transform infrared emission spectroscopy
Shang-Chen Huang, N. T. Nghia, Raghunath Putikam, Hue M. T. Nguyen, M. C. Lin, Soji Tsuchiya, and Yuan-Pern Lee
Citation: The Journal of Chemical Physics 141, 154313 (2014); doi: 10.1063/1.4897418
View online: http://dx.doi.org/10.1063/1.4897418
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/15?ver=pdfcov Published by the AIP Publishing
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Reaction dynamics of O(
1D)
+ HCOOD/DCOOH investigated with
time-resolved Fourier-transform infrared emission spectroscopy
Shang-Chen Huang,1N. T. Nghia,2Raghunath Putikam,1Hue M. T. Nguyen,3 M. C. Lin,1,a)Soji Tsuchiya,1,a),b) and Yuan-Pern Lee1,4,a)
1Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan
2School of Chemical Engineering - Hanoi University of Science and Technology, Hanoi, Vietnam 3Center for Computational Science and Faculty of Chemistry, Hanoi National University of Education, Hanoi, Vietnam
4Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
(Received 22 August 2014; accepted 26 September 2014; published online 21 October 2014) We investigated the reaction dynamics of O(1D) towards hydrogen atoms of two types in HCOOH. The reaction was initiated on irradiation of a flowing mixture of O3 and HCOOD or DCOOH at 248 nm. The relative vibration-rotational populations of OH and OD (1 v 4, J ≤ 15) states were determined from time-resolved IR emission recorded with a step-scan Fourier-transform spectrom-eter. In the reaction of O(1D)+ HCOOD, the rotational distribution of product OH is nearly Boltz-mann, whereas that of OD is bimodal. The product ratio [OH]/[OD] is 0.16± 0.05. In the reaction of O(1D)+ DCOOH, the rotational distribution of product OH is bimodal, but the observed OD lines are too weak to provide reliable intensities. The three observed OH/OD channels agree with three major channels of production predicted with quantum-chemical calculations. In the case of O(1D)+ HCOOD, two intermediates HOC(O)OD and HC(O)OOD are produced in the initial C−H and O−D insertion, respectively. The former undergoes further decomposition of the newly formed OH or the original OD, whereas the latter produces OD via direct decomposition. Decomposition of HOC(O)OD produced OH and OD with similar vibrational excitation, indicating efficient in-tramolecular vibrational relaxation, IVR. Decomposition of HC(O)OOD produced OD with greater rotational excitation. The predicted [OH]/[OD] ratio is 0.20 for O(1D)+ HCOOD and 4.08 for O(1D) + DCOOH; the former agrees satisfactorily with experiments. We also observed the v3 emission from the product CO2. This emission band is deconvoluted into two components corresponding to internal energies E= 317 and 96 kJ mol−1of CO2, predicted to be produced via direct dehydration of HOC(O)OH and secondary decomposition of HC(O)O that was produced via decomposition of HC(O)OOH, respectively. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4897418] I. INTRODUCTION
The reactions of electronically excited oxygen atom O(1D) with many atmospheric species have been exten-sive investigated because of their importance in atmospheric chemistry.1,2 The reactions are typically characterized by an initial insertion of O(1D) into the C−H bond of reactants to produce an energetic intermediate that proceeds via several reaction channels before further fragmentation.3–6In the case of O(1D) + CH
4, the abstraction channel is also important according to the observation of OH product scattered in the forward and backward directions in significant proportions.6
Investigations of the reactions of O(1D) with species that possess H atoms of two types is important because of the com-petition of two attacking sites for O(1D) and also the compe-tition of insertion or abstraction reactions. In particular, when a molecule, such as CH3OH, possesses both C−H and O−H a)Authors to whom correspondence should be addressed. Electronic addresses: [email protected], [email protected], and [email protected].
b)Present address: Research Institute of Science and Engineering, Waseda University, Ookubo, Shinjuku-ku, Tokyo 169-8555, Japan.
bonds, O(1D) might insert into either bond; the former pro-duces a new OH moiety that compete with the original OH moiety during further fragmentation. Previously, we reported the observations of rotationally resolved IR emission spec-tra of OH and OD that were produced from the reaction of O(1D) with CH
3OD or CD3OH.7For O(1D)+ CD3OH, the product ratio [OH]/[OD] was 1.56± 0.36 with the rotational distribution of OD being nearly Boltzmann whereas that of OH being bimodal. For O(1D)+ CH3OD, the product ratio [OH]/[OD] was 0.59± 0.14 and the rotational distribution of OH was nearly Boltzmann whereas that of OD was bimodal. With quantum-chemical calculations of the potential-energy surfaces (PES) and microcanonical rate coefficients of var-ious channels, we concluded that the observed three inter-nal distributions of OH are consistent with those produced via decomposition of the newly formed OH and the origi-nal OH moiety of HOCH2OH that is produced from inser-tion of O(1D) into the C−H bond of CH
3OH, and decompo-sition of CH3OOH that is produced via insertion of O(1D) into the O−H bond of CH3OH. The decomposition of the newly formed OH in HOCH2OH produces more vibrationally excited OH because of incomplete intramolecular vibrational 0021-9606/2014/141(15)/154313/15/$30.00 141, 154313-1 © 2014 AIP Publishing LLC
relaxation (IVR), and decomposition of CH3COOH produces OH with greater rotational excitation, likely due to a large torque angle during dissociation.
Although the observed [OH]/[OD] ratio in the reaction of O(1D)+ CH
3OD (CD3OH) indicated a preference for the formation of OD (OH) from the hydroxyl moiety over the methyl moiety of CH3OH, it is not in conflict with a theoret-ical prediction that O(1D) prefers to attack the methyl moiety of CH3OH. The reason is partly that, upon insertion of O(1D) into a C−H bond to form HOCH2OH, the subsequent disso-ciation occurred for both the newly formed OH and the origi-nal OH group, and partly because some inserted intermediate HOCH2OH also decomposed to form H+ OCH2OH and H2O + H2CO, whereas the decomposition of CH3OOH, produced from insertion of O(1D) into the O−H bond, produced mainly CH3O+ OH.
We extended the investigation to the reaction of O(1D) with formic acid (HCOOH) in which the methyl moiety in CH3OH is replaced by a formyl moiety. In addition to the fundamental importance of the reactivity towards H atoms of two types discussed previously, this reaction is related to the reaction of OH + HOCO that is important in combus-tion systems;8 both reactions share a common intermediate HOC(O)OH and produce CO2 + H2O or CO2 + H + OH. Surprisingly, this reaction has been little studied; no report on the reaction kinetics or dynamics of this reaction is avail-able. The only information is the infrared (IR) identification of the intermediate peroxyformic acid HC(O)OOH from the reaction of O(1D) with trans-HCOOH in a cryogenic matrix.9 Here we report our observations of rotationally resolved IR emission spectra of OH and OD that were produced from the reaction of O(1D) with HCOOD and DCOOH. In addi-tion to the vibraaddi-tion-rotaaddi-tional distribuaddi-tions of OH and OD we determined also the ratio of [OH]/[OD]. We observed also unresolved emission of CO2. To assist the interpretation of ex-perimental data, we calculated quantum-chemically the PES of various reaction channels and predicted the branching ra-tios accordingly.
II. EXPERIMENTS
The step-scan Fourier-transform spectrometer (FTS) for emission detection was described previously;10–12only a brief summary is presented here. Ozone (O3) and HCOOD or DCOOH were injected separately into the reaction chamber. A KrF laser (248 nm, 23 Hz) was employed to photolyze O3 to form O(1D). A telescope mildly focused this photol-ysis beam to an area∼12 × 10 mm2at the reaction center to yield a fluence∼55 mJ cm−2. IR emission was collected with two Welsh mirrors (focal length 10 cm) before being detected with the InSb detector (rise time 0.34 μs and responsivity 3.2 × 106 V W−1) of a step-scan FTS. The preamplified tran-sient signal from the detector was further amplified 20 times with a voltage amplifier (bandwidth 1 MHz) before being dig-itized with an external data-acquisition board (12-bit, 25-ns resolution).
Data were typically averaged over 60 laser pulses at each scan step. For simultaneous detection of OH and OD, 4569 scan steps were performed to yield an interferogram
result-ing in spectra of resolution 0.8 cm−1to cover a spectral range of 2170−3580 cm−1. For detection of CO
2, 1883 scan steps were performed to yield an interferogram resulting in spectra of resolution 8 cm−1to cover a spectral range of 1700–2400 cm−1. To increase further the ratio of signal to noise, eight spectra recorded under similar conditions were averaged. The temporal response period of the detection system is approx-imately 1 μs, determined with an IR laser emission.13 The spectral response function was calibrated with a black-body radiation source.
To decrease the collisional quenching of OH and OD, a minimal pressure yielding satisfactory signals was used:
PO3= 12−16 mTorr, PDCOOHand PHCOOD∼= 84−88 mTorr. Flow rates were FO3 = 1.6−2.3 sccm, FDCOOH and FHCOOD = 12.7−12.8 sccm, in which sccm denotes cm3 min−1 un-der standard conditions (1 atm and 298.15 K). Approximately 60% of O3 was dissociated upon irradiation at 248 nm ac-cording to the employed laser fluence, the reported absorption cross section of∼1.1 × 10−17cm2molecule−1 for O
3, and a quantum yield of ∼0.90 ± 0.05 for the formation of O(1D) from O3at 248 nm.14,15
DCOOH (isotopic purity 98%) and HCOOD (isotopic purity 98%, both Cambridge Isotope Laboratories) were em-ployed without further purification. For experiments with HCOOD, the reaction chamber was heated to 343 K under vacuum, followed by passivation with D2O (10 Torr) at 298 K for 1 h. After evacuation, the system was filled with D2O (10 Torr) overnight and was treated with passivation and evacua-tion three times before each experiment. Producevacua-tion and mea-surements of O3 were described previously.7 The formation of dimeric HCOOH has G= −7.2 kJ mol−1at 343 K.16At 343 K and partial pressure 0.10 Torr, the fraction of dimer is estimated to be <0.2% of the monomeric HCOOH.
III. COMPUTATIONAL METHOD
The geometries of the reactants, transition states and products for the reaction O(1D)+ HCOOH were optimized with hybrid density functional theory (DFT) at the B3LYP/6-311++G(3df,2p) level.17 The stationary points were iden-tified as local minima or transition states according to a vibrational analysis. The geometries of transition states were then used as an input for IRC calculations to ver-ify the connectivity of the reactants and products. An en-ergy path representing a barrierless insertion or an associa-tion process was obtained on calculating the potential-energy curve at the CASPT2(8,8)/6-311++G(3df,2p)//CAS(8,8)/6-311G++G(3df,2p) level of theory along its reaction co-ordinate: O· · · H (for C−H or O−H abstraction) from its equilibrium separation to ∼8 ´Å at step size 0.2 ´Å and O· · · C (for C−H insertion) and O · · · O (for O−H, C−O, or C=O insertion) from its equilibrium separation to ∼5 ´Å at step size 0.1 ´Å. For more accurate evalu-ation of energies, we calculated energies at single-points on the B3LYP-optimized geometries with the CCSD(T)/6-311++G(3df,2p) method.18 The relative energies presented in the PES are corrected for unscaled zero-point vibra-tional energies (ZPVE). For the abstraction channels, of
which the transition states could not be found with the DFT method, we optimized the structures and calculated the en-ergies with the MRCI(8,8)/6-311++G(3df,2p)//CAS(8,8)/6-311++G(3df,2p) method.19 These calculations were per-formed using the MOLPRO program,20 whereas all DFT-based calculations were performed with the Gaussian 09 package.21
Rate coefficients and product branching ratio in the temperature range 200−2000 K were calculated with the Master Equation (RRKM/ME) method implemented in the VARIFLEX code22 based on the microcanonical RRKM (Rice-Ramsperger-Kassel-Macus) theory.23,24 The numbers of states for the tight transition states were evaluated ac-cording to the rigid-rotor harmonic-oscillator approximation. For those paths involving hydrogen atom transfer, Eckart tunneling25corrections were made in calculations of the rate coefficients; however, the effect was found to be negligible, as one would expect, because of the large excess energies above those transition states involved; see Table SI in the sup-plementary material.26 For the barrierless transition states, a Morse potential V(R)= De{1 – exp[−β(R – Re)]}2was used to represent the potential energy along the minimum energy path (MEP) of an individual reaction coordinate. In the above equation, Deis the binding energy of a dissociation reaction excluding the contribution of the zero-point vibrational en-ergy, R is the reaction coordinate, and Reis the equilibrium value of R at the stable intermediate structure. In the RRKM calculations, the Lennard-Jones parameters for HOC(O)OH and HC(O)OOH were approximated with parameters
σ = 3.95 Å and ε/κ = 519 K of HCOOH.27–29
IV. RESULTS AND DISCUSSION
A. IR emission of OH and OD from O(1D)+ DCOOH
Figure1shows the time-resolved spectra in the spectral region 3000−3600 cm−1 recorded at 1-μs intervals for the first 3 μs upon irradiation at 248 nm of a flowing mixture of O3/DCOOH (12/88, 0.100 Torr, 343 K); O(1D) was
gener-FIG. 1. Observed IR emission spectra of the reaction system O(1D) + DCOOH recorded at 1-μs intervals. The spectral resolution is 0.8 cm−1.
Partial pressures of O3and DCOOH are 12 and 88 mTorr, respectively. The assignments of vibration-rotational transitions are shown as stick diagrams for OH; the numbers correspond to Jand (v–v) represents the vibrational transition.
ated on photolysis of O3 to react with DCOOH. Sharp lines located in these regions are identified as the v = −1 tran-sitions of OH. Weak lines of OD in the region 2200−2600 cm−1 were also observed, but the intensities of OD lines were too small to provide reliable information. In addition to sharp lines of OH and OD, a broad feature that cov-ered a region 1800–2400 cm−1 was observed. We assigned this feature to the emission of the antisymmetric stretching (ν3) mode of vibrationally excited CO2, to be discussed in Sec.IV C.
For the assignment of our observed emission spectra, please refer to our previous paper.7 Most doublet e and
f lines are unresolved because of insufficient resolution. For J > 10.5, the e/f splitting exceeds 1 cm−1, resulting in broadened or partially resolved lines. In this experiment, we made no attempt to separate the populations of the e and f transitions, but used the total population for each vibration-rotational transition. To analyze these observed lines, we as-sumed a Gaussian line shape and performed curve fitting on each line, including overlapped ones.
The intensities of emission lines of OH and OD rise to-ward their maxima∼4 μs after irradiation of the flowing sam-ple at 248 nm. Because the initial concentration of DCOOH, ∼2.4 × 1015 molecule cm−3, was much greater than that of O3, the condition of pseudo-first-order reaction is valid. The rate coefficient for the reaction O(1D) + HCOOH is unre-ported. We expect the rate coefficient of the reaction to be slightly smaller than that of O(1D)+ CH
3OH, reported to be 5× 10−10cm3molecule−1s−1,30because of the smaller num-ber of H atoms. The corresponding pseudo-first-order rate co-efficient kI<1.2× 106s−1is in accord with the observed rise time for emission of OH.
The micropopulation of OH was determined from spec-tral lines integrated at 1-μs intervals after irradiation. Each vibration-rotational line in the P branch was normalized with the instrument spectral-response function and divided by its Einstein A coefficient31 to yield a relative population
P(v, J, F). In Fig.2, the logarithm of the micropopulation defined as P (v, J, F)/(2J+ 1), is plotted as a function of the rotational energy that is defined as the average of the e and f term values from which the vibrational term value is subtracted. The micropopulations of the F1 and F2 compo-nents are similar. The rotational distribution of OH (v= 1 and v= 2) is evidently not singly exponential; we thus fitted it with biexponential functions and derived rotational temper-atures TR for the low-J and the high-J components, respec-tively. For 0−1 μs, TRare 1470± 70 and 540 ± 40 K for the high-J and low-J components of v= 1, respectively, and 820 ± 60 and 430 ± 30 K for the high-J and low-J components of v= 2, respectively. For v= 3, because of the limited lev-els observed, we fitted them with only a single exponential function with TR= 250 ± 60 K. The bimodal rotational dis-tribution suggests formation of OH from at least two reaction channels.
To derive the nascent rotational temperatures, we esti-mated the quenching effects on measuring the rotational tem-perature as a function of time, as shown in Fig. S1 of the supplementary material.26 The correction factors for the av-erage energy in the 0−1 μs range to the nascent one are
FIG. 2. Semilogarithmic plots of the rotational populations of OH as a func-tion of the rotafunc-tional energy Erotin respective vibrational states formed from the O(1D)+ DCOOH reaction. The average period is 0−1 μs. Solid lines
represent the fitting; dashed lines represent a bimodal fitting.
approximately 1.03 ± 0.14 for the high-J component and 1.06 ± 0.15 for the low-J component, indicating that rota-tional quenching plays an insignificant role during the first 1 μs.
We obtained relative vibrational populations (v= 1):(v = 2):(v= 3) = 1.00:0.63:0.36 for the low-J component and (v = 1):(v = 2) = 1.00:0.43 for the high-J component. We assumed a Boltzmann distribution of vibrational popula-tion and estimated the populapopula-tion of level v = 0 to be 1.76 ± 0.10 times that of v= 1 for the low-J component on ex-trapolation from the populations of levels v >1. Similarly, the population of v = 0 was estimated to be 2.43 ± 0.30 times that of v= 1 for the high-J component. After renormal-ization, we derived relative vibrational populations (v = 0): (v= 1):(v= 2):(v= 3) = 46:27:17:10 for the low-J compo-nent of OH and (v= 0):(v= 1):(v= 2) = 63:26:11 for the high-J component of OH. As the correction for vibrational quenching is small, these values are taken as nascent
vibra-FIG. 3. Relative vibrational populations of OH and OD produced from (a) O(1D)+ DCOOH and (b) O(1D)+ HCOOD as a function of vibrational
energy. Populations in ν= 0 are derived by extrapolation. The data for OD from O(1D)+ DCOOH were unobtainable because of a poor signal-to-noise
ratio.
tional energies, as shown in Fig. 3(a). With an assumption of a Boltzmann distribution, the vibrational temperatures are 9700 ± 300 and 5800 ± 300 K, respectively, for the low-J and high-J components of OH. Using this distribution of vi-brational populations, we calculated the average vivi-brational energies Ev of OH to be 38 ± 4 and 20 ± 3 kJ mol−1 for the low-J and high-J components, respectively, as listed in Table I; these values should be taken as the lower limits of the vibrational energy because emission bands from higher vibrational levels might have some contributions but were too weak to observe.
The average rotational energies Er of OH are calculated to be 7± 2 and 25 ± 4 kJ mol−1, respectively, for the low-J and high-J components of OH. After correction for the ro-tational quenching according to the factors discussed above, the nascent rotational energies are 7± 2 and 26 ± 4 kJ mol−1 for the low-J and high-J components of OH, respectively, as listed in TableI.
TABLE I. Summary of experimental results for reactions O(1D)+ HCOOD/DCOOH.
O(1D)+ DCOOHa O(1D)+ HCOOD
OH OD
low-J high-J OH low-J high-J
TR(v= 1)b/K 580± 60 1530± 150 490± 60 450± 60 1180± 160 TR(v= 2)b/K 450± 30 830± 40 400± 60 380± 80 850± 110 TR(v= 3)b/K 250± 60 270± 30 350± 40 TR(v= 4)b/K 350± 50 ERb/kJ mol−1 7± 2 26± 4 8± 2 6± 2 25± 6 Tv/K 9700± 300 5800± 300 10 600± 400 9100± 300 7900± 500 Evc/kJ mol−1 38± 4 20± 3 40± 4 38± 4 22± 3 [OH]/[OD]c 0.16± 0.05
aUnable to determine OD because of small intensity. bNascent values, extrapolated from data at 0−5 μs to t = 0. cIncluding estimated population at v= 0; see text.
FIG. 4. Observed IR emission spectra of the reaction system O(1D)
+ HCOOD integrated for 1–5 μs. The spectral resolution is 0.8 cm−1. Partial
pressures of O3and HCOOD are 12 and 88 mTorr, respectively. The assign-ment of vibration-rotation transitions are given as stick diagrams; the number corresponds to Jand (v–v) represents the vibrational transition. B. IR emission of OH and OD from O(1D)+ HCOOD
To understand the relative reactivity of the insertion of O(1D) into the C−H and O−H bonds of HCOOH, we inves-tigate also the reaction of O(1D)+ HCOOD; a flowing mix-ture of O3/HCOOD (12/88, 0.100 Torr, 343 K) was irradiated at 248 nm. The time-resolved IR emission spectra observed after photolysis are shown in Fig.4; because observed lines are weak, we integrated the spectra for the period 0−5 μs to achieve a satisfactory ratio of signal to noise. Similar to the reaction of O(1D)+ DCOOH, two groups of sharp lines located in regions 2800–3600 and 2200–2600 cm−1 are as-signed as the v= −1 vibration-rotational transitions of OH and OD, respectively. In addition, a broad emission feature, assigned to the ν3emission band of vibrationally excited CO2, is observed in the region 1800–2400 cm−1, to be discussed in Sec.IV C.
The relative rotational micropopulations of the respective vibrational states of OH and OD are shown as a function of rotational energy in Fig.5. The rotational distributions of OH are nearly singly exponential, whereas those of OD are biex-ponential, similar to those of OH produced in the reaction of O(1D)+ DCOOH. Following the method similar to that de-scribed in Sec.IV A, we derived, for OH in the range 0–5 μs,
TR = 430 ± 60, 430 ± 30, and 270 ± 30 K for v= 1−3,
respectively. For OD in the range 0−5 μs, TR= 1100 ± 160, and 400 ± 50 K for the high-J and low-J components of v = 1, respectively, and TR = 750 ± 80 and 370 ± 40 K for the high-J and low-J components of v= 2, respectively. For
v= 3 and 4, we fit them with a single exponential function
with TR= 340 ± 30 and 320 ± 50 K, respectively, because of the limited levels observed. The average rotational energies of
FIG. 5. Semilogarithmic plots of the rotational populations of (a) OH and (b) OD as a function of rotational energy Erotin respective vibrational levels formed from the O(1D)+ DCOOH reaction. The average period is 0−5 μs.
Solid lines represent the fitting; dashed lines represent a bimodal fitting.
OH and low-J and high-J components of OD observed in the period 0−5 μs are thus calculated to be 7 ± 2, 5 ± 2, and 22 ± 4 kJ mol−1, respectively. Using data of OH from O(1D) + DCOOH, the correction factors for the average energy in the 0−5 μs range to the nascent ones are approximately 1.10 ± 0.26 for the high-J component and 1.08 ± 0.29 for the
low-J component. We hence derive the nascent rotational energy
to be 8 ± 2 kJ mol−1 for OH, 6 ± 2 and 25 ± 6 kJ mol−1 for the low-J and high-J components of OD, respectively, as listed in TableI.
Similarly, the relative vibrational populations (v= 1):(v = 2):(v= 3) = 1.00:0.66:0.38 for OH, (v= 1):(v = 2):(v = 3):(v = 4) = 1.00:0.68:0.40:0.33 for the low-J compo-nent and (v = 1):(v = 2) = 1.00:0.64 for the high-J com-ponent of OD were derived. Assuming a Boltzmann distribu-tion of vibradistribu-tional populadistribu-tions, we estimated the populadistribu-tion of level v= 0 to be 1.49 ± 0.21 and 1.59 ± 0.20 times that
of level v= 1 for the low-J and high-J components of OD on extrapolation from the populations of levels v>1. The pop-ulation of level v= 0 was estimated to be 1.72 ± 0.17 times that of level v= 1 for OH. After renormalization, we derived relative vibrational populations (v= 0):(v= 1):(v= 2):(v = 3) = 45:27:18:11 for OH, (v = 0):(v = 1):(v = 2):(v = 3):(v= 4) = 38:26:17:11:8 and (v= 0):(v= 1):(v= 2) = 49:32:19 for the low-J and high-J components of OD, respectively, as shown in Fig. 3(b). With an assumption of a Boltzmann distribution, the vibrational temperatures are 10 600± 400 K for OH and 9100 ± 300 and 7900 ± 500 K for the low-J and high-J components of OH, respectively. Using this distribution of vibrational populations, we calculated the average vibrational energies to be 40± 4 kJ mol−1for OH and 38± 4 and 22 ± 3 kJ mol−1for the low-J and high-J compo-nents of OD, respectively, as listed in Table I; these values should be taken as the lower limits.
The ratio of total populations of OH (v= 1−3) to those of OD (v= 1−4) from O(1D)+ HCOOD are derived to be (14 ± 3)/(86 ± 5), with the low-J component to the high-J component of OD ∼ 22/78. If we take into account the es-timated populations of the v= 0 levels of OH and OD, the ratio of total populations of OH (v= 0−3) to those of OD(v = 0−4) becomes (14 ± 3)/(86 ± 5) = 0.16 ± 0.05, with the low-J component to the high-J component of OD ∼25/75. This ratio is much smaller than the value (37± 9)/(63 ± 9) = 0.59 ± 0.14 reported for the reaction of O(1D)+CH
3OD,7 but if we consider the number of C−H bonds to be three in CH3OD and one in HCOOD, the ratios observed in both re-actions are consistent.
C. Emission spectra of CO2from O(1D)+ HCOOH
By comparison with the CO2emission spectra observed in the reaction O(1D)+ CO2 (Ref. 32) we assigned the ob-served broad feature in the range 1800−2400 cm−1as the ν
3 emission of highly internally excited CO2. An emission spec-trum of CO2recorded from 0 to 5 μs after irradiation of the O3/HCOOH mixture at 248 nm is also shown in Fig.6; this feature shows a maximum near 2280 cm−1 with a long tail extending toward 1800 cm−1. At a later time, the long tail disappeared completely and the remaining feature agreed sat-isfactorily with the P and R branches of CO2, with the band center located near 2327 cm−1corresponding to the band ori-gin of the transition (v3= 1) → (v3= 0) of CO2at 300 K.
We simulated the observed feature with an approximate method that we employed previously for analysis of the ν3 emission of highly vibrationally excited CO2produced from O(1D) + CO2.32 We introduced a polyad quantum num-ber vb= 2v1+ v2 with degeneracy gb to describe the vi-brational levels of CO2 as (vb, v3); v1 and v2 are quan-tum numbers of strongly Fermi-coupled vibrational modes ν1 and ν2, respectively. The emission intensity of the transition (vb, v3)→ (vb, v3− 1), I [(vb, v3)→ (vb, v3− 1)], is
pro-portional to ω[(vb, v3)→ (vb, v3− 1)] N(vb, v3) A[(vb, v3) → (vb, v3− 1)], in which ω is the transition frequency for (vb, v3)→ (vb, v3− 1), N(vb, v3) is the population of the (vb, v3) state, and A is the Einstein coefficient that is assumed
FIG. 6. Comparison of emission of CO2 observed in the reaction O(1D) + HCOOD (symbols o) with those deconvoluted with two components with
E∗= 8000 and 26 500 cm−1and a population ratio 53:47 (a); the contribu-tion of each component is also shown. The simulated vibracontribu-tional distribucontribu-tions based on statistical distribution of internal energies as discussed in the text are shown in (b).
to be proportional to v3 but independent of vb. To estimate the population distribution N (vb, v3) in the (vb, v3) vibrational state, we assumed that an energy E∗is partitioned statistically into the rotation and vibrational degrees of freedom of CO2 and the relative translational degree of freedom of CO2with its counter products, as described previously.32
The observed feature was approximately decomposed into two components with the statistically partitioned energy
E∗= 8000 cm−1= 96 kJ mol−1and E∗= 26 500 cm−1= 317 kJ mol−1, respectively, as shown in Fig.6(a), with a popula-tion ratio∼53:47. The population distributions of these two components are shown in Fig.6(b).
D. Potential-energy surfaces and reaction mechanism Formic acid possesses two stable geometric conformers in the gas phase—cis and trans. The ground state minimum has a planar trans-conformation with the two hydrogen atoms
trans to the C−O bond.33The trans-conformer is predicted to be∼17 kJ mol−1more stable than the cis-structure, in agree-ment with the experiagree-mental value of 16 kJ mol−1.34 In this calculation, we considered only the reaction of trans-HCOOH with O(1D).
After an exhaustive search, we established a potential-energy surface with 11 product channels PR1−PR11 in which the major paths led to products PR6 (CO2+ H2O), PR7 [OH + HC(O)O], and PR8 (OH + HOCO); the minor paths led to PR4 (H2+ CO3), PR5 (CO+ H2O2), and other products. The major product channels are depicted in Fig.7; a detailed PES including other minor channels is available in Fig. S2 of the supplementary material.26 The optimized geometries of key intermediates and transition states are presented in Figs. 8 and 9, respectively; the geometries of other related species are shown in Fig. S3 of the supplementary material.26 The transition states are denoted as Tx/y or TxPz in which x and y designate the intermediates (ISx and ISy) and Pz
FIG. 7. Simplified potential-energy scheme of the reaction O(1D) + HCOOH. (a) Insertion reactions computed with the CCSD(T)/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p) + ZPVE method. (b) H-abstraction reactions computed with the MRCI(8,8)//CASSCF(8,8)/6-311++G(3df,2p) method. Energy is in kJ mol−1.
designates the product (PRz) with which the transition state is associated.
The direct insertion into the C−H bond of HCOOH occurs without an intrinsic transition state to form a sta-ble intermediate IS8, cis-cis-HOC(O)OH, with energy of −680.7 kJ mol−1 relative to the reactants; this energy is con-firmed with the VTST MEP scan and is also in agreement with previous related work indicating that the O(1D) atom can in-sert directly into a C−H bond with large exothermicity.7,35,36 Theoretical and experimental investigations37–39showed that IS8 has three structures of which the cis-cis is the most stable; the barrier for interconversion from cis-trans (∼6 kJ mol−1 greater in energy than cis-cis) to cis-cis conformers is only ∼33 kJ mol−1. The trans-trans conformer has energy ∼38 kJ mol−1 above that of the cis-cis conformer. IS8
(cis-cis) and IS8 (cis-trans) can thus be regarded as one
inter-mediate. Additional insertion reactions occur via two com-plexes in which O(1D) attacks the O atom in the OH group
to form complex IS1, HC(O)O(O)H, and the O atom in the C=O group to form complex IS9, OOC(H)OH, with ener-gies of−94.6 and −169.5 kJ mol−1, respectively, relative to the reactants. Atoms in these complexes can migrate to form other intermediates or complexes; the energy-rich interme-diates can undergo dissociation to yield products. For ex-ample, in IS1 the H atom in the OH group can migrate to the added O atom via T1/2 (−75.7 kJ mol−1) to form IS2 (HC(O)OOH, −341.0 kJ mol−1), or to the carbonyl O atom via T9/1 (14.6 kJ mol−1) to form IS9, or to the C atom via T1P1 (21.3 kJ mol−1), followed by C−O bond rupture to yield PR1 (H2CO+ O2,−190.0 kJ mol−1).
1. Formation of dehydration products PR6 (CO2+ H2O)
Several paths lead to PR6. O(1D) can insert directly into the C−H bond of HCOOH to form IS8, cis-cis-HOC(O)OH,
FIG. 8. Geometries of representative reactants and intermediates of the O(1D)+ HCOOH reaction optimized with the B3LYP/6-311++G(3df,2p) method.
Bond length in Å and bond angle in degree.
with a large exothermicity (−680.7 kJ mol−1), followed by dehydration via T8P6 (−500.4 kJ mol−1) to produce PR6 (CO2 + H2O;−711.7 kJ mol−1). This process is clearly the most feasible because the first step to form IS8 is barrierless and highly exothermic, and the second step IS8→ PR6 pro-ceeds via the transition state T8P6 with the lowest barrier. In addition, PR6 can also be produced on O(1D) attacking the C=O group of HCOOH without a barrier to give IS9, which then transforms to a triangular ring intermediate IS6 (trans-HOC(O2)H;−277.0 kJ mol−1) via T9/6 (−145.2 kJ mol−1). IS6 subsequently transforms to IS5 (cis-HOC(O2)H;−297.1 kJ mol−1) via state T5/6 (−221.3 kJ mol−1), and IS8 via T5/8 (−228.4 kJ mol−1). The third path involving decomposition of IS2 to PR6 via T2P6 (−119.7 kJ mol−1) is less important because it proceeds via a transition state with much greater energy. In summary, two main paths yielding PR6 are: RA
→ IS8 → PR6 and RA → IS9 → IS6 → IS5 → IS8 → PR6; when O(1D) reacts with HCOOD or DCOOH, PR6 becomes CO2+ HDO.
2. Formation of radical products PR7 (OH+ HC(O)O) and PR8 (OH and HOCO)
PR8 (OH+ HOCO, −227.6 kJ mol−1) are produced via several paths. First, IS8 dissociates directly to PR8 without a barrier. The product HOCO has two conformers, cis and
trans; cis-HOCO can readily isomerize to trans-HOCO that
lies ∼7.9 kJ mol−1 below cis-HOCO,40 so the process IS8 → cis-HOCO + OH → trans-HOCO + OH can be regarded as entailing one step. Although the energy of PR8 is much greater than T8P6 (−500.4 kJ mol−1), the formation of PR8 is competitive with formation of PR6 because IS8→ PR8 is
FIG. 9. Geometries of the representative transition states of the O(1D)+ HCOOH reaction optimized with the B3LYP/6-311++G(3df,2p) method. Bond
length in Å and bond angle in degree.
barrierless. Other paths, such as IS1→ T1P8 (10.0 kJ mol−1) → PR8 (Fig. S2 in the supplementary material),26are uncom-petitive because of greater barriers. The two major paths for the formation of PR8 (OH + HOCO) are thus RA → IS8 → PR8 and RA → IS9 → IS6 → IS5 → IS8 → PR8. The two H atoms in IS8 play the same role; when RA involves HCOOD or DCOOH, PR8 hence represents both products OH + DOCO and OD + HOCO.
PR7 (OH + HC(O)O, −168.2 kJ mol−1) is produced mainly from IS1 (−94.6 kJ mol−1), which readily isomerizes to form IS2 (−341.0 kJ mol−1) via T1/2 (−75.7 kJ mol−1); the O−O bond in IS2 ruptures to yield PR7. IS2 can also iso-merize to form IS3 or IS5 via T2/3 (−23.0 kJ mol−1) or T2/5 (−166.9 kJ mol−1), respectively, or dissociate to yield other products: PR4 (CO3+ H2), PR5 (CO+ H2O2), and PR6 (CO2
+ H2O) via T2P4, T2P5, and T2P6 with relative energies of −28.5, −76.6, and −119.7 kJ mol−1, respectively (Fig.7 and Fig. S2 in the supplementary material).26These reactions compete unfavorably with the process IS2→ PR7 that occurs directly with loose variational transition states along the path of least energy. The two H atoms in IS2 have distinct roles; when RA involves HCOOD, PR7 becomes OD+ HC(O)O. In contrast, when RA involves DCOOH, PR7 becomes OH + DC(O)O.
3. Formation of other minor products
Minor decomposition products of IS8 and IS2 include PR4 (CO3 + H2, −243.5 kJ mol−1), formed from IS8 via T8P41 (−120.9 kJ mol−1) and PR5 (CO
−325.1 kJ mol−1), formed from IS2 via T2P5 (−76.6 kJ mol−1). Two additional minor products are also shown in Fig.7; they are much less important because of the greater energies of the transition states. PR1 (H2CO + O2,−190.0 kJ mol−1) is formed from IS1 (−94.6 kJ mol−1) and IS7 (−160.2 kJ mol−1) via T1P1 (21.3 kJ mol−1) and T7P1 (79.9 kJ mol−1), in which the H atom migrates from OH to a neighboring C atom. PR2 (H2O + cyc-CO2, −127.2 kJ mol−1) is produced from the migration of the H atom from CH in IS6 (trans-HOC(O2)H) to the neigh-boring OH group via T6P2 (55.2 kJ mol−1). Other minor product channels are shown in Fig. S2 of the supplementary material.26
4. Direct H abstraction reactions
The direct H-abstraction might proceed via two channels: attacking the OH group to form HC(O)O+ OH (HO abstrac-tion) or attacking the CH group to form HOCO+ OH (HC abstraction). As shown in Fig.7(b), both abstraction reactions occur via shallow complexes (Com1 and Com2) and transi-tion states (TS1 and TS2) with relative energies of 9.6 and −2.1 kJ mol−1, respectively. The H
O abstraction channel is unimportant because of the large barrier. The HCabstraction channel with a smaller barrier is more important, but its con-tribution still competes less successfully with the major chan-nels involving IS2 and IS8 because the energy of the transition state of the former channel is much greater than those of the transition states of the latter. Furthermore, both abstraction reactions have tighter transition-state structures than those in the processes described in Secs.IV D 1–IV D 3.
Yang et al. provided experimental and theoretical evidence that, in the reaction of O(1D) with CHD
3, the complex-forming reaction actually proceeds via a trapped abstraction mechanism, rather than an insertion mechanism as has long been thought.41 Our MRCI calculations for the direct abstraction reactions did locate similar but much weaker pre-reaction complexes. Because the yields of OH from the abstraction channels are too small to compete with those from the insertion/decomposition channels, we are unable to characterize the importance of this trapped abstraction mechanism with experiments.
E. Calculations of rate coefficients 1. Kinetics of O(1D) reaction with HCOOH
According to the predicted PES, the energetically favored channels in the reaction of O(1D)+ HCOOH are summarized below:
O(1D)+ HCOOH → IS8∗(C− H insertion)
→ CO2+ H2O, (1)
→ OH + HOCO, (2)
→ CO3+ H2, (3)
O(1D)+ HCOOH → IS1∗→ IS2∗(O− H insertion)
→ OH + HC(O)O, (4)
→ CO2+ H2O, (5)
in which ISn∗denotes an internally activated intermediate and reactions(3)and(5)are minor.
The initial average kinetic energy of O(1D) that is pro-duced upon photolysis of O3at 248 nm was determined to be 36 kJ mol−1in the laboratory coordinates.42 In the center-of-mass coordinates of the collision of O(1D) with HCOOD or DCOOH, the kinetic energy is estimated to be 26.9 kJ mol−1. The reactants thus have excess energy ∼27 kJ mol−1. This amount of energy is included in the calculations for fragmen-tation.
As discussed above, the initial association path via a di-rect C−H insertion forms an excited IS8 intermediate carry-ing internal energy as much as 27 + 681 = 708 kJ mol−1 and produces various products H2O, OH, and H2 (reactions (1)–(3)). This process has no well-defined transition state; its potential-energy function for association, computed variation-ally to cover the C−O separations from 1.4 to 5.0 Å at the CASPT2//CASSCF level, was fitted to a Morse function with
β = 2.96 Å−1. The internal rotation of the OH group in
cis-cis-HOC(O)OH (IS8) has a barrier of 39.7 kJ mol−1. This in-ternal rotation gives rise to a torsional vibrational mode near 197 cm−1, which is treated as a hindered rotor.
The excited IS2 intermediate, produced via IS1∗, carries internal energy as much as 27+ 341 = 368 kJ mol−1. For the initial association channel of O(1D)+ HCOOH→ IS1∗, we used a Morse potential with β = 2.64 Å−1. The rate coeffi-cients were calculated with the unified statistical formulation of Miller,43 taking into account the multiple reflection cor-rections above the shallow wells of the pre-reaction complex IS2 on treating T1/2 as the inner TS and the VTS for the pre-complex formation as the outer TS.
The rate coefficients of important product channels via IS8 and IS2 for reactions O(1D)+ HCOOH, HCOOD, and DCOOH are listed in TableII. At T= 350 K and P = 0.1 Torr, the internally-excited adducts readily undergo H-migration and fragmentation producing various products; these reac-tions are competitive with the collisional quenching process that depends on pressure. The rate coefficients for the initial association path of O(1D)+ HCOOH → IS8∗at 350 and 298 K are predicted to be 9.6 and 9.1× 10−11cm3molecule−1s−1, respectively. The rate coefficients for O(1D) + HCOOH → IS2∗ at 350 and 298 K are predicted to be 7.3 and 7.0 × 10−11cm3molecule−1s−1. As discussed in Sec.IV D, the contributions from the abstraction channels of H atoms on the O−H and C−H moieties of HCOOH to form OH are negli-gible because of their tighter transition states with energies of 9.6 (TS1) and−2.1 (TS2) kJ mol−1, respectively, relative to the reactants:
O(1D)+ HCOOH → Com1(HOabstraction)
→ OH + HC(O)O, (6)
O(1D)+ HCOOH → Com2(HCabstraction)
→ OH + HOCO. (7)
Rate coefficient k7 = 1.5 × 10−11 cm3molecule−1s−1 for the HC-abstraction at 350 K is much greater than that for
TABLE II. Rate coefficients (in cm3molecule−1s−1) predicted for important reactions of O(1D)+ HCOOH with excess energy E∗(in kJ mol−1) based on
potential-energy surfaces predicted with the CCSD(T)/6-311++G(3df,2p)// B3LYP/6-311++G(3df,2p) method.
T= 350 Ka Reaction T= 298 Ka Products E∗= 0 E∗= 0 E∗= 12.6 E∗= 26.0 k1 IS8∗→ CO2+ H2O 5.12× 10−11 5.32× 10−11 4.95× 10−11 4.66× 10−11 k2 IS8∗→ OH + HOCO 4.03× 10−11 4.30× 10−11 4.63× 10−11 5.02× 10−11 k3 IS8∗→ CO3+ H2 2.52× 10−16 2.92× 10−16 4.73× 10−16 7.67× 10−16 k4 IS2∗→ OH + HC(O)O 7.01× 10−11 7.30× 10−11 7.52× 10−11 7.74× 10−11 k5 IS2∗→ CO2+ H2O 7.17× 10−15 7.86× 10−15 1.07× 10−14 1.44× 10−14 k6 OH+ HC(O)O (HO-abs) 3.99× 10−14 3.86× 10−14 . . . . k7 OH+ HOCO (HC-abs) 1.55× 10−11 1.48× 10−11 . . . .
aRate coefficients are independent of pressure for P≤ 20 atm.
the HO-abstraction, k6 = 3.9 × 10−14 cm3molecule−1s−1, but contributes only∼8% of the total rate coefficient. Other channels have rate coefficients smaller than 4 × 10−14 cm3molecule−1s−1. The predicted total rate coefficients for reaction of O(1D) + HCOOH at 298 K is 1.8 × 10−10 cm3molecule−1s−1 for pressure less than 20 atm. This re-sult is in accord with the rate coefficient of reaction O(1D) + CH3OH reported as 5.1× 10−10cm3molecule−1s−1;30this reaction involves three H atoms on the carbon atom and one on the oxygen atom as compared with one H atom on the carbon atom and one on the oxygen atom for the reaction of O(1D)+ HCOOH.
The rate coefficients for the unimolecular decomposition of excited intermediate IS8∗ at varied energies, presented in Fig.10, indicate that reactions(1)and(2)that produce CO2 + H2O and OH+ HOCO, respectively, are competitive, but reaction (3)for the production of CO3 + H2 is unimportant in the energy range of interest. According to Fig.10, reaction (1) dominates up to E ∼= 700 kJ mol−1; above that, reaction (2) becomes more important. The rate coefficients of these two channels are similar, with <50% variations, for excess energy 0−63 kJ mol−1. The rate coefficients for the unimolec-ular decomposition of IS2∗are shown in Fig.11; channel IS2∗ → OH + HC(O)O, reaction(4), is much more important than
FIG. 10. Predicted rate coefficients k1−k3of the unimolecular decomposi-tion channels of HOC(O)OH (IS8) as a funcdecomposi-tion of energy.
the channel for formation of CO2 + H2O, reaction (5), be-cause of the much larger barrier for the latter. Based on the calculated rate coefficient for the formation of IS8, IS2, and the ratios of unimolecular rate coefficients for each decompo-sition channel, we derived rate coefficients for each product channel at 350 K and below 20 atm with excess energies 0, 12.6, and 26.0 kJ mol−1, as listed in TableII; the two abstrac-tion channels are also listed for comparison.
2. Formation of OH and OD from O(1D)+ HCOOD Taking into account of the isotopic effects, we calculated rate coefficients for the unimolecular decomposition of ex-cited intermediates IS8∗ and IS2∗ at varied energies in the reaction O(1D) + HCOOD, as presented in Figs. S4 and S5, respectively, available in the supplementary material.26 The bimolecular rate coefficients for each product channel of O(1D)+ HCOOD at 350 K and below 20 atm, with excess en-ergies 0, 12.6, and 26.0 kJ mol−1, are listed in TableIII; those at 298 K with no excess energy are also listed for comparison. The following paths are important for O(1D)+ HCOOD: O(1D)+ HCOOD → HOC(O)OH (IS8∗,C− H insertion)
→ CO2+ HDO, (8)
FIG. 11. Predicted rate coefficients k4and k5of the unimolecular decompo-sition channels of HC(O)OOH (IS2) as a function of energy.
TABLE III. Rate coefficients (in cm3molecule−1s−1) predicted for major channels of production of OH/OD and CO
2in reactions O(
1D)+ HCOOD and
DCOOH with excess energy E∗(in kJ mol−1) based on potential-energy surfaces predicted with the CCSD(T)/6-311++G(3df,2p)// B3LYP/6-311++G(3df,2p) method. T= 350 Ka T= 298 Ka Reaction E∗= 0 E∗= 0 E∗= 12.6 E∗= 26.0 O(1D)+ HCOOD k8 IS8∗→ CO2+ HDO 2.18× 10−11 2.27× 10−11 2.06× 10−11 1.89× 10−11 k9 IS8∗→ OH + DOCO 1.56× 10−11 1.66× 10−11 1.75× 10−11 1.87× 10−11 k10 IS8∗→ OD + HOCO 1.51× 10−11 1.61× 10−11 1.69× 10−11 1.80× 10−11 k11 IS2∗→ OD + HC(O)O 7.02× 10−11 7.34× 10−11 7.40× 10−11 7.63× 10−11 k12 IS2∗→ CO2+ HDO 7.89× 10−15 8.74× 10−15 1.17× 10−14 1.59× 10−14 O(1D)+ DCOOH k13 IS8∗→ CO2+ HDO 2.15× 10−11 2.22× 10−11 2.01× 10−11 1.79× 10−11 k14 IS8∗→ OD + HOCO 2.20× 10−11 2.33× 10−11 2.44× 10−11 2.53× 10−11 k15 IS8∗→ OH + DOCO 2.41× 10−11 2.41× 10−11 2.53× 10−11 2.62× 10−11 k16 IS2∗→ OH + DC(O)O 7.02× 10−11 7.43× 10−11 7.47× 10−11 7.71× 10−11 k17 IS2∗→ CO2+ HDO 3.28× 10−15 3.11× 10−15 4.14× 10−14 6.01× 10−14
aRate coefficients are independent of pressure for P≤ 20 atm.
→ OH + DOCO (fission of new C−O bond), (9) → OD + HOCO (fission of original C−O bond), (10) O(1D)+ HCOOD → IS1∗
→ HC(O)OOH (IS2∗,O−D insertion)
→ OD + HC(O)O (fission of O−O bond), (11)
→ CO2+ HDO. (12)
The predicted results indicate one production channel for OH (rate coefficient k9) and two for OD (k10and k11) in O(1D) + HCOOD. At 350 K with the center-of-mass kinetic energy of 26 kJ mol−1, the rate coefficients are k9 = 1.9 × 10−11 cm3molecule−1s−1 for the production of OH and k
10 = 1.8 × 10−11 and k
11 = 7.6 × 10−11 cm3molecule−1s−1 for the production of OD. Thus, for O(1D) + HCOOD, the ratio of kOH/kOD = (k9)/(k10 + k11) is 0.20, which is in good agreement with the experimental value of [OH]/[OD]= 0.16 ± 0.05. The predicted ratios kOH/kODas a function of excess energy are presented in Fig.12; these values are insensitive to the excess energy carried by the O(1D) atom. For example, at no excess energy the predicted ratio of kOH/kODis 0.185. Ra-tio kOH/kODis independent of pressure below 20 atm because of the large energy content of the adducts, similar to the case of O(1D)+ CH3OH.7
In the O(1D)+ HCOOD reaction, the rotational distri-bution of the product OD is bimodal, whereas that of OH is of Boltzmann-like. The bimodal rotational distribution of OD is consistent with the model that predicts OD be pro-duced via two channels, reactions(10)and(11). The former resulted from the insertion of O(1D) into the C−H bond to form IS8, followed by fission of the “original” OD; the lat-ter resulted from the insertion of O(1D) into the O−D bond to form IS2, followed by fission of OD. We expect that the
OD produced from the latter channel via IS2 has greater ro-tational excitation because the torque angle for OD fission in IS2 is much greater than that of IS8 (Fig. 8); a similar sit-uation was observed for O(1D) + CH
3OD.7 For the chan-nels from IS8, HOC(O)OD, products OD+ HOCO and OH + DOCO have more excess energy (227.6 kJ mol−1) than that of products OD+ HC(O)O from IS2 (168.2 kJ mol−1); prod-uct OD+ HOCO resulted from fission of the original C−O bond, whereas OH + DOCO was produced from fission of the newly formed C−O bond. Our observation of a similar vibrational energy for OH than for the low-J component of OD in the reaction of O(1D)+ HCOOD might indicate that IVR was nearly complete before the bond fission because OD was indirectly activated through IVR from the locally excited intermediate HOC(O)OD produced from the C−H insertion. The Boltzmann-like distribution of OH is consistent with a single channel for the production of OH from reaction(9).
FIG. 12. Predicted ratios of kOH/kODfor reactions of O(1D)+ HCOOD
(symbol ) and O(1D)+ DCOOH (symbol o) as a function of excess
en-ergy Eexcrelative to the reactants at 350 K.
3. Formation of OH and OD from O(1D)+ DCOOH The rate coefficients for the unimolecular decomposi-tion of excited intermediates IS8∗and IS2∗at varied energies in the reaction O(1D)+ DCOOH are presented in Figs. S6 and S7 of the supplementary material, respectively.26The bi-molecular rate coefficients for each product channel of O(1D) + DCOOH at 350 K and below 20 atm, with excess energies 0, 12.6, and 26.0 kJ mol−1, are listed in TableIII; those at 298 K with no excess energy are also listed for comparison.
The pathways for O(1D)+ DCOOH can be summarized as follows:
O(1D)+ DCOOH → DOC(O)OH (IS8∗,C−D insertion)
→ CO2+ HDO, (13)
→ OD + HOCO (fission of new C−O bond), (14) → OH + DOCO (fission of original C−O bond), (15) O(1D)+ DCOOH → IS1∗
→ DC(O)OOH (IS2∗,O−H insertion)
→ OH + DC(O)O (fission of O−O bond), (16)
→ CO2+ HDO. (17)
At 350 K with the center-of-mass kinetic energy of 26 kJ mol−1, the rate coefficients are k15 = 2.6 × 10−11and
k16 = 7.7 × 10−11 cm3molecule−1s−1 for the production of OH and k14 = 2.5 × 10−11 cm3molecule−1s−1 for the production of OD. For reaction O(1D) + DCOOH, the ra-tio of kOH/kOD= (k15 + k16)/(k14) is thus 4.08. Predicted ra-tios kOH/kODas a function of kinetic energy are presented in Fig.12; they are insensitive to the excess energy carried by the O(1D) atom. For example, at no kinetic energy the predicted ratio of kOH/kODis 4.2. The experimental value of [OH]/[OD] is unavailable because the OD signal was too weak to yield reliable data; [OD] is much smaller than [OH], and the Ein-stein coefficients of OD are smaller than those of OH by more than a factor of four.
The rotational distribution of OH was found to be bi-modal, consistent with the model that OH is produced via two channels, reactions (15)and(16). The former resulted from insertion of O(1D) into the C−D bond to form IS8, followed by fission of the “original” OH, whereas the latter resulted from insertion of O(1D) into the O−H bond to form IS2, fol-lowed by fission of OH. We expect that OH produced from the latter channel via IS2 has greater rotational excitation be-cause the torque angle for OD fission in IS2 is much greater than that of IS8 (Fig.8); a similar situation was observed for O(1D)+ CH3OD.7
4. Formation of CO2
The major channel for formation of CO2 is predicted to be from IS8 (C−H insertion) via T8P6 at −500.5 kJ mol−1. The formation of CO2is unaffected by the deuterium isotopic
substitution; reaction products (8) and(13) are hence iden-tical. Products from reactions (12)and (17) via IS2 (O−H or O−D insertion) and T2P6 at −119.7 kJ mol−1 are negli-gible because of the large barrier, but the product of reaction (11)or(16), HC(O)O or DC(O)O, might undergo a secondary decomposition to form CO2 because the barrier is less than 1.3 kJ mol−1. Secondary decomposition of HOCO or DOCO, produced in reaction(10)and(15), is less likely because of a large barrier of 109.2 kJ mol−1with TP8P11 lying at−118.4 kJ mol−1. Hence, the decomposition of the C−H insertion in-termediate IS8 and the secondary decomposition of HC(O)O that is produced from the decomposition of O−H insertion intermediate IS2 are two major channels for the formation of CO2. If we assume that the yield of secondary decomposi-tion of HC(O)O to H+ CO2is large, CO2produced from this channel is expected to be dominant.
Assuming that the translational energy is mainly con-tributed by the downhill slope from the transition state, we estimate the translational energy of H+ CO2 to be approx-imately the energy difference between TP7P11 and PR11, 64 kJ mol−1. Considering the exothermicity for the formation of PR11 (OH+ H + CO2), 231 kJ mol−1, and the estimated translational energy of 64 kJ mol−1, our observed internal en-ergy of OH (OD), 46 (47) kJ mol−1for the high-J component observed in O(1D)+ DCOOH/HCOOD, implies that the in-ternal energy of CO2might be as large as∼120 kJ mol−1, con-sistent with the observed low-energy component of CO2with
E∗= 8000 cm−1(96 kJ mol−1). The predicted C−O bond of length∼1.176 Å in TP7P11 is slightly greater than the bond length of 1.160 Å for CO2, also indicating a moderate vibra-tional excitation of the CO2 product from this channel. The relative population of this component is∼53%.
For the minor channel from the decomposition of IS8, taking the exothermicity for formation of PR6 (H2O+ CO2) to be 712 kJ mol−1, and assuming that the translational en-ergy is contributed mainly from the enen-ergy difference of 211 kJ mol−1 between T8P6 and PR6, ∼501 kJ mol−1 en-ergy is partitioned among the internal energies of CO2 and H2O. The quantum-chemical calculations predicted struc-ture of the transition state T8P6 with a H2O moiety with a bond angle of 119.8◦ and bond lengths of OH as 1.247 and 0.965 Å, and a CO2 moiety with bond angle 145.8◦ and bond lengths of CO as 1.257 and 1.167Å, respec-tively (Fig. 9). Considering the equilibrium bond lengths of 0.958 Å for H2O and 1.160 Å for CO2 and the linear struc-ture of CO2, we expect that CO2 be more vibrationally ex-cited than H2O. The observed high-energy component of CO2 with E∗ = 26 500 cm−1 (317 kJ mol−1) is consistent with this model. The relative population of this component is∼47%.
V. CONCLUSION
On monitoring the IR emission of products OH and OD with a step-scan Fourier-transform infrared spectrometer, we investigated the reactions O(1D)+ HCOOD/DCOOH. In the reaction O(1D)+ HCOOD, product OD showed bimodal ro-tational distributions with nascent average roro-tational ener-gies 6 ± 2 and 25 ± 6 kJ mol−1 and vibrational energies
38 ± 4 and 22 ± 3 kJ mol−1, respectively, whereas prod-uct OH showed a Boltzmann-like rotational distribution with nascent average rotational energies 8± 2 kJ mol−1and vibra-tional energies 40± 4 kJ mol−1. The product ratio [OH]/[OD] was estimated to be 0.16 ± 0.05. For reaction O(1D) + DCOOH, product OH showed a bimodal rotational distri-bution with nascent average rotational energies 7 ± 2 and 26 ± 4 kJ mol−1 and vibrational energies 38 ± 4 and 20 ± 3 kJ mol−1, respectively. Lines of OD were too weak to provide reliable information.
In both reactions, similar unresolved internally excited
ν3 emission of CO2 was observed. The emission band was deconvoluted to two components that were simulated accord-ing to a statistical partition of excess energy; the low-energy component with E∗ = 96 kJ mol−1 is dominant with ∼53% population, whereas the high-energy component with E∗ = 317 kJ mol−1has∼47% population.
The experimental observations are explicable according to a mechanism of O(1D)+ HCOOH that involves two in-sertion intermediates, HOC(O)OH (IS8, from C−H inser-tion) and HC(O)OOH (IS2, from O−H inserinser-tion), and three major decomposition channels, reactions (1) and (2) from IS8 to produce CO2 + H2O and OH + HOCO, respec-tively, and reaction(4)from IS2 to produce OH+ HC(O)O. The internally excited HC(O)O further decomposed to H + CO2. In reaction(2), upon insertion of O(1D) into the C−H bond to form HOC(O)OH, subsequent fission of the newly formed C−O bond and fission of the “original” C−O bond in HOC(O)OH produced vibrationally excited OH with similar vibrational excitation, indicating nearly completed IVR. In-sertion of O(1D) into the O−H bond to form HC(O)OOH fol-lowed by fission of the O−O bond, reaction(4), produced OH with greater rotational excitation, likely due to a large torque angle during dissociation. In the reaction O(1D)+ HCOOD, the observed ratio of [OH]/[OD]= 0.16 ± 0.05 is near a value of 0.20 predicted with theory. The two abstraction channels are unimportant.
For the production of CO2, the high-energy compo-nent corresponded to direct decomposition of the C−H in-sertion intermediate HOC(O)OH (IS8), whereas the low-energy component was due to secondary decomposition of internally excited HC(O)O that was produced from decom-position of the O−H insertion intermediate HC(O)OOH (IS2).
Even though the observed [OH]/[OD] indicates a signif-icant preference of the formation of OH from the hydroxyl moiety over the CH moiety of HCOOH, the theoretical pre-dictions indicate that the rate coefficients for O(1D) to at-tack the CH moiety and the OH moiety of HCOOH are sim-ilar, with the former more favored in O(1D)+ HCOOH by ∼30% and the latter more favored in O(1D)+ HCOOD or DCOOH by ∼40%. The reason for production of more OH from the hydroxyl site is partly that, upon insertion of O(1D) into the C−H bond to form HOC(O)OH, subsequent dissoci-ation occurred for both the newly formed OH and the orig-inal OH group, and partly that this C−H insertion interme-diate HOC(O)OH also decomposed to form CO2 and H2O, whereas the decomposition of O−H insertion intermediate HC(O)OOH produced mainly OH+ HC(O)O.
ACKNOWLEDGMENTS
Ministry of Science and Technology of Taiwan (Grant No. MOST103-2745-M-009-001-ASP) and the Ministry of Education, Taiwan (“Aim for the Top University Plan” of National Chiao Tung University) supported this work. The National Center for High-performance Computing provided computer time and facilities. M.C.L. acknowledges the sup-port from the NSC for the distinguished visiting professorship at National Chiao Tung University in Hsinchu, Taiwan.
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