures, the formation, isomerization, and loss rates all have similar magnitudes (≈104 s−1), and therefore, these processes compete.

Additional evidence for this interplay can be found in the observed ratio of Embedded Image from the inset of Fig. 4B. Under these conditions, the fitted ratio of Embedded Image varies apparently with CO pressure, indicating that these empirical parameters in our model include isomer-specific formation and loss processes. However, at higher pressures ([CO] > 6.4 × 1017 molecules cm−3), isomerization dominates (≈105 s−1) and Embedded Image converges to a constant value, which suggests that the high pressure ratio is the true ratio of isomerization rates and hence the pressure-independent equilibrium constant, Kiso ≈ 5(2):1.

The trans- and cis-DOCO equilibrium constant is a fundamental thermodynamic quantity. Our measured equilibrium constant is consistent with that determined from the experimental well depths of HOCO isomers reported by Johnson and co-workers (19). We can also compare our measurement with predictions by state-of-the-art calculations. Using a theoretical method that combines semiclassical transition state theory (SCTST) (2931) with two-dimensional (2D) master equations (18, 25, 32), the calculated pressure-dependent isomerization rate coefficients are displayed in fig. S3. The theoretical equilibrium constant is Kiso,th ≈ 14:1. Although the measured value disagrees with theory, a change of ≈2 kJ mol−1 in the relative energies (enthalpy) of cis- and trans-DOCO would account for the difference in the measured and predicted equilibrium constants. Because the entropy component of the Keq calculation comes from the use of theoretical rovibrational parameters that are in good agreement with the experimentally measured values, it is unlikely that entropy accounts for a majority of the discrepancy. Our observed equilibrium concentrations also rely on ab initio calculations of the absorption cross sections of cis- and trans-DOCO, which are challenging for accurate determination.

New experimental insight into the energy transfer processes is obtained from the formation rate dependence on collision partner and total pressure for both cis- and trans-DOCO isomers. We demonstrate that DOCO exhibits isomer-specific formation rates. CO is more than twice as effective in collisionally stabilizing trans-DOCO* compared to cis-DOCO*. The unusually large enhancement by the CO collision partner for the trans-DOCO isomer relative to cis-DOCO may be a consequence of complex formation between trans-DOCO* and CO from a stronger interaction potential, which would facilitate energy transfer. This mechanism is further supported by spectroscopic observation of the trans-HOCO(CO) complex in the molecular beam environment by Oyama et al. (33).

Finally, the identification and quantification of cis-DOCO, trans-DOCO, and D + CO2 account for all possible branching pathways for OD + CO. It is now experimentally possible to deconstruct the effective bimolecular rate coefficient k1 in the low-pressure limit as a sum of elementary reaction steps, that is, k1([M],T) = k1a,cis([M],T) + k1a,trans([M],T) + k1b(T), where k1b(T) is the bimolecular rate coefficient for the pressure-independent well skipping the D + CO2 channel (6, 7, 28). This approximation is valid in the low-pressure limit, provided that k1 is only strongly dependent on k1a while k1b remains constant with total pressure and collision partner. The latter is independently verified from our measurements of the pressure-dependent formation rate of CO2 (28). Previously, k1 was determined only with contributions from trans-DOCO and CO2. Mass balance dictates that cis-DOCO also contributes to the total k1; the pressure dependence of k1 has been plotted in fig. S4. The observed agreement in k1 with previous studies by Golden et al. (8) and Paraskevopoulos and Irwin (11) provides additional confirmation that k1 can be treated as a sum of the rate coefficients of independent channels, k1a and k1b, in the low-pressure limit. The k1b value measured previously (28) reproduces the measured [CO2]t in this work (Fig. 3A, dotted line fit to eq. S8), which provides additional confirmation of the OD + CO → D + CO2 channel. We note that at t > 300 μs, [CO2] significantly exceeds [OD] because (i) there are no known reactive channels causing CO2 loss and (ii) secondary reactions that produce CO2 (for example, DOCO + O3 → OD + CO2 + O2) result in its accumulated concentration.


We have unambiguously identified and quantified the time-dependent concentrations of all the reactant, intermediate, and product channels in the direct kinetics of OD + CO using time-resolved frequency comb spectroscopy. Each step of the reaction was analyzed to obtain detailed information about the elementary chemical reactions and product branching ratios. How each step quantitatively contributes to the apparent reaction rate coefficient k1—the main observable for previous studies—is now experimentally confirmed. In addition, new insights into both the reaction mechanism and the energy transfer processes from the observed differences in the formation rate and reactivity of DOCO isomers are obtained. For the first time, these experimental observations capture DOCO dynamics, where the formation of DOCO is directly followed by isomerization reactions between the cis- and trans-DOCO isomers. Typically, isomers of intermediate species are either observed in equilibrium or isolated (34, 35): To see the transition in this intermediate regime is unusual and highlights the richness of the reaction landscape. Finally, we anticipate that the next exciting frontier for the OH + CO reaction is in the low-temperature regime, where tunneling is particularly conspicuous. With the rapid emergence and success of cold molecule physics (36), the OH + CO reaction provides an ideal system to learn new physics and chemistry ranging from cold to the ultracold regime, especially from the perspective of quantum control of chemical reactions.


Time-resolved frequency comb spectroscopy

The OD + CO reaction was initiated in a room temperature (T ≈ 295 K) flow cell enclosed by high-reflectivity mirrors (for cavity-enhanced absorption spectroscopy). Absorption spectra were obtained from a mid-IR frequency comb (probe beam) propagating collinearly with the cavity axis. Details for the frequency comb source, enhancement cavity, and dispersive spectrometer can be found in previous reports (20, 27). Ultraviolet light at 266 nm (≈30 mJ per pulse and ≈10 ns) orthogonal to the cavity axis photodissociated O3 at t = 0, which produces O(1D) and O2 at a near-unity yield. In the presence of D2 gas, the reaction O(1D) + D2 produced OD(v = 0 to 4) and D atoms. OD(v > 0) populations were rapidly quenched to the vibrational ground state at our experimental conditions. OD(v ≥ 0) internal state distributions were thermalized at t > 10 μs (20). Addition of CO gas initiated the OD + CO reaction. The total pressure range for all experiments was 20 to 100 torr. The reaction kinetics was obtained by setting a variable time delay between the photolysis pulse and the IR probe beam acquisition.

Several key experimental modifications have led to an improvement of the measurement signal-to-noise ratio compared to our previous work (20). The absorption sensitivity and spectral coverage were improved by the use of high-finesse mirrors with a larger bandwidth (≈3.6 to 4.2 μm). This broad spectral span granted access to a larger number of species formed from OD + CO, including OD(v ≥ 0), DO2, CO2, cis-DOCO, and trans-DOCO. To observe each species, we tuned the optical parametric oscillator wavelength to its respective spectral windows. The 266-nm photolysis beam profile was shaped to be 130 mm × 6 mm to optimize the production of DOCO and spatial overlap with the mid-IR probe beam. We also used a retroreflector mirror for the photolysis beam to double the photolysis fraction. These combined changes have resulted in a net threefold increase in the measured signal of trans-DOCO relative to the previous apparatus.

Data extraction and analysis

Spectral fitting. The total intracavity absorbance was fit to a linear sum of absorbances for molecular species A, B, etc.Embedded Image(10)where A(Embedded Image) is the cavity absorbance, np (p = A, B, etc.) is the molecular density (in molecules per cubic centimeter), σp is the molecular absorption cross section (in square centimeters), leff is the effective absorption path length (in centimeters), and Embedded Image is the wave number (in reciprocal centimeters). The reference intensity, IR(Embedded Image), was recorded 4 ms before the photolysis pulse, and the signal intensity, IS(Embedded Image), was recorded after the photolysis pulse at variable delay time t.

Spectral line intensities. The OD, D2O, and trans-DOCO line positions and intensities used in this work have been described previously (20). The CO2 line positions and intensities were obtained from HITRAN2012 (37). The cis-DOCO spectral parameters compiled in table S2 were used to simulate the rovibrational spectrum in PGOPHER (38). The theoretical cis-DOCO v = 1 band strength of Scis-DOCO = 14.4124 km mol−1 was calculated using VPT2 at the CCSD(T)/ANO1 level of theory.

Photolysis path length and finesse. The effective absorption path length, leff, was determined from the width of the photolysis beam, lphot, and the cavity finesse, F, asEmbedded Image(11)where β = 1. The cavity finesse as a function of wavelength was measured using the cavity ring-down technique. From Eq. 11, the effective path length was 331 ± 26 m at the peak finesse at 3920 nm. This effective absorption path length as a function of wavelength was used to determine the absolute densities displayed in Fig. 3A. However, the k1a,sum measurements are independent of finesse because we calculated the time derivative of [DOCO] normalized to [OD]t, which cancels out the path length contribution.


Supplementary material for this article is available at

section S1. cis-DOCO isotope shift and spectral parameters

section S2. k1a,sum fitting

section S3. Theoretical calculations for OD + CO

section S4. k1 for OD + CO as a function of N2

table S1. Experimental spectral features for cis-DO12CO and cis-DO13CO and their rovibrational assignments.

table S2. Summary of spectral parameters for cis-DO12CO and cis-DO13CO.

table S3. Comparison of experimental and theoretical isotopic shifts for cis-DOCO.

table S4. Summary of statistical and systematic errors for k1a,sum.

table S5. Summary of fitted rate coefficients.

fig. S1. Variation of rloss,sum with O3 concentration.

fig. S2. Variation of k1a,sum with D2 concentration.

fig. S3. Calculated cis/trans isomerization rates for DOCO isomers using SCTST and 2D master equations.

fig. S4. Measured k1 comparison with previous works.

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Acknowledgments: We thank J. M. Bowman and H. Guo for stimulating discussions. Funding: We acknowledge the financial support from the Air Force Office of Scientific Research (FA9550-15-1-0111 P00002), Defense Advanced Research Projects Agency Spectral Combs from UV to THz, National Institute of Standards and Technology, and NSF JILA Physics Frontier Center (NSF PHY-1734006). J.F.S. and T.L.N. acknowledge the financial support from the U.S. Department of Energy, Office of Basic Energy Sciences, under award number DE-FG02-07ER15884. M.O. acknowledges the support of the NSF (grant CHE-1413712) and NASA’s Upper Atmosphere Research Program. T.Q.B. is supported by the National Research Council Research Associate Fellowship, and P.B.C. is supported by the NSF Graduate Research Fellowships Program. Author contributions: T.Q.B., B.J.B., M.O., and J.Y. conceived and designed the experiments. T.Q.B., B.J.B., P.B.C., and J.Y. discussed and implemented the experimental technique. T.Q.B. and B.J.B. analyzed all the data. T.L.N. and J.F.S. provided the supporting theory. All authors contributed to technical discussions and writing of the manuscript. Competing interests: All authors declare that they have no competing interests. Data and materials availability: Data are archived on a network-attached storage drive located at JILA. All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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