## Abstract

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.

## INTRODUCTION

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 (*2*–*4*). 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 nonreactive(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, *k*_{1}, 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 + CO_{2}. Figure 1 shows the PES for the OH + CO reaction.

Over the past four decades, the HOCO formation mechanism had been derived from fits of the observed *k*_{1}(*P*,*T*) to theoretical models (*6*–*17*). These studies led to the following proposed reaction mechanism for OH + CO, starting from the calculated asymptotic (stationary) states in Fig. 1(2)(3)(4)(5)

Reaction 1 initially produces energized HOCO*, which either back-reacts to OH + CO or proceeds to form H + CO_{2} (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, *k*_{1}([M],*T*) = *k*_{1a}([M],*T*) + *k*_{1b}([M],*T*), where *k*_{1a} and *k*_{1b} describe the formation of stabilized HOCO and H + CO_{2}, 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 + CO_{2} 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 + CO_{2} 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*, *26*–*28*). Using a room temperature flow cell, the OD + CO reaction is initiated at *t* = 0 by photodissociation of O_{3} in the presence of D_{2}, CO, and N_{2} (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 CO_{2} 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.

## RESULTS AND DISCUSSION

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 ^{12}C and ^{13}C isotopologues of *cis*-DOCO are obtained. The predicted and measured spectroscopic constants for both ^{12}C and ^{13}C 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 CO_{2} 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 *k*_{1a,i}([M],*T*), *k*_{iso,ij}([M],*T*), and *k*_{loss,i} (*i*,*j* = *cis* or *trans*), respectively, with the following rate equations (Eq. 6)(6)

The subscript *t* denotes time. The time-dependent [*cis*-DOCO]_{t} and [*trans*-DOCO]_{t} are denoted by [*cis*]_{t} and [*trans*]_{t}, respectively. *k*_{iso,ct}([M],*T*) and *k*_{iso,tc}([M],*T*) are the pressure-dependent effective isomerization rate coefficients for *cis* → *trans* and *trans* → *cis*, respectively. *k*_{loss} 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 + CO_{2}, 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, *k*_{1a,sum}([M],*T*) ≡ *k*_{1a,cis}([M],*T*) + *k*_{1a,trans}([M],*T*), and a similar expression for *k*_{loss,sum} (Eq. 7)(7)where [DOCO_{sum}] ≡ [*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 (N_{2}, CO, D_{2}, and O_{3}).

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 reaction(8)

The effective bimolecular rate coefficient *k*_{1a,sum}([M],*T*) can be decomposed into three terms dependent on N_{2}, CO, and D_{2} concentrations(9)where *k*_{1a,sum}^{(CO)}, *k*_{1a,sum}^{(N2)}, and *k*_{1a,sum}^{(D2)} are the termolecular rate coefficient dependence on M = CO, N_{2}, and D_{2}, respectively. *k*_{1a,sum}^{(0)} is an offset term that accounts for additional background species. O_{3} is not included in Eq. 9 because its concentration is smaller by a factor greater than 10^{2} compared to the other buffer gas species. Its main contribution is to DOCO loss.

By simultaneously fitting [DOCO_{sum}]_{t} and [OD]_{t} from data in Fig. 3A across varying [CO], [N_{2}], and [D_{2}], the effective bimolecular rate coefficients for the DOCO_{sum} formation, *k*_{1a,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 [DOCO_{sum}]_{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 *k*_{1a,sum} and *r*_{loss,sum}; the latter is an effective first-order rate for the loss of DOCO_{sum}.

DOCO must be lost by reaction with one or more species, which we define as *X*; then, *r*_{loss,sum} = *k*_{loss,sum}[*X*], where *k*_{loss,sum} is a bimolecular rate coefficient. We hypothesized that *X* = O_{3}, because O_{3} is the highest concentration candidate that is reactive with DOCO. To test this, *r*_{loss,sum} is determined independently by measuring [*cis*]_{t} and [*trans*]_{t} while varying the density of O_{3}; the results are shown in fig. S1. The observed loss rate is proportional to O_{3} and is invariant to [CO], [N_{2}], and [D_{2}], leading to an empirical bimolecular rate coefficient for DOCO loss to O_{3}, *k*_{loss,sum} = 2.5(6) × 10^{−11} cm^{3} molecules^{−1} s^{−1}, from a global fit across all CO, N_{2}, and D_{2} data sets. We conclude that *X* is predominantly O_{3}. One possible outcome from the reaction of DOCO with O_{3} is to recycle OD, which, together with the reaction of D + O_{3} → 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 O_{2} present in the O_{3} flow, some of the loss is due to reaction with O_{2}, which will also appear to vary linearly with O_{3}. Any contribution to *r*_{loss,sum} from the reaction with O_{2} is likely to be minor, because [O_{2}] << [O_{3}], and in addition, the rate coefficient for DOCO + O_{2} is an order of magnitude lower than that for *k*_{loss,sum}.

After establishing that *r*_{loss,sum} is due to reaction with O_{3}, we next determine the effective bimolecular rate coefficients, *k*_{1a,sum}, to form DOCO from Eq. 8 for each buffer gas ([CO], [N_{2}], and [D_{2}]). The results from experiments varying each gas concentration independently while fixing [O_{3}] = 2 × 10^{15} molecules cm^{−3} (*r*_{loss,sum} = 5 × 10^{4} s^{−1}) are displayed as data points in Fig. 3 (B and C) and fig. S2, respectively.

Fits of *k*_{1a,sum} reveal that, under our conditions, CO and N_{2} contribute to DOCO stabilization; there is no observable dependence on D_{2} 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 *k*_{1a,sum}^{(CO)}, *k*_{1a,sum}^{(N2)}, and *k*_{1a,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 *k*_{1a,sum} on CO or *k*_{1a,sum}^{(CO)}. The offset in the linear fit comes from the N_{2} termolecular dependence of *k*_{1a,sum} or *k*_{1a,sum}^{(N2)}. A similar linear dependence is seen for varying N_{2} (Fig. 3C), with the offset being the *k*_{1a}^{(CO)} component. The results obtained from the multidimensional linear regression are *k*_{1a,sum}^{(CO)} = cm^{6} molecules^{−2} s^{−1}, *k*_{1a,sum}^{(N2)} = cm^{6} molecules^{−2} s^{−1}, and *k*_{1a,sum}^{(D2)} = cm^{6} molecules^{−2} s^{−1}. We observe an additional offset in the effective bimolecular rate constant, *k*_{1a,sum}^{(0)} = cm^{3} molecules^{−1} s^{−1}. More than 80% of the offset term, *k*_{1a,sum}^{(0)}, can be accounted for by a combination of the upper bound of *k*_{1a,sum}^{(D2)} and competition from DOCO loss processes (*r*_{loss,sum}). The D_{2} concentrations are too low (<10% of total gas) to determine *k*_{1a,sum}^{(D2)} accurately. Discussions of all statistical and systematic error sources for *k*_{1a,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 (*k*_{1a}) and subsequent relaxation by *trans*/*cis* isomerization (*k*_{iso}).

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 (*k*_{1a,trans}/*k*_{1a,cis}). This initial ratio then rises/decays to a steady-state value. The rate of the exponential rise/decay increases with the sum of *k*_{iso,tc} and *k*_{iso,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*] = *k*_{iso,ct}/*k*_{iso,tc} = *K*_{iso}, the equilibrium constant (*K*_{iso}) 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 ( ≈ 0.9 to 1.7) in Fig. 4A are results obtained from fitting the formation rate coefficients, *k*_{1a,cis} and *k*_{1a,trans}, and isomerization coefficients, *k*_{iso,tc} and *k*_{iso,ct}, to all nine experimental data sets (differing in CO pressures) simultaneously. Here, *k*_{1a,sum} = *k*_{1a,cis} + *k*_{1a,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 *k*_{loss} to the fitted value in Eq. 8.

The CO dependence of the fitted isomer-specific and *k*_{1a} 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 *k*_{1a,trans}^{(CO)} = 1.4(4) × 10^{−32} cm^{6} molecules^{−2} s^{−1} and *k*_{1a,cis}^{(CO)} = 6(2) × 10^{−33} cm^{6} 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 *k*_{iso,tc}^{fit} and *k*_{iso,ct}^{fit}.

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 × 10^{17} molecules cm^{−3}. This trend can now be explained by comparing the and *k*_{1a,trans}/*k*_{1a,cis} ratios given in the insets of Fig. 4, B and C, respectively. This transition is also the intersection point of the decreasing and increasing *k*_{1a,trans}/*k*_{1a,cis}. At the lowest CO pressures, the formation, isomerization, and loss rates all have similar magnitudes (≈10^{4} s^{−1}), and therefore, these processes compete.

Additional evidence for this interplay can be found in the observed ratio of from the inset of Fig. 4B. Under these conditions, the fitted ratio of 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 × 10^{17} molecules cm^{−3}), isomerization dominates (≈10^{5} s^{−1}) and 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, *K*_{iso} ≈ 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) (*29*–*31*) 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 *K*_{iso,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 *K*_{eq} 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 + CO_{2} account for all possible branching pathways for OD + CO. It is now experimentally possible to deconstruct the effective bimolecular rate coefficient *k*_{1} in the low-pressure limit as a sum of elementary reaction steps, that is, *k*_{1}([M],*T*) = *k*_{1a,cis}([M],*T*) + *k*_{1a,trans}([M],*T*) + *k*_{1b}(*T*), where *k*_{1b}(*T*) is the bimolecular rate coefficient for the pressure-independent well skipping the D + CO_{2} channel (*6*, *7*, *28*). This approximation is valid in the low-pressure limit, provided that *k*_{1} is only strongly dependent on *k*_{1a} while *k*_{1b} remains constant with total pressure and collision partner. The latter is independently verified from our measurements of the pressure-dependent formation rate of CO_{2} (*28*). Previously, *k*_{1} was determined only with contributions from *trans*-DOCO and CO_{2}. Mass balance dictates that *cis*-DOCO also contributes to the total *k*_{1}; the pressure dependence of *k*_{1} has been plotted in fig. S4. The observed agreement in *k*_{1} with previous studies by Golden *et al.* (*8*) and Paraskevopoulos and Irwin (*11*) provides additional confirmation that *k*_{1} can be treated as a sum of the rate coefficients of independent channels, *k*_{1a} and *k*_{1b}, in the low-pressure limit. The *k*_{1b} value measured previously (*28*) reproduces the measured [CO_{2}]_{t} in this work (Fig. 3A, dotted line fit to eq. S8), which provides additional confirmation of the OD + CO → D + CO_{2} channel. We note that at *t* > 300 μs, [CO_{2}] significantly exceeds [OD] because (i) there are no known reactive channels causing CO_{2} loss and (ii) secondary reactions that produce CO_{2} (for example, DOCO + O_{3} → OD + CO_{2} + O_{2}) result in its accumulated concentration.

## CONCLUSIONS

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 *k*_{1}—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.

## MATERIALS AND METHODS

### 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 O_{3} at *t* = 0, which produces O(^{1}D) and O_{2} at a near-unity yield. In the presence of D_{2} gas, the reaction O(^{1}D) + D_{2} 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), DO_{2}, CO_{2}, *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.(10)where *A*() is the cavity absorbance, *n*_{p} (*p* = A, B, etc.) is the molecular density (in molecules per cubic centimeter), σ_{p} is the molecular absorption cross section (in square centimeters), *l*_{eff} is the effective absorption path length (in centimeters), and is the wave number (in reciprocal centimeters). The reference intensity, *I*_{R}(), was recorded 4 ms before the photolysis pulse, and the signal intensity, *I*_{S}(), was recorded after the photolysis pulse at variable delay time *t*.

Spectral line intensities. The OD, D_{2}O, and *trans*-DOCO line positions and intensities used in this work have been described previously (*20*). The CO_{2} 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 *S*_{cis-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, *l*_{eff}, was determined from the width of the photolysis beam, *l*_{phot}, and the cavity finesse, *F*, as(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 *k*_{1a,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 MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/1/eaao4777/DC1

section S1. *cis*-DOCO isotope shift and spectral parameters

section S2. *k*_{1a,sum} fitting

section S3. Theoretical calculations for OD + CO

section S4. *k*_{1} for OD + CO as a function of N_{2}

table S1. Experimental spectral features for *cis*-DO^{12}CO and *cis*-DO^{13}CO and their rovibrational assignments.

table S2. Summary of spectral parameters for *cis*-DO^{12}CO and *cis*-DO^{13}CO.

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

table S4. Summary of statistical and systematic errors for *k*_{1a,sum}.

table S5. Summary of fitted rate coefficients.

fig. S1. Variation of *r*_{loss,sum} with O_{3} concentration.

fig. S2. Variation of *k*_{1a,sum} with D_{2} concentration.

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

fig. S4. Measured *k*_{1} comparison with previous works.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is **not** for commercial advantage and provided the original work is properly cited.

## REFERENCES AND NOTES

**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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