Cavity Ringdown Spectroscopy of the Hydroxy-Methyl-Peroxy Radical

Article pubs.acs.org/JPCA

Cavity Ringdown Spectroscopy of the Hydroxy-Methyl-Peroxy Radical Matthew K. Sprague, Laura A. Mertens, Heather N. Widgren, and Mitchio Okumura* Arthur Amos Noyes Laboratory of Chemical Physics, MC 127-72, California Institute of Technology, Pasadena, California 91125, United States

Stanley P. Sander* NASA Jet Propulsion Laboratory, MC 183-901, California Institute of Technology, Pasadena, California 91109, United States

Anne B. McCoy* Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States S Supporting Information *

ABSTRACT: We report vibrational and electronic spectra of the hydroxy-methylperoxy radical (HOCH2OO• or HMP), which was formed as the primary product of the reaction of the hydroperoxy radical, HO2•, and formaldehyde, HCHO. The ν1 vibrational (OH stretch) spectrum and the Ã ← X̃ electronic spectrum of HMP were detected by infrared cavity ringdown spectroscopy (IR-CRDS), and assignments were verified with density functional calculations. The HMP radical was generated in reactions of HCHO with HO2•. Free radical reactions were initiated by pulsed laser photolysis (PLP) of Cl2 in the presence of HCHO and O2 in a flow reactor at 300−330 Torr and 295 K. IR-CRDS spectra were measured in mid-IR and near-IR regions over the ranges 3525−3700 cm−1 (ν1) and 7250−7800 cm−1 (Ã ← X̃ ) respectively, at a delay time 100 μs after photolysis. The ν1 spectrum had an origin at 3622 cm−1 and exhibited partially resolved P- and R-branch contours and a small Q-branch. At these short delay times, spectral interference from HOOH and HCOOH was minimal and could be subtracted. From B3LYP/6-31+G(d,p) calculations, we found that the anharmonic vibrational frequency and band contour predicted for the lowest energy conformer, HMP-A, were in good agreement with the observed spectrum. In the near-IR, we observed four well spaced vibronic bands, each with partially resolved rotational contours. We assigned the apparent origin of the Ã ← X̃ electronic spectrum of HMP at 7389 cm−1 and two bands to the blue to a progression in ν15′, the lowest torsional mode of the Ã state (ν15′ = 171 cm−1). The band furthest to the red was assigned as a hot band in ν15″, leading to a ground state torsional frequency of (ν15″ = 122 cm−1). We simulated the spectrum using second order vibrational perturbation theory (VPT2) with B3LYP/631+G(d,p) calculations at the minimum energy geometries of the HMP-A conformer on the X̃ and Ã states. The predictions of the electronic origin frequency, torsional frequencies, anharmonicities, and rotational band contours matched the observed spectrum. We investigated the torsional modes more explicitly by computing potential energy surfaces of HMP as a function of the two dihedral angles τHOCO and τOOCO. Wave functions and energy levels were calculated on the basis of this potential surface; these results were used to calculate the Franck−Condon factors, which reproduced the vibronic band intensities in the observed electronic spectrum. The transitions that we observed all involved states with wave functions localized on the minimum energy conformer, HMP-A. Our calculations indicated that the observed near-IR spectrum was that of the lowest energy X̃ state conformer HMP-A, but that this conformer is not the lowest energy conformer in the Ã state, which remains unobserved. We estimated that the energy of this lowest conformer (HMP-B) of the Ã state is E0 (Ã , HMP-B) ≈ 7200 cm−1, on the basis of the energy difference E0(HMP-B) − E0(HMP-A) on the Ã state computed at the B3LYP/6-31+G(d,p) level.

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INTRODUCTION Formaldehyde (HCHO) is a trace oxygenated organic species that is ubiquitous in Earth’s lower atmosphere. In addition to being emitted directly into the atmosphere by biogenic and anthropogenic sources, formaldehyde is formed during the atmospheric oxidation of volatile organic compounds (VOCs) and organic aerosols. The primary loss processes of HCHO in © XXXX American Chemical Society

Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: January 12, 2013 Revised: May 3, 2013

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dx.doi.org/10.1021/jp400390y | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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the atmosphere are photolysis and reaction with the hydroxy radical, •OH. Recently, Hermans et al. have proposed that the reactions of the hydroperoxyl radical HO2• with formaldehyde and other carbonyl compounds may also be a significant sink for both HO2• and carbonyl compounds at the lower temperatures (190−220K) characteristic of the upper troposphere/lower stratosphere (UT/LS) and the tropopause (the boundary between the troposphere and stratosphere).1−3 Studies on the reaction of HO2• with formaldehyde1,2,4−23 paint a consistent picture of the reaction mechanism. The reaction is a termolecular reaction that forms the hydroxymethyl-peroxy radical, HOCH2OO•, or HMP: HO2• + HCHO + M ⇄ HOCH 2OO• + M

(1)

On the basis of the experimental studies, the JPL Data Evaluation panel recommends an effective bimolecular rate coefficient of k1 ≈ 5 × 10−14 cm3 molecule−1 s−1 at room temperature (factor of 5 uncertainty, pressure dependence unknown).24 The recommended negative activation energy24 Ea = −600 K results from the barrierless formation of an adduct. Theoretical studies indicate that a prereactive hydrogen-bonded complex HO2•(HCHO) is formed initially. This hydrogen-bonded complex then isomerizes to form the HMP radical:

Figure 1. Geometries and electronic energies of the three conformers and lowest transition state of the hydroxy-methyl-peroxy (HMP) radical at the B3LYP/6-31+G(d,p) level of theory, relative to the X̃ state energy of HMP-A. The electronic energies (not corrected for the zero-point energy) are listed as (X̃ state, Ã state). TS is the transition state between HMP-A conformers, with torsional coordinates τOOCO = τHOCO = 0°.

absorb in this region,25 and the resulting spectral interference contributes to the large uncertainties (a factor of 5) in the observed rate constant of HO2• + HCHO.11,12,24 Cavity ringdown spectroscopy (CRDS) utilizes a high-finesse optical cavity to measure very small absorbances by providing a significant path-length enhancement. CRDS is an increasingly popular method for the monitoring of trace species in lab experiments and in the field.26−30 In principle, pulsed IR-CRDS detection provides a general method for detecting a wide range of intermediates with a time resolution of approximately 10−100 μs, that is limited by the ringdown time. The Miller group has pioneered the use of near-IR CRDS for detecting the characteristic Ã ← X̃ spectra of organic peroxy radicals.31 This transition is a bound-to-bound n ← n transition localized on the O−O group, with the exact position and structure dependent on the structure and functional groups of the peroxy radical. They have reported detection of the Ã ← X̃ transition for two hydroxy-peroxy radicals, the 2,1-hydroxyethyl-peroxy and 2,1-hydroxy-propyl-peroxy radicals.32−34 These authors have performed thorough investigations of the bands arising both from progressions of Franck-Condon active modes and from low-lying conformers that have significant populations. We have shown that pulsed Infrared cavity ringdown spectroscopy (IR-CRDS) provides a sensitive means for the selective detection of transient intermediates in the mid-IR, especially in the OH stretch region. We have detected reactive intermediates and primary products of free radical reactions in time-resolved flow cell experiments, including the initial HOONO and HONO2 products formed from the reaction of • OH + NO2•, and the 4,1-hydroxy-butyl and 4,1-hydroxy-butylperoxy radicals formed from the isomerization of the n-butoxy radical.35−37 In this work, we use CRDS to detect the HMP radical formed from the reaction HO2• + HCHO. We report the OH stretch vibrational (ν1) spectrum in the mid-IR and the Ã ← X̃ electronic spectrum in the near-IR. We confirm our assignments with the use of quantum chemistry calculations. We examine the role of torsions in the electronic spectrum more explicitly by calculating two-dimensional torsional potential surfaces, determining wave functions for the τHOCO and τOOCO torsional coordinates for both

•

HO2 + HCHO + M ⇄ HO2•(HCHO) + M ⇄ HOCH 2OO• + M

(1)

The hydrogen-bonded complex is predicted to have three conformers, with the primary hydrogen bond between the OH group of the HO2• radical and the carbonyl oxygen. The most stable conformer2,15 has a dissociation energy of 5−7 kcal mol−1.19 The subsequent isomerization is predicted to occur by a concerted process, with C−O bond formation occurring synchronously with H-atom transfer to the carbonyl oxygen. Anglada computes a low activation barrier for isomerization that is 3−4 kcal mol−1 below the energy of the initial reactants.19 The final isomerization product HMP has two heavy-atom torsional degrees of freedom. There are three predicted conformers.2 Anglada calculated at the CCSD(T)/aug-ccpVTZ level and basis that the lowest energy conformer, shown in Figure 1 and labeled HMP-A, is bound by 16.8 kcal mol−1, significantly more stable than the hydrogen-bonded complex.19 Using B3LYP/aug-cc-pVTZ calculations, Hermans et al. predicted that the remaining two conformers are higher in energy by 1.4−1.5 kcal mol−1 and thus would have minimal populations at room temperature.2 The dissociation energies of all HMP conformers are relatively small. Hermans et al. performed statistical rate calculations and showed that the two adducts are in equilibrium with the reactants at temperatures and pressures of the UT/LS, on time scales relevant to the atmosphere.2,3 HMP was first detected spectroscopically by Veyret et al. and Burrows et al.11,12 They observed the B̃ ← X̃ electronic transition, centered at 230 nm, and used the spectrum to determine the rate coefficient and equilibrium constant of reaction 1, K1. The transition is broad and structureless (fwhm of 80 nm) with a large peak absorption cross section (σpeak = 3.5 × 10−18 cm2 molecule−1). All peroxy radicals, including HO2•, exhibit this characteristic σ* ← n electronic transition, a broad peak centered at 220−240 nm. However, many other molecules such as HO2• and hydroxy-methyl-hydroperoxide (HMHP) also B



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the X̃ and Ã states and computing Franck-Condon factors for these torsional vibrations.

HO2• + HCHO + M ⇄ HOCH 2OO• + M

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The output beam of the excimer laser was focused perpendicular to the flow axis with a cylindrical lens and expanded along the flow cell axis with a negative focal length lens, resulting in a beam 6 cm × 0.2 cm. The relative timing of the excimer laser pulse to the Nd:YAG laser pulse was controlled by a digital delay generator (Stanford Research Systems SRS-535). Cl2 was introduced into the cell from a gas cylinder consisting of 3.5% Cl2 in He (Air Liquide or Matheson Tri-Gas) with concentrations of [Cl2] = (1.5−20) × 1016 cm−3. The absorption cross section of Cl2 at 351 nm is σ351 nm = 1.8 × 10−19 cm2 molecule−1.24 For the mid-IR experiments, the typical fluence of UV photons entering the cell was F ≈ 2 × 1017 photons cm−2, resulting in a photolysis yield of φCl2 ≈ 3.5% of the Cl2; for the near-IR, the typical fluence was F ≈ 4 × 1017 photons cm−2, resulting in φCl2 ≈7%. HCHO was introduced to the cell by flowing nitrogen through a vessel filled with paraformaldehyde powder (Sigma Aldrich, 95%), heated to 110 °C. The resulting vapor was flowed through a liquid nitrogen trap to remove formaldehyde oligomers, ensuring that only formaldehyde monomers entered the cell. The concentration of HCHO was determined in a separate experiment measuring the spectrum of HCHO in the UV (300−310 nm)38 and verified to be consistent with the mid-IR experiment by measuring the R branch of the 2ν2 band of HCHO (3510−3520 cm−1).39 At the high HCHO concentrations used here (to minimize spectral interference from products of secondary reactions, especially in the infrared), the HMP is formed rapidly (50−200 μs). While in equilibrium, all HO2• is effectively converted to HMP. The rate of the back-reaction to reactants (reaction −1), is on the order of 100 s−1 at room temperature and is negligible. Experimental Conditions. Typical conditions for the spectroscopy experiments are summarized in Table 1. Experiments were performed at room temperature (295 K), at

EXPERIMENTAL SECTION Apparatus. The reaction HO2• + HCHO was studied in a flow cell reactor by pulsed laser photolysis (PLP) to photoinitiate free radical reactions. HO2• radicals were formed by photolysis of Cl2 in the presence of HCHO and O2, at 295 K and typical pressures of 300−330 Torr. We detected intermediates and primary products by IR-CRDS, with 10 μs temporal resolution. Our PLP-IR-CRDS apparatus has been described in detail elsewhere;36,37 here, we present a brief overview of the apparatus. A schematic of the laser system can be found in the Supporting Information. Our spectrometer as originally reported operated in the midIR (2.7−3.7 μm). We have extended the range to the near-IR (1.1−1.4 μm). Tunable mid-IR light used to measure the ν1 spectrum was generated by difference frequency generation using an optical parametric amplifier pumped by the output of a frequency doubled Nd:YAG (Continuum Surelite III) as the pump, and the output of a dye laser (Spectra Physics PDL-3) as the signal. For 65 mJ of 532 nm light and 4−12 mJ of tunable red light (620−665 nm), 0.6−0.8 mJ of tunable infrared light was generated (2900−3800 cm−1). Tunable near-IR light used to measure the electronic spectrum was generated by stimulated Raman scattering of visible radiation from the Nd:YAG pumped dye laser in a high-pressure cell of H2 in a double-pass arrangement. For 370 mJ of 532 nm light, 40 mJ of tunable red light (590−665 nm) was generated, yielding 100 μJ of tunable infrared light (6900−8700 cm−1). The resulting mid-IR or near-IR beam was focused into a 52 cm long optical cavity consisting of two highly reflective R = 99.98% mirrors (Los Gatos Research, peak reflectivity at 2.8 μm for IR, and 1.35 μm for nearIR). Light exiting the cavity was focused with a CaF2 f/1 lens onto a photodiode. The detector in the mid-IR was a liquid-nitrogencooled InSb detector (Judson J10D-M204-R01M-60) with external Analog Modules 351A-3 amplifier. The near-IR detector was an InGaAs photodiode with an internal transimpedance amplifier (ThorLabs PDA400). Ringdown traces were collected by a GageScope CS1450 waveform digitizer (50 GSa s−1, 14bit ADC). Ringdown time traces were collected for 80 μs after the Nd:YAG laser fired, at a digitizing rate of 25 MSa s−1. Ringdown traces from 16 shots were averaged and then fit to an exponential decay using the Levenberg−Marquardt algorithm. To reduce the effects of noise from the photolysis (excimer) laser near the peak of the ringdown decay curve, a preliminary fit was performed to estimate the lifetime, and then a final fit was performed only on data after the first 1/8 of the estimated lifetime. Typical empty cell ringdown times were 7−11 μs. The empty cell noise was typically στ/τ ≈ 0.3%, giving a minimum detectable absorbance of 2 × 10−6 within a 50 μs time window, at 10 Hz and 1 s averaging. Generation of HMP via Photolysis. HMP was generated by photolyzing Cl2 in the presence of HCHO and O2 with the output of an excimer laser (Lambda-Physik LPX 210i) at 351 nm: Cl 2 + hv → Cl• + Cl•

(2)

Cl• + HCHO → HCl + HCO•

(3)

HCO• + O2 → CO + HO2•

(4)

(1)

Table 1. Experimental Conditions mid-IR spectrum

near-IR spectrum

K torr cm cm × cm photons cm−2 μs sccm sccm sccm sccm sccm sccm sccm

295 300 52 5 × 0.3 2 × 1017 100 450 450 250 14 1250 650 2614

295 330 52 5 × 0.12 4 × 1017 100 450 450 250 170 1250 650 2770

ms molecules cm−3 molecules cm−3 molecules cm−3 molecules cm−3 molecules cm−3 molecules cm−3 cm−1

30 1.0 × 1017 1.8 × 1015 2.4 × 1018 5 × 1015 7.2 × 1018 1 × 1014 0.2

25 1.0 × 1017 2.3 × 1016 2.5 × 1018 6 × 1017 7.4 × 1018 3 × 1015 0.1

units temperature cell pressure optical cavity length photolysis beam dimensions excimer fluence (351 nm) time after photolysis N2 purge flow, left mirror N2 purge flow, right mirror N2/HCHO flow 3.5% Cl2/He Flow N2 dilution flow O2 flow flow rate through photolysis volume residence time [HCHO] [Cl2] [O2] [He] [N2] [Cl]0 ∼ [HO2•] spectrum step size C



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pressures of 300−330 Torr. Typical buffer gas concentrations were N2/O2/He = 0.735:0.25:0.005. [HCHO] was 1 × 1017 cm−3 for both spectra. The [Cl•] generated from photolysis was ≈ 1 × 1014 cm−3 in the mid-IR experiments. In the near-IR experiments, chlorine atom concentrations were higher ([Cl•] ≈ 3 × 1015 cm−3) to generate the larger quantity of HMP necessary to detect the weaker electronic spectrum. The HMP spectra were measured by scanning across a range of frequencies in the mid-IR (3520−3700 cm−1, step size 0.2 cm−1) and near-IR (7100−8000 cm−1, step size 0.1 cm−1) while at a constant photolysis-probe time delay (100 μs). Preliminary measurements of HMP formation and reaction were measured by scanning across a range of photolysis-probe delay times (0−1 ms) at constant frequencies within the ν1 and near IR bands. In either configuration, ringdown traces were collected at each point with the excimer-on and with the excimer-off in succession in consecutive shots. The frequency-dependent background arising from absorption by precursor gases and mirror reflectivity could then be subtracted.

HOCH 2OO• + HOCH 2OO• → HOCH 2O• + HOCH 2O• + O2 HOCH 2OO• + HOCH 2OO• → HCOOH + HOCH 2OH + O2

HOCH 2O• + O2 → HCOOH + HO2•

to form formic acid and HO2 with rate constant k11 = 3.5 × 10−14 cm3 molecule−1 s−1. We show in the Supporting Information that, on the time scale of our experiments (0−100 μs), reactions of HMP (all radicalradical reactions) to form other hydroxy-containing species is minimal. Additionally, no other alkyl peroxy radicals form on the time scale of the experiment (0−100 μs). To further confirm that secondary chemistry effects are minimal, we modeled the kinetics using rate constants available in the literature11,12,24,40,41 with the Kintecus kinetics modeling software.42 We predict that in the mid-IR experiment, 92% of the hydroxy containing species will be HMP, whereas in the near-IR experiment, HO2• is the only absorber that is present in large enough quantities to cause spectral interference (sharp peaks 200 μs), HMP will be consumed by reaction with HO2• (reactions 7 and 8) or by self-reaction (reactions 9 and 10), HOCH 2OO• + HO2• → HOCH 2OOH + O2

(7)

HOCH 2OO• + HO2• → HCOOH + H 2O + O2

(8)

Figure 2. Fundamental ν1 (OH stretch) spectrum of the hydroxymethyl-peroxy radical. Black: experimental mid-IR CRD spectrum of the products of HO2• + HCHO with the background spectrum (mirror reflectivity and reactants) subtracted. Blue: CRD spectrum after subtraction of spectra of HCOOH (3570 cm−1) and H2O2. Green: simulated ν1 spectrum of the HMP-A conformer, computed at the B3LYP/6-31+G(d,p) level, including anharmonicities from secondorder vibrational perturbation theory (VPT2). D



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Figure 3. Time dependence of the total absorbance measured at two frequencies (faint line (left)/squares (right) = 3610 cm−1, bold lines (left)/triangles (right) = 3630 cm−1). The 3630 cm−1 absorbance has been scaled to the 3610 cm−1 absorbance. The left plot shows the absorbance up to 1 ms after Cl2 photolysis, whereas the right plot is a blowup of the first 50 μs. Both plots were taken with [HCHO] = 1 × 1017 molecules cm−3, for [Cl•] = (1−5) × 1014 molecules cm−3 (labeled on plots).

Figure 4. Comparison of experimental and calculated near-IR spectrum of the Ã ← X̃ transition of the hydroxy-methyl-peroxy radical, formed as a product of the reaction HO2• + HCHO. Upper panel: experimental CRD spectrum of the products of HO2• + HCHO. The background spectrum (mirror reflectivity and reactants) has been subtracted. Lower panel: simulated Ã ← X̃ spectrum computed at the B3LYP/6-31+G(d,p) level. The absolute frequency was shifted to match the origin for the HMP-A conformer. Vibrational frequencies were computed from anharmonic vibrational frequencies using second-order vibrational perturbation theory (VPT2). Band contours were computed using vibrationally averaged rotational constants at the optimized geometries for the ground and upper states. Relative integrated intensities of the simulated bands were scaled by the FranckCondon factors computed from the two-dimensional wave functions obtained by our DVR analysis of the 2-d (τOOCO and τHOCO torsions) B3LYP/631+G(d,p) surfaces.

ringdown loss). The unsubtracted spectra (excimer-off and excimer-on) can be found in the Supporting Information. In Figure 3, we show the time dependence of the total absorption (measured at the apparent peaks of two sub-bands) for four different Cl-atom concentrations ((1−5) × 1014 cm−3). The right panel shows the rise of the absorbance at early times ( 200 μs). We assign the second feature, the 3570 cm−1 band, to formic acid. This band has structure with lines spaced by 5 cm−1; its shape, position, and structure are consistent with formic acid.39 The 3570 cm−1 band also appears stronger at lower HCHO concentrations, in agreement with the predicted behavior of formic acid in our kinetics model. The third absorption, embedded within the R-branch, is readily identified by distinct sharp peaks (the strongest at 3630, 3645, and 3650 cm−1) as hydrogen peroxide. The sharp features are signatures of the ν1 and ν5 absorption spectrum of H2O2 and match peaks in a spectrum of hydrogen peroxide taken with our instrument (shown in the Supporting Information). The time dependence is also that expected of H2O2, which is a secondary product from the slower HO2 self-reaction. The spectrum at 100 μs is relatively free of contributions from the two secondary products. We can subtract the contributions of the formic acid and hydrogen peroxide by using reference spectra, from known FTIR spectra of formic acid39 and from our CRDS measurements of hydrogen peroxide, respectively. Figure 2 shows such a subtraction from a spectrum recorded at a 100 μs delay. The subtracted band is roughly 90% as intense as the measured band, indicating minimal spectral interference from formic acid and hydrogen peroxide. The resulting absorption band at 3622 cm−1 is similar to the unsubtracted band, with a fwhm width of 50 cm−1, structureless P and R branches, and a weak Q branch. The HCOOH and H2O2 spectra are more significant at lower HCHO concentrations. We therefore recorded all spectra with the relatively large concentration of [HCHO] = 1 × 1017 cm−3. The absorption band at 3622 cm−1, after subtraction of formic acid and hydrogen peroxide spectra, is similar in width and position to the OH stretch absorption spectra of methanol and ethanol, though shifted approximately 60−70 cm−1 to the red of those bands.39 The observed appearance rate of the absorption band at early times (the first 50 μs, seen in Figure 3, right panel) is consistent with that of a primary product from the HO2• + HCHO reaction. A pseudo-first-order kinetics analysis, using an approximate absorption cross section derived from B3LYP calculations and an estimate of the initial HO2• concentration from a separate HO2• + HO2• experiment, leads to values for the rate constant k1 that are well within the factor of 5 uncertainty of the JPL recommended value of 5 × 10−14 cm3 s−1. On the basis of these considerations, we assign the absorption band at 3622 cm−1 to the OH stretch (ν1) spectrum of the hydroxy-methyl-peroxy radical. Near IR Spectrum: The Ã ← X̃ Electronic Transition. Figure 4 shows the near-IR spectrum following photolysis of Cl2 in the presence of HCHO and O2. This spectrum was taken with a 0.1 cm−1 step size and 0.5 cm−1 precision, 100 μs after Cl2 photolysis, with the background spectra in the absence of

Figure 5. Time dependence of the absorbance at 7563 cm−1, the combination band (1510) of the Ã ← X̃ transition of HMP. CRD data (●) with [HCHO] = 1 × 1017 cm−3, [Cl•] ≈ 3 × 1015 cm−3. Comparison with modeled HMP concentration vs time (dashed line).

peak at 100 μs after photolysis and decrease with a lifetime of 1 ms. The observed time dependence agrees roughly with our kinetics simulation of HMP (blue dashed line). The observed peaks occur in the spectral region expected for a peroxy radical Ã ← X̃ spectrum, possess the partially resolved structure one expects of the bound-to-bound transition of a small molecule, and have the time dependence expected of a transient intermediate formed from HO2• and HCHO. We therefore assign this spectrum to the Ã ← X̃ transition of HMP. As can be seen in Table 2, the first peak lies 122 cm−1 to the red of the strongest band at 7392 cm−1. The separations between the remaining peaks are similar to each other, 171 and 167 cm−1. A cluster of peaks of similar intensities within 500 cm−1 could result from multiple low-lying conformers with similar populations, vibrational progressions in one or more low-frequency torsional modes that have significant Franck−Condon intensities, hot bands, or a combination of these causes. The assignment of these bands will be given below, on the basis of results of the quantum chemical calculations. As noted above, the O−O bond typically changes significantly from the X̃ state to the Ã state, and we expected to see significant Franck−Condon intensity for excitation of the OO stretch. We therefore extended the scan to 8500 cm−1; however, we found no additional peaks, most likely because the signal-to-noise ratio was poor.

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QUANTUM CHEMISTRY AND THEORETICAL CALCULATIONS Stationary Point Calculations. Properties of the lowest energy structure of the hydroxy−methyl−peroxy radical in its

F



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Table 2. Comparison of Observed and Computed Spectral Transitions and Vibrational Frequencies of the HMP-A Conformer of the Hydroxy-Methyl-Peroxy Radicala 15-d calculationb B3LYP/631+G(d,p)

experiment vibration ν1 (X̃ ) origin(Ã ) ν14(X̃ )f ν15(X̃ )g ν14(Ã ) ν15(Ã ) 2ν15(Ã )

assigned band

bandhead/band origin

vibrational frequency

harmonic

anharmonicd

3622

3800

3602 7360e

474 113 412 176 352

427 111 380 168 333

OH stretch HMP-A origin 000

3622

1501

7270/7267

122

1510 1520

7563/7560 7730/7727

171 338

2-d calculationc B3LYP/631+G(d,p) harmonic

anharmonic

466 161 412 249

426 137 368 230

7392/7389

a

First row refers to the mid-IR spectrum. Remaining rows refer to the near-IR spectrum. Experimental band origins are estimated from the origin of the computed rotational contour. All values are reported in cm−1. bEvaluated at optimized geometry of HMP-A conformer. Harmonic frequencies are unscaled. cEvaluated using the two-dimensional potential energy surface, described in the text. dVPT2 as implemented in Gaussian 03W. eThe origin of the Ã ← X̃ transition with anharmonic zero point energy correction. fv14 is HOCO torsion. gv15 is OOCO torsion.

Figure 6. Two-dimensional potential energy surfaces of HMP’s X̃ state (left) and Ã state (right), as a function of the dihedral angles τHOCO and τOOCO. Surfaces were computed at B3LYP/6-31+G(d,p). Potential energies are in cm−1, relative to the (τHOCO = 0°, τOCOO = 0°) X̃ state energy (HMP-TS).

Table 2 lists frequencies for the three modes that are most relevant to the present studies. Additional results are given in the Supporting Information. Table S2 in the Supporting Information highlights the differences in the geometries of the HMP-A conformer upon excitation from the X̃ state to the Ã state. As can be seen, the two states differ significantly in two of the torsional angles, τHOCO and τOOCO, and in the OO bond length. While the two torsion angles τHOCO and τOOCO change by 6.5° and 13.5°, respectively, the values of the other angles change by less than ∼2°. Likewise, the bond length change is largest for the terminal OO distance (0.06 Å), with the next largest change being roughly half that value. These geometry changes likely reflect the changes to the electron charge density following the n ← n excitation on the peroxy group. As we consider the measured spectrum, we are hesitant to employ the usual harmonic models due to the relatively large geometry changes in the two torsion angles. 2-d Potential Energy Surface. To explore the potential energy landscape and spectroscopic implications of the large change in the two torsion angles upon excitation from the X̃ state to the Ã state, we generated a two-dimensional cut through the fifteen-dimensional potential surfaces of the two states. This was achieved by scanning τHOCO and τOOCO in increments of 10° over the full range of their values and optimizing the values of the remaining thirteen internal coordinates. Calculations of the potential energy surfaces were performed in Gaussian 03W.44

ground electronic state have been reported elsewhere, using density functional theory and ab initio methods up to CCSD(T).2,19 Here, we perform quantum chemistry calculations on both the ground X̃ and electronically excited Ã states, to have a consistent data set to interpret the vibrational and electronic spectra. All electronic structure calculations were performed in Gaussian 03W.44 As noted in the Introduction, there are three low-energy conformers of HMP in the ground electronic state.2 We label these as HMP-A, HMP-B, and HMP-C, in order of increasing energy. Their geometries are shown in Figure 1 from the B3LYP/ 6-31+G(d,p) calculation. Computed energies and vibrational frequencies for these conformers can be found in the Supporting Information. The HMP-A conformer has both the OO and OH groups nearly coplanar. This is the conformer computed by Anglada.19 We find that the other two conformers are roughly 550 cm−1 (1.6 kcal mol−1) higher in energy in the ground state, consistent with the B3LYP/aug-cc-pVTZ calculations of Hermans et al., who find that HMP-B and HMP-C are higher in energy by 1.4 (kcal mol−1).2 These higher energy conformers are unlikely to have significant populations at 298 K, and we therefore focus on the ground state properties of the HMP-A conformation. We have calculated harmonic and anharmonic vibrational frequencies for all conformers on both states, with the anharmonic frequencies obtained using second order vibrational perturbation theory (VPT2) as implemented in Gaussian 03W. G



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Figure 7. Wave functions computed by DVR analysis of the potential energy surfaces of the X̃ and Ã states (B3LYP/6-31+G(d,p)) shown in Figure 6. Purple: lowest energy vibrational level. Red: lowest vibrational state of the HMP-A conformer on the Ã state surface. Green: excited vibrational states of the OOCO torsional mode of the HMP-A conformer.

Figure 6 shows these 2-dimensional potential energy surfaces of HMP, calculated at B3LYP/6-31+G(d,p); we found that CCSD/6-31+G(d,p) calculations gave similar results. The surfaces are labeled with the positions of the three minima (HMP-A, HMP-B, and HMP-C) and the transition state (HMPTS) at (τHOCO, τOOCO) = (0°, 0°). The structures of these conformers are shown in Figure 1, calculated at the B3LYP/631+G(d,p) level. Here we compare the features of the two states at the B3LYP/ 6-31+G(d,p) level. For the ground X̃ state, the minimum energy structure corresponds to τHOCO = −68.9° and τOOCO = +63.1° (HMP-A). In contrast, the minimum energy structure for the Ã state has τHOCO = −62.0° and τOOCO = −70.2° (HMP-B). Clearly this is not the part of the potential that is accessed by electronic excitation. Rather, the local minimum on the A state that is accessed (HMP-A) has τHOCO = −75.5° and τOOCO = +76.7°. The barrier that separates these minima is roughly 1400 cm−1 (X̃ state, along τHOCO) and 975 cm−1 (Ã state, along τHOCO). With the potential energy surface cuts in hand, the vibrational energies and corresponding wave functions were evaluated in a discrete variational representation (DVR), using the Hamiltonian:

with a sum over all the Cartesian coordinates of the seven atoms. We also used the analytical expressions for the G-matrix elements reported by Frederick and Woywod.45 The DVR that was employed is based on the one described by Colbert and Miller for angles that are defined over the range from 0 to 2π.46 The description of this DVR applies to one-dimensional systems with constant masses. Because the G-matrix elements depend on the values of the two torsion angles and due to the inclusion of the momentum cross term, some minor modifications to the approaches first described by Colbert and Miller46 were made. First, following our earlier work47,48 we replaced each term in the kinetic energy witha 2

pG p + pj Gi , jpj = ppG + Gi , jpp +ℏ i i,j j i i i,j i j

ℏ2 ∂ ∂ G2,2 + V (τ1 ,τ1) 2 ∂τ2 ∂τ2

Tj′i2′ , j i2 = 1

(12)

where τ1 = τHOCO and τ2 = τOOCO. The needed G-matrix elements were evaluated numerically using Gi , j =

∑ k

∂xk 1 ∂xk ∂τi mk ∂τj

∂τi ∂τj

(14)

Because the DVR functions are taken to be eigenfunctions of τ1 and τ2 (and by extension all of the Gi,j matrix elements), the kinetic energy is readily evaluated in this form. The evaluation of the p1p2 cross terms required matrix elements for these operators in the DVR. A derivation is provided in the Supporting Information for this paper, and the results are reported below:

ℏ2 ∂ ∂ ℏ2 ∂ ∂ ℏ2 ∂ ∂ − − Ĥ = − G1,1 G1,2 G2,1 ∂τ1 ∂τ1 ∂τ2 2 ∂τ1 2 ∂τ1 2 ∂τ2 −

∂ 2Gi , j

1

(1) (2) (2) G1,2(τ j(1) ′ ,τi 2′ ) + G1,2(τ j ,τi 2 ) 1

1

2 2 −ℏ ( −1) j1 + i2 − j1′− i2′ × ⎛ τ j(1) − τ j(1) ⎞ ⎛ τi(2) − τi(2) ⎞ ′ ′ 4 sin⎜ 1 2 1 ⎟ sin⎜ 2 2 2 ⎟ ⎠ ⎝ ⎠ ⎝ ×(1 − δ j , j′)(1 − δi2 , i2′) 1 1

(15)

Additional discussion of this basis and its properties may be found in the work of Stenger.49,50 With this in place, we evaluated the energies and wave functions in a 2-dimensional DVR, and on

(13) H



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(anharmonic frequency calculation) and 3626 cm−1 at CCSD/631+G(d,p) (applying a scaling factor of 0.947 to the harmonic frequency).51 The frequency alone, however, does not allow us to identify the specific conformer, because all three low-lying conformers have the same OH stretch frequency, to within 20 cm−1. Frequencies at other levels of theory and using different basis sets bases are in the Supporting Information. The simulated rotational envelope, shown in Figure 2, is qualitatively similar to the observed band contour. The simulation uses the ab initio rotational constants (which includes rovibrational coupling but not centrifugal distortion) and predicted electric dipole transition moments. The spectrum is predicted to be a hybrid band with μa:μb:μc = 1:10:3, leading to prominent P and R branches and a small Q-branch, with a width (fwhm = 45 cm−1) in reasonable agreement with the observed spectrum. Observed contours tend to be broader than those predicted in rigid rotor simulations, because of centrifugal distortion, and overlapping sequence bands. The rotational envelopes predicted by the DFT calculations allow us to assign the band definitively to the HMP-A conformer. As seen in the Supporting Information (Figure S6), the HMP-B and HMP-C conformers are predicted to have band contours that differ considerably from the observed spectrum, in particularly possessing strong Q-branches. Thus, we can assign HMP-A as the ground state conformer. There does not appear to be evidence for significant population (10% or more) in the other conformers. The HMP-B and HMP-C conformers should absorb at frequencies 20 cm−1 to the blue, but no significant peak is observed. We cannot assign the two subpeaks to different conformers, because the overall width of the band is comparable to the width expected for a single transition. The two peaks are consistent with the predicted prominence of the P- and R- branches in the rotational contour. Near-IR Spectrum of the Ã ← X̃ Transition. Our simulation of the Ã ← X̃ electronic spectrum of HMP is compared to the experimental spectrum in Figure 4. The stationary point B3LYP/6-31+G(d,p) calculations provide us with anharmonic vibrational frequencies and rotational band contour parameters (vibrationally averaged structures and harmonic transition dipole intensities). The contours allow us to estimate the band origins, which are typically 3 cm−1 to the red of the peak of the R-branch bandhead (see Table 2). The origin of the transition (zero-point corrected) is computed to be 7360 cm−1, very close to the strongest vibronic band, with a bandhead observed at 7392 cm−1 and origin estimated (from contour fit) as 7389 cm−1. In the simulation, we have shifted the spectrum so that the origin matches the frequency of the strongest band. We use our 2-d wave functions to obtain Franck−Condon intensities that are more accurate than could be computed from overlap of stationary-point harmonic wave functions for the two heavyatom torsional coordinates. These Franck−Condon factors are used to scale the integrated intensities of the computed rotational contours of each vibronic band. Our calculations indicate that the spectrum arises from excitation from only one conformer (HMP-A) in the ground electronic state. The other conformers are too high in energy to be populated significantly. In the upper Ã state, the lowest energy conformer is HMP-B. However, the lowest energy 2-d torsional wave functions are localized on specific conformers, and the HMP-B conformer in the upper state has negligible Franck− Condon overlap with the ground state. The simulated spectrum

the basis of the overlaps of the wave functions that were calculated, we were able to approximate the electronic spectrum within this 2-d Franck−Condon approximation. 2-d Wave Functions. Figure 7 shows the HMP wave functions for the lowest vibrational states on the X̃ and Ã state surfaces as well as any other states that are likely to be important in the spectroscopy. As expected, the ground vibrational state wave function on the X̃ state is localized in the potential minimum that corresponds to HMP-A. At the temperatures of the experiment, both this state and the first excited state (one quantum in the OOCO torsion) will be populated. On the Ã state, the lowest energy vibrational level will be localized in the minimum that corresponds to the HMP-B conformer. Given the large geometry difference between the two conformers, no Franck−Condon activity is expected for this transition. The next lowest energy state on the Ã surface is the ground vibrational state in the HMP-A conformer. This state does have significant Franck−Condon activity with the lowest level of the X̃ state, as do transitions to the states with one and two quanta in the OOCO torsion (also shown). Other transitions are found to be much weaker. As we compare the frequencies for the two torsions, obtained from harmonic and anharmonic calculations in full- and reduceddimensionality, there are some clear discrepancies. In particular, although the agreement between the full- and reduceddimensional frequencies for the higher frequency (HOCO) torsion is good, differences of 50−70 cm−1 are found for the frequency of the lower frequency torsion. These differences are seen in both the harmonic and anharmonic results and reflect the fact that the normal modes that describe this vibration in the fulldimensional calculation include contributions from the heavyatom bends. This is not captured in the two-dimensional treatment. Though such mixing will certainly affect the frequencies, inclusion of these modes in the reduced-dimensional treatment is not anticipated to affect the qualitative conclusions drawn from the analysis of the two-dimensional wave functions as the torsions are considerably more anharmonic than the OOC or OCO bends. Rotational Band Contour Simulations. We simulated rotational band contours for both the ground state ν1 vibrational spectrum (Figure 2, dashed line) and the vibronic bands of the Ã ← X̃ spectra (Figure 4, bottom panel). We used the computed geometries and transition dipole moments from the stationary point calculations as inputs for the PGopher program. The simulations were smoothed to simulate the reduced resolution of the experimental spectra. For all three conformers, the rotational constants obtained from anharmonic frequency calculations of HMP-A at B3LYP/6-31+G(d,p), as well as the rotational band contour simulations, are given in the Supporting Information. Excitation of ν1 did not appreciably change the rotational constants, although excitation of ν15 in either state did increase the A rotational constant by ≈1%. Furthermore, the A′ constant increased by ≈5% upon excitation to the Ã state.

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SPECTRAL ASSIGNMENTS: COMPARISON OF EXPERIMENT AND THEORY IR Spectrum of the Ground State ν1 = 1 ← 0 Transition. Our quantum chemistry calculations support the assignment of the observed 3622 cm−1 band to the ν1 (OH stretch) band of the hydroxy−methyl−peroxy radical. The position of the observed absorption is in good agreement with the frequency of ν1 for HMP-A predicted by the quantum chemical calculations, as given in Table 2. We compute 3602 cm−1 at B3LYP/6-31+G(d,p) I



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sensitivity, due to strong background absorption that effectively reduced the path length advantage by 2 orders of magnitude. For kinetics experiments, lowering [HCHO] has the benefit of increasing the sensitivity of the experiment, while lowering the radical concentrations reduces the effects of secondary reactions and nonthermal processes. Time resolved spectroscopy in the IR region allows us to simultaneously detect the HMP and HO2• radicals, as well as the products HCOOH and H2O2. Varying HCHO should provide a stringent test of the reaction kinetics in the presence of multiple competing reactions. Time-resolved spectroscopy in the near-IR region provides us with unique signatures of the peroxy radicals HO2• and HMP, but at 1−2 orders of magnitude less sensitivity. The detection limits can be improved somewhat by reducing background and increasing the near-IR power. The current scheme is limited by the relatively low pump power of the dye laser pumping the SRS cell; substantially higher powers can be obtained by multipass SRS or optical parametric amplification, allowing us to use higher reflectivity mirrors. Mid-IR experiments, where our sensitivity is higher, could provide the best opportunity to examine subsequent reactions of HMP. As we have shown in the case of •OH + NO2•,35 we can record time-dependent IR transient absorption spectra that can be deconvoluted to extract product yields vs time. We can detect HO2•, HMP, HCOOH, and H2O2. These methods together should provide a means for examining the recent suggestions by Jenkin21 and by Nguyen22 concerning •OH and HCOOH formation from HO2• + HMP.

thus involves excitation from the ground state HMP minimum to the torsional states localized on the HMP-A conformer. The simulated spectrum of the HMP-A conformer accurately reproduces the main features of the observed spectrum: the vibronic frequencies, the relative intensities, and the rotational band contours. The frequencies of the vibronic band origins (located using the origin of the calculated rotational contours) the band assignments, and vibrational frequencies along with comparisons to calculated frequencies are given in Table 2. We assign the origin as the strongest peak, which was observed at 7389 cm−1. The other vibronic bands are progressions in the lowest frequency mode ν15 mode, the OOCO torsion. The dominance of the Franck−Condon progression in the ν15 mode is not surprising, because the lowest frequency torsional angle τOOCO is the geometric parameter that changes the most in exciting the HMP-A conformer from the X̃ state to the Ã state. We assign the band with an origin at 7267 cm−1, to the red of the origin, to the torsional hot band 1501, giving a ground state torsional frequency of ν15″ = 122 cm−1. This is in good agreement with the single-point anharmonic value of 111 cm−1 for HMP-A. In contrast, the predictions for the frequency of ν15″ in the X̃ state are 91 and 51 cm−1, for HMP-B and HMP-C, respectively, and do not agree. We assign the remaining peaks to combination bands in the ν15′ mode in the Ã state, 1510 and 1520, giving ν15′ = 171 cm−1 or ω15′ = 174 cm−1 and x1515′ = 1.5 cm−1. These values agree with the values for both HMP-A and HMP-B, but not with HMP-C (ω15′ = 99 cm−1). Overall, the relative spacing of the four observed vibronic bands thus agree best with the single-point predictions of the anharmonic vibrational frequencies of HMP-A in both electronic states and confirm the small anharmonicity in the Ã state ν15 mode found in the 2-d DVR calculation. The simulated band contours match the observed band contours well, indicating that the calculations correctly describe the geometry changes and transition dipole orientation of the transition (μa:μb:μc = 1:0:1). The relative intensities of the bands computed with the 2-d DVR wave functions are also in good agreement with our CRD spectrum, with the 000 band stronger than the 1510 and 1520 bands by a factor of 2−4. Given the magnitude of the 1501 hot band, we might expect to observe a strong sequence band 1511, predicted to be 54 cm−1 to the blue of the origin. However, we find that the Franck− Condon factor for the expected sequence band is a factor of 2 smaller than the hot band; there is some signal there, but the noise is too large to definitively attribute a peak at that position. As noted above, the minimum on the Ã state potential energy surface is the HMP-B conformer. The overlap with the ground state HMP-A conformer is negligible and hence the true minimum of the Ã state is unobserved. From our B3LYP/631+G(d,p) calculation of the zero-point corrected energy E0 of the HMP-B conformer of the Ã state, we estimate that the energy of the lowest energy conformer of the Ã state to be E0′(HMP-B) ≈ 7200 cm−1.

■

CONCLUSIONS We have reported spectra in the mid-IR and near-IR of the hydroxy-methyl-peroxy (HMP) radical formed from the reaction of HO2• and HCHO. Our detection of both the OH stretch fundamental at 3622 cm−1 and the Ã ← X̃ electronic spectrum at 7389 cm−1 provide a definitive identification of this radical as the primary product. For the mid-IR spectrum, the vibrational frequency and rotational band contours are in excellent agreement with density functional calculations of the minimum energy conformer. In the near-IR spectrum, we observe four vibronic bands with partially resolved rotational structure. We have simulated this spectrum using calculated anharmonic vibrational frequencies and rotational envelopes, coupled with Franck−Condon factors obtained from explicit 2-d wave functions computed on a 2-d potential energy surface of the heavy atom torsional angles, τHOCO and τOOCO. We find that the potential energy surface is relatively flat, justifying our explicit calculation of the reduced dimensionality wave functions in these coordinates. Our simulated spectra agree quantitatively with our experimental spectra and allow us to assign the observed bands in terms of transitions involving changes in the lowest frequency torsional mode, ν15, associated with the OOCO torsion, the geometric parameter that exhibits the largest change upon excitation. We find that the electronic spectrum involves excitation from a single conformer, HMP-A, the minimum on the X̃ state potential surface. Cavity ringdown detection of these spectra is a promising method for future studies of HMP chemistry.

■

DISCUSSION We have shown that CRDS provides a method for directly and selectively detecting the HMP radical in the course of reactions in a PLP experiment. We can thus monitor the kinetics of HMP formation, as well as its subsequent reactions. The current experiments were performed at high [HCHO] and large radical concentrations, to obtain “clean” spectra of HMP free of interference from other product absorption spectra. These conditions had the disadvantage of greatly reducing our IR

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ASSOCIATED CONTENT

S Supporting Information *

Schematic of the laser system in its two configurations. The primary and secondary chemistry is discussed in more detail. Figures are provided that show the background and unsubtracted J



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signal spectra. CRD spectrum of the hydrogen peroxide (H2O2) ν1/ν5 transition that is used in the spectral interference subtraction in the mid-IR is presented. A figure illustrates the subtraction of HCOOH and H2O2 spectra to obtain the HMP-A ν1 spectrum. Additional quantum chemistry results are provided (geometric parameters, energies, harmonic frequencies and anharmonic frequencies for the three conformers in both the X̃ and Ã states). A derivation of the momentum operator in the discrete variable representation is given. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*M.O.: phone, 1-626-395-6557; fax, 1-626-395-6948; e-mail, [email protected]. S.P.S.: phone, 1-818-354-2625; fax, 1-818393-5019; e-mail, [email protected]. A.B.M.: phone, 1-614-292-9694; fax, 1-614-292-1685; e-mail, mccoy@ chemistry.ohio-state.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was provided by the National Aeronautics and Space Administration (NASA) Upper Atmosphere Research Program (grants NNX09AE21G and NNX12AI01G), the National Science Foundation (NSF, Grant CHE-0957490 for experimental work at Caltech and Grant CHE-1213347 for computational work by ABM), and the NASA Tropospheric Chemistry Program. Part of this research was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). We acknowledge support of a National Defense Science and Engineering Graduate Fellowship for M.K.S., an NSF Graduate Fellowship for L.A.M., and the Caltech Student-Faculty Programs office for H.N.W. through the Summer Undergraduate Research Fellowship program. We thank Dr. Andrew Mollner, who performed the initial setup of the experiment and the formaldehyde sampling system, Dr. Ralph Page for vital technical assistance and optimization of the spectrometer optics, Michael Roy for machining support, and Richard Gerhart for glassware construction and repair. We acknowledge the inspiration provided by Takeshi Oka for this work.

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ADDITIONAL NOTE Note that there was a sign error in the last term in eq 2 of ref 48. REFERENCES

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NOTE ADDED IN PROOF After the submission of this manuscript, Delcey et al.52 reported high-level calculations of both the X̃ and Ã states of HMP, computed at the CASPT2 and RCCSD(T) levels of theory. The more accurate RCCSD(T) calculations provide values for the adiabatic transition energy of T0 = 7360 cm−1, in excellent agreement with those observed here. The relative energetics among the conformers, for the ground X̃ tate predicted by Hermans et al. and Anglada,2,19 and for the Ã state reported here, are confirmed in these higher level calculations. They also computed harmonic vibrational frequencies and rotational constants for both electronic states. The experimental results presented here appear to corroborate the main results of these high-level calculations.

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Cavity Ringdown Spectroscopy of the Hydroxy-Methyl-Peroxy Radical

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