The impact of water vapor on the OH reactivity towards CH₃CHO at ultra-low temperatures (21.7-135.0 K): Experiments and Theory

Abstract

The role of water vapor (H2O) and its hydrogen-bonded complexes in the gas-phase reactivity of organic compounds with hydroxyl (OH) radicals has been subject of many recent studies. Contradictory effects have been reported at temperatures between 200 and 400 K. For the OH+acetaldehyde reaction, a slight catalytic effect of H2O was previously reported at temperatures between 60 and 118 K. In this work, we used Laval nozzle expansions to reinvestigate the impact of H₂O on the OH-reactivity with acetaldehyde between 21.7 and 135.0 K. The results of this comprehensive study demonstrate that instead water slows down the reaction by a factor of ˜3 (21.7 K) and ˜2 (36.2 – 89.5 K), almost no effect of added H₂O was observed at 135.0 K.

I. Introduction

Water vapor, H₂O, is one of the most abundant species in the Earth’s atmosphere (up to 4% in the troposphere, T = 220-298 K). One of the most relevant processes involving H₂O in our atmosphere is the formation of the main diurnal oxidant, the hydroxyl (OH) radical, which acts as a major sink for many species. Water has also been found in the atmosphere of many objects in the solar system at low temperature conditions (T≤150 K), such as Europa¹, one of Jupiter’s moons, and Enceladus² or Titan³, both orbiting Saturn. Furthermore, in comets and lower temperature environments like the interstellar medium, H₂O^4–6 and OH radicals^7–9, and some organics such as acetaldehyde (CH3CHO)^10–13, were also detected. The effect of water vapor on the kinetics of the OH-reactions with some organics compounds at temperatures of interest for the Earth’s atmosphere has been investigated, mainly by theoretical calculations^14–21. In those studies, the predicted effect of water in the OH-reactivity varies depending on the organic molecule or the theoretical method used. This is demonstrated in Table I which summarizes the investigated OH-reactions to date. The ratio of the rate coefficients in the presence of water (k _water(T)) to the one in absence of water (k _{no_water}(T)) is given in this table. Changes by many orders of magnitude according to the reactant of concern can be observed. For example in the case of ethanol, the theoretical work¹⁹ predicts a decrease of the effective OH-rate coefficient for the monohydrated and dehydrated reaction patterns compared to non-hydrated reaction. It has been found that the effective rate coefficients of corresponding monohydrated reactions are 3-4 orders of magnitude lower than those of the non-hydrated reaction, indicating that water has a decelerating effect on the studied reaction. Several mechanisms have been considered including hydration of either the OH radical or the organic reactant and formation of an adduct in the specific case of methanol. Interestingly, the extent of the computed decrease in k(T) is somewhat different for HC(O)OH, depending on the water complex formed, OH(H₂O) or HC(O)OH(H₂O). For CH₃C(O)CH₃, (HCO)₂ and CH₃CHO only hydration of the organic reactant that further reacts with OH radicals has been suggested.^15–17,22 In the specific case of acetaldehyde, Iuga et al.¹⁷ computed that k _water(T) is several orders of magnitude lower than k _{no_water}(T) at 298 K. Further, their calculation at 220 K indicates a significant increase of the k _water(T)/ k _{no_water} (T) ratio.

Table 1. Summary of the theoretical works on some OH-reactions in the presence of H₂O.

Organics	T/K	Water complex reaction	kwater(T)/ k no_water(T)	Reference
CH4	298	OH(H2O) + CH4	4.3×10-3	Allodi et al. 18
CH3CH2OH	298.2	OH(H2O) + CH3CH2OH	1.1×10-3	Xu et al. 19
	216.7	OH(H2O) + CH3CH2OH	1.4×10-4	Xu et al. 19
HC(O)OH	298	OH(H2O) + HC(O)OH	0.69	Anglada et al. 14
	298	OH + HC(O)OH(H2O)	0.27	Anglada et al. 14
CH3C(O)CH3	298	OH + CH3C(O)CH3(H2O)	0.01	Iuga et al. 16
	220	OH + CH3C(O)CH3(H2O)	0.64	Iuga et al. 16
(HCO)2	298	OH + (HCO)2(H2O)	8×10-4	Iuga et al. 15
CH3CHO	298	OH + CH3CHO(H2O)	5.3×10-4	Iuga et al. 17
	220		0.22	Iuga et al. 17
CH3OH	298	CH3OH + OH + H2O	2.96×10-3	Chao et al. 20
	298	CH3OH + OH + 2H2O	5.81×10-4	Chao et al. 20
	200-400	OH(CH3OH) + H2O	˜1.0	Wu et al. 21

Experimentally, the investigation of the role of water vapor on OH removal is very scarce and also contradictory. As far as we know, only for saturated alcohols^20,23–25 and aldehydes^22,26 the effect of water vapor on the measured OH-rate coefficient, k_obs(T), has been reported. At room temperature, Jara-Toro et al. reported, at a relative humidity (RH) between 20 and 95 %, a slight increase of k_obs(T) for the OH-reactions of methanol²³, ethanol and n-propanol²⁴ with respect to those measured in the absence of added H₂O. This was rebated, however, for methanol and ethanol by Chao et al.²⁰ and Weber et al.²⁵, respectively, who did not observe any catalytic effect of H₂O at similar RHs.

Vöhringer-Martinez et al. also reported a non-catalytic effect of H₂O for CH₃CHO²² and propanal²⁶ at 298 K. In contrast, these authors observed that k _obs(T) at 60 K increases about twice in the presence of about 3% of H₂O in the case of CH₃CHO. To support their experimental observation, Vöhringer- Martinez et al.²² performed a quantum chemical study finding that the complexation in CH₃CHO(H₂O) opens an additional channel for OH removal, with an energetically more favorable submerged reaction barrier than in absence of water. However, no theory-based rate coefficients were reported.

Smith²⁷ suggested that new experimental and theoretical works are required to understand the effect of water on chemical kinetics at temperatures lower than 60 K. Therefore, in this study, we address the challenging and interesting questions: how does water influence the OH-reactivity towards CH₃CHO? Is water a real active catalyst as it has been proposed previously²²? For this purpose, herein, we report a comprehensive experimental kinetic study of the gas phase OH removal in the presence of CH₃CHO, both in the absence and presence of water between 21.7 and 135.0 K. To compare against the previous work from Vöhringer-Martinez et al.²², we carried out the kinetic experiments under similar conditions of gas temperature and pressure and also extended our investigations down to ˜20 K. In addition, quantum chemical calculations that support the obtained results are also presented.

II. Experimental Technique

A. CRESU apparatus coupled to Pulsed Laser Photolysis – Laser Induced Fluorescence (PLP-LIF) technique

The kinetic experiments of the OH removal by reaction with CH₃CHO in the presence and absence of water were performed using the pulsed CRESU machine built in the department of Physical Chemistry (University of Castilla-La Mancha) in Ciudad Real (Spain). The apparatus and technique were described in detail elsewhere,²⁸ and is only briefly discussed here.

The principle of this technique is to use a carrier gas flow, containing small mixing ratios of OH- precursor (H₂O₂) and co-reactants (CH₃CHO and H₂O) expanded from a high-pressure reservoir to a low-pressure chamber through a pulsed convergent-divergent nozzle (Laval type). During the expansion, an isentropic core is generated in the jet, where its velocity, temperature and density (n) are essentially constant throughout many tens of centimeters from the exit of the Laval nozzle. The time corresponding to the optimal length of uniformity, usually called hydrodynamic time, t_hydro, is dependent on the Laval nozzle geometry and the flow conditions expanding through.

Electronic ground state OH radicals, OH(X²Π), were generated in situ in the jet by pulsed laser photolysis (PLP) of gaseous H₂O₂ at 248 nm, using a KrF excimer laser. The loss of OH(X²Π) in the time scale provided by the hydrodynamic time (t _hydro) was monitored by exciting the OH(²Π, v’=0) → OH(²Σ, v’=1) transition at ca. 282 nm doubled the output of a dye laser (Lambda Physik, model Scanmate) pumped by the second harmonic of a Nd:YAG laser (Continuum, model Surelite) and by subsequently collecting its laser induced fluorescence (LIF) at ca. 310 nm OH(²Σ, v’=0) → OH(²Π, v’=0) by a filtered photomultiplier tube (PMT) (Electron Tube, model 9813B). The PMT signal was sent to a gated boxcar integration unit (Stanford Research System, model SRS250). The integrated signal was treated and recorded by a homemade LabView program.

The kinetic experiments were carried out under pseudo-first-order conditions, i.e. the initial concentrations of CH₃CHO, H₂O, and H₂O₂ in the supersonic jet ([CH₃CHO]₀, [H₂O]₀, and [H₂O₂]₀) were in large excess with respect to [OH]₀. Under these conditions, from the analysis of the exponential OH LIF signal (I _LIF) decays after rotational relaxation of OH, the pseudo-first-order rate coefficients, k’, were obtained as a function of [CH₃CHO]₀ and a well-known quantity of water in the jet. In Fig. 1, examples of the OH LIF temporal profiles are presented for the lowest and highest temperature of this work, i.e. 21.7 K and 135.0 K. In Panels A and B of Fig. 1, the OH temporal profiles were obtained either in the absence of CH₃CHO and H₂O (red decays), or in the presence of only H₂O (black decays) or lastly in the presence of both CH₃CHO and H₂O (same concentration as for the black curve) (blue decays).

Fig. 1.

LIF profiles of OH radicals registered at (A) 21.7 K and (B) 135.0 K in the absence of CH₃CHO and H₂O (red decays), in the presence of only H₂O (black decays) and in the presence of both CH₃CHO and H₂O (same concentration as in the black curve) (blue decays).

B. Liquid and gas handling

The main carrier gas (He, N₂ or a binary mixture of them²⁹, 80% N₂+20% He) was introduced in the reservoir using a calibrated mass flow controller (Sierra Instruments, Inc., models: Smart-Trak 2 and Smart-Trak 100).

Since the OH-precursor (H₂O₂) and water are liquids in the laboratory conditions, to introduce them into the reservoir of the CRESU reactor a controlled flow of carrier gas was passed through independent glass bubblers containing a pre-concentrated commercial aqueous solution of H₂O₂ ^30,31 and ultra-purity H₂O, respectively (see Scheme 1). These bubblers were submerged in a water bath to keep liquid H₂O₂ and H₂O at room temperature thus ensuring a constant vapor pressure. For H₂O two different bubblers were used: one with a porous diffuser for small carrier gas flows (lower than 0.35 slpm) and the other one without a diffuser for higher gas flows (higher than 0.35 slpm).

Scheme 1.

Schematic illustration of the gas flows (blue arrows) introduced in the FTIR to measure the water concentration before entering the reservoir. MFC: mass flow controller.

Acetaldehyde is also liquid in the usual laboratory conditions. The sample is degassed with several freeze-pump-thaw cycles before every use. Since its vapor pressure at room temperature is significant (1200 mbar at 25 °C), it was easily evaporated from a round flask (V = 250 mL) connected to a vacuum line into a 50-L glass bulb preliminary pumped under vacuum. The acetaldehyde partial pressure (P_CH3CHO) introduced in the 50-L storage bulb was measured with a pressure gauge (Ceravac CTR 100N from Leybold). The bulb was filled up to about 1 bar of carrier gas (PT). The dilution factor f _CH3CHO is then obtained as the P_CH3CHO/P_T ratio. Since a precise knowledge of the acetaldehyde and water concentrations is crucial in the determination of the rate coefficients, a careful protocol has been established for both reactants. This is discussed in the next two sections.

C. Measurement of gas-phase CH₃CHO concentrations

The acetaldehyde concentration in the jet, [CH₃CHO]₀, was varied by changing the mass flow rate (F _CH3CHO) of the diluted acetaldehyde set in the storage bulb and maintaining the total mass flow rate (F _Total) constant. To calculate [CH₃CHO]₀, all mass flow rates (F _i), the dilution factor f _CH3CHO in the storage bulb and the total gas density n provided by Pitot tube measurements are considered.

$${\left[{\text{CH}}_3\text{CHO}\right]}_0=\frac{F_{\text{CH3CHo}}}{{\text{F}}_{\text{total}}}n{f}_{CH3CHo}$$ (I)

F _Total is the sum of all flow rates: the main flow of the buffer gas (F _{buffer main}), the buffer gas flows through the H₂O (F _{buffer H2o}) and H₂O₂ (F _{buffer_H2O2}) glass bubblers and F _CH3CHO (see Table II).

Table II. Calibrated flow rates introduced in the pre-expansion chamber.^[a] .

T / K	F buffer main / slpm	F buffer H2O / slpm	F buffer H2O2 / slpm	F CH3CHO / sccm	F Total/ slpm
21.7±1.4	8.6-12.7	0.04-0.76	0.077	15.1-237	9.3-12.9
36.2±1.2	7.4-12.3	0.58-4.6	0.048-0.059	24.4-102	12.1-13.2
64.1±1.2	1.1-1.9	0.094-0.66	0.010-0.023	7.4-143	1.30-1.90
89.5±1.2	4.0-5.6	1.27-2.82	0.020-0.038	31.3-165	1.30-1.90
135.0±0.8	4.4-8.2	0.65-2.82	0.029	7.3-130	5.70-8.20

^[a]In standard liters per minute (slpm) or standard cubic centimeters per minute (sccm).

The values of f _CH3CHO were checked offline by measuring the CH₃CHO concentration in the storage bulb by UV spectroscopy between 240 and 360 nm, as explained by Blázquez et al. ³². In Fig. 2A an example of the recorded UV spectra (absorbance in base e (A_γ) versus wavelength λ) from diluted CH₃CHO from the storage bulb is shown at different total pressures together with a reference CH₃CHO spectrum built using a concentration of 1.5 ×10¹⁶ molecules cm^-3, the optical path length (107 cm) and the absorption cross sections recommended by the Jet Propulsion Laboratory.³³ The experimental UV system used was described previously.^32,34–37 A 30 W deuterium lamp (Oriel, model: Q Series Low Power) was used to irradiate the gas mixture in the absorption cell. The transmitted light was focused on a 0.5 m spectrometer (Chromex 500 is/ms), which has a grating (300 groves per mm with a spectral resolution of 0.19 nm) that disperses the radiation. The dispersed light was detected with a cooled CCD detector (Andor, model: DB401-UV, 1024 x 128 pixel²).

Fig. 2.

A) Examples of the UV spectrum of samples from the storage bulb at three different total pressures in the UV cell (P_UV,cell). B) Plots of equation (II) for the data presented in the upper panel.

As shown in Fig. 2B, f _CH3CHO can be obtained considering the ratio between the experimental and reference spectra given in equation (II):

$$\frac{{\text{A}}_{\lambda ,\text{exp}}}{{\text{A}}_{\lambda ,\text{ref}}}=\frac{{\left[{\text{CH}}_3\text{CHO}\right]}_{\exp }}{{\left[{\text{CH}}_3\text{CHO}\right]}_{\text{ref}}}$$ (II)

where [CH₃CHO]_exp is given by equation (III)

$${\left[{\text{CH}}_3\text{CHO}\right]}_{\exp }=F_{\text{CH3CHo}}\frac{pu{v}_{cell}}{RT}$$ (III)

Then, [CH₃CHO]_exp is determined from the slope of the absorbance A_λ,exp vs the reference absorbance A_λ,ref plots and P_UVcell is the total pressure in the UV cell (P_UVcell = 19-73 mbar in the example in Fig. 2B). The measured mixing ratios f _CH3CHO from UV measurements agreed with those obtained from pressure measurements (9×10^-3 - 4.7×10^-2) with differences less than 6% between the f _CH3CHO.

D. Spectroscopic measurement of H₂O concentrations

The initial water concentration was spectroscopically measured online before the supersonic expansion (i.e. at room temperature) by a Fourier Transform Infrared (FTIR) spectrometer described earlier.^36,38 For this, the main flow of the buffer gas seeded with gaseous H₂O, coming from the glass bubbler was introduced into an IR cell placed upstream of the CRESU reservoir (see Scheme 1). This cell is a multipass one (Specac, model Cyclone C5) sealed by ZnSe windows.^36,38 The optical path length was set to 800 cm. The total pressure in the IR cell (P_{IR cell}) was between 215 and 600 mbar. The IR spectrum of diluted H₂O was recorded between 500 and 4000 cm^-1 using a FTIR spectrometer (Bruker, model Tensor 27) with a Globar lamp and a mercury cadmium telluride (MCT) detector cooled by liquid nitrogen.

The followed procedure was:

• 1)Once the IR spectrum of diluted H₂O was recorded, the MALT ^39,40 (Multiple Atmospheric Layer Transmission) software was used to retrieve the mole fraction of H₂O vapor in the gas flow before the supersonic expansion, x(H₂O)_{IR cell}.
• 2)Neglecting the H₂O₂/buffer gas flow directly introduced in the reservoir, the water concentration in the cooled jet, [H₂O]₀, can be deduced by simply multiplying the total gas density of the jet (n) by x(H₂O)_{IR cell}.

MALT uses a non-linear least squares spectral fitting computational procedure developed by Griffith ⁴⁰. This method simulates the spectrum of the mixture from a set of initial concentrations and then varies the concentrations iteratively to minimize the residual between the measured and simulated spectrum. MALT takes the line parameters (positions, strengths, widths, and the temperature dependences for each absorption line) from HITRAN08 ⁴¹ database to generate a reference spectrum, considering the experimental conditions such as temperature (298 K), P_{IR cell} and path length (800 cm) of the IR cell and the instrumental resolution of the IR spectrometer (1 cm^-1). An iterative procedure is applied to obtain the best match to the experimental spectra and to yield the mole fraction of H₂O in the IR cell.

III. Theoretical Methodology

The geometries of the molecules studied were optimized at the M06-2X-D3/aug-cc-pVTZ level of theory,^42–44 where the inclusion of diffuse orbitals and Grimme D3 dispersion correction ^44,45 aims specifically to provide a good description even for the long-distance interactions in the complexes. To further improve the relative energies, single point CCSD(T)/aug-cc-pVTZ energy calculations were performed,⁴⁶ which were combined with zero-point energy corrections at the M06-2X-D3 level of theory (wavenumber scaling 0.971).⁴⁷ It was attempted to exhaustively characterize all conformers for the CH₃CHO + OH, CH₃CHO + H₂O, CH₃CHO + H₂O + OH, CH₃CHO + CH₃CHO, and CH₃CO + H₂O complexes.

This was done by generating a large number of starting geometries (200 to 400) at a moderate distance of the pertaining agents for each complex, spanning the entire (half)sphere of the approach vectors and for each approach a set of different relative rotations of the constituents. These initial geometries were allowed to relax in M06-2X/cc-pVDZ energy minimization calculations, initiated with an explicit Hessian calculation to get an optimal start of the downhill trajectory. The resulting minimum geometries were then further optimized at the M06-2X-D3/aug-cc-pVTZ level of theory. Equilibrium constants for these complexes were calculated at the high-pressure limit based on the ratio of the temperature-dependent partition functions and the aforementioned ZPE-corrected relative energies, using the rigid rotor harmonic oscillator approximation.

Semi-quantitative theoretical kinetic calculations were performed based on equilibrium constants, transition state theory, and RRKM theory;^48–51 the relevant formulas are given below. All these calculations were performed in a rigid rotor harmonic oscillator approximation. The quantum chemical calculations were done using the Gaussian16 program suite.⁵² The thermodynamic and kinetic calculations were performed using in-house software.

IV. Experimental Results And Discussion

A. Determination of the onset for CH₃CHO dimerization at ultralow temperatures.

It is recognized for a long time that the clustering process is enhanced and favored at low temperatures. The first step of a clustering process, the dimerization, has been widely discussed in the literature for different organic compounds^31,32,53 At the ultralow temperatures of the present work, formation of (CH₃CHO)₂ may occur in the timescale of the kinetic experiments when high initial concentrations of CH₃CHO are introduced in the CRESU chamber.

$${\text{CH}}_3{\text{CHO+CH}}_3\text{CHO}\to {\left({\text{CH}}_3\text{CHO}\right)}_2{k}_{\text{dimer}}$$ (1)

Since reaction 1 reduces the amount of “free” acetaldehyde in the cooled jet, the measured rate coefficient can be underestimated.^32,34 For that reason, at first, kinetic studies are performed without added water in a wide concentration range of [CH₃CHO]₀ in order to identify the threshold of dimerization, which means the acetaldehyde concentration beyond which the pseudo-first order plots start to present a clear downward curvature (see Fig. 3 as an example at 21.7 K). To compare different experiments at the same temperature, k’-k’₀ is plotted vs [CH₃CHO]₀ using Eq. IV.

$$k\text{'}-k\text{'}o=k_{obs}\left(T\right){\left[{\text{CH}}_3\text{CHO}\right]}_0$$ (IV)

where k’ ₀ is k’ obtained in the absence of CH₃CHO at a constant [H₂O]₀.

Fig. 3.

Examples of the corrected pseudo-first order rate coefficients, k’-k ₀’, as a function of initial acetaldehyde concentration without and with added H₂O (4.16 x 10¹⁴ cm^-3) at 21.7 K.

Once the threshold of dimerization is identified, all kinetic experiments without added water at a given temperature were carried out in the linear part of the k’-k’0 vs [CH₃CHO]₀ plots to ensure that the dimerization process is negligible and not affecting the measured k(T).

As shown in Fig. 3, the red circles correspond to kinetic data in the curved zone, where dimerization occurs, and they were disregarded in the kinetic analysis. In the presence of water, no downward curvature of k’-k’0 vs [CH₃CHO]₀ plots was observed in the same concentration range and beyond (as shown in Fig. 3 for T=21.7K). That means that much higher (more than twice at 21.7 K) initial concentrations of CH₃CHO can be added when water is present and the k’-k’₀ versus concentration plots remain linear. Our experimental observations of the effect of H₂O on the (CH₃CHO)₂ formation are in good agreement with the theoretical results (see Fig. 8 and Fig.S1) which indicate that the water complex, CH₃CHO(H₂O), is sufficiently stable to evacuate CH₃CHO from its dimer complexes, if any are present as in the experiment by Vöhringer-Martinez et al.

Fig. 8.

ZPE-corrected potential energy surface for the CH₃CHO + OH and CH₃CHO(H₂O) + OH reaction systems at the CCSD(T)/aug-cc-pVTZ//M06-2X-D3/aug-cc-pVTZ level of theory.

B. Effect of H₂O on the observed rate coefficient, k _obs(T), as a function of temperature.

As exemplified in Fig. 4 for selected temperatures, k’-k’₀ is linearly correlated with [CH₃CHO]₀, both in the absence and presence of a constant [H₂O]₀, as reflected by Eq. IV. As can be deduced from the slopes of the plots presented in Fig. 4 and summarized in Table III, k _obs(T) decreases in the presence of H₂O, making the OH-reactivity slower. In Table III, the uncertainties in k _obs(T) are statistical ±2σ, while uncertainties in k’0 are statistical ±1σ. The systematic errors in k _obs(T) are mainly related with inaccuracies or miscalibrations of instruments such as mass flow controllers or pressure gauges, which directly affect the determination of the acetaldehyde concentration. Based on the typical differences (6%) between the mass flow and optical measurements of [CH₃CHO]₀, a conservative 10% systematic error can be added to the statistical uncertainties. In the absence of added H₂O, k _obs(T) are in agreement with those previously reported by Blázquez et al.³² for the OH+CH₃CHO reaction (k(T)) at ultralow temperatures. At the highest temperature, 135 K, however, a slightly higher k _obs(T) was found in the present investigation.

Fig. 4.

Examples of the corrected pseudo-first-order rate coefficients, k’-k’0, as a function of the initial acetaldehyde concentration with and without added H₂O at 21.7 K, 64.1 K, and 135.0 K. Uncertainties are ±1σ.

Table III. Initial concentrations of added H₂O, CH₃CHO and the observed rate coefficients in absence (k’ 0) and in presence of CH₃CHO (k _obs(T)) as a function of temperature.

T / K	[H2O]0 /1014 molecules cm-3	[CH3CHO]0 /1013 molecules cm-3	k’0 ±1σ / s-1	k obs(T) ±2σ /10-10 cm3 s-1
21.7±1.4	0	0.33-1.80	5307±235	3.69±0.44
	0.10	0.81-3.64	8791 ± 274	3.42±0.30
	0.13	0.72-3.56	6989 ± 223	3.31±0.44
	0.15	0.71-3.57	6855 ± 227	2.86±0.46
	0.33	0.34-3.53	8410 ± 259	3.17±0.49
	0.50	0.76-3.00	8830 ± 241	2.34±0.18
	0.59	0.36-3.49	8884 ± 279	2.77±0.70
	0.67	0.36-3.54	10571 ± 273	2.71±0.60
	0.82	0.55-3.57	10881 ± 237	2.47±0.36
	1.48	0.41-1.78	10161 ± 361	1.73±0.14
	2.80	0.40-1.97	16843 ± 120	1.38±0.12
	4.16	0.42-3.33	15063 ± 180	1.34±0.12
	7.56	0.77-3.06	19083 ± 236	1.30±0.19
	7.67	0.50-3.29	16898 ± 218	1.12±0.13
36.2±1.2	0	0.34-3.83	7447 ±147	2.18±0.16
	0.36	2.01-4.08	17083 ± 411	1.56±0.19
	0.46	1.16-4.24	14078 ± 259	2.14±0.18
	0.71	2.01-4.08	19880 ± 716	1.47±0.26
	0.89	2.08-4.21	18073 ± 856	1.17±0.11
	1.06	1.16-4.68	19564 ± 294	1.12±0.26
	1.94	1.63-4.76	24620 ± 657	1.27±0.12
	2.13	2.09-4.66	24062 ± 788	1.01±0.25
	3.07	2.48-4.17	27314 ± 771	0.95±0.12
	3.55	2.11-5.15	25324 ± 1000	0.97±0.12
	4.24	1.67-3.97	28478 ± 893	0.85±0.55
64.1±1.6	0	0.17-3.05	2812±62	1.45±0.14
	1.85	0.18-1.59	8708 ± 81	0.94±0.10
	5.84	0.18-1.61	10928 ± 100	0.86±0.37
	8.17	0.18-1.56	11314 ± 220	0.79±0.13
	11.5	0.18-1.61	12790 ± 197	0.86±0.12
	13.7	0.18-1.58	13798 ± 410	0.79±0.06
	16.7	0.19-1.64	15526 ± 307	0.64±0.10
	22.4	0.18-1.61	14720 ±576	0.64±0.14
89.5±0.6	0	0.41-3.96	3054±74	0.85±0.06
	11.5	0.80-4.21	10523 ± 605	0.60±0.20
	14.2	0.80-4.23	14018 ± 735	0.53±0.08
	22.3	0.80-4.21	15897 ± 894	0.50±0.11
	29.4	0.79-4.21	17649 ± 743	0.47±0.11
135.0±0.8	0	1.66-16.4	2661±188	0.58±0.04
	3.77	3.86-16.2	8889 ± 337	0.42±0.10
	10.5	3.81-16.0	15749 ± 670	0.41±0.08
	20.0	3.78-15.9	17517 ± 566	0.41±0.06
	26.9	2.61-8.79	22558 ± 53	0.43±0.05
	28.6	1.58-13.0	31048 ± 702	0.34±0.03
	38.0	3.75-15.7	17473 ±532	0.41±0.06

In the presence of a large excess of H₂O, k _obs(T) drastically decreases in the 21.7-89.5 K range with respect to those measured without added water, while at 135.0 K, k _obs(T) is not affected by [H₂O]₀, within the experimental uncertainties, confirming that at high temperatures the OH+CH₃CHO reaction is not water-assisted. These observations are contradictory to those previously reported by Vöhringer- Martinez et al. ²², who observed an increase, about a factor of two, of k _obs(60-118 K) in the presence of about 3% H₂O in the gas flow (i.e. [H₂O]₀ = 1.5×10¹⁵ cm^-3 at 60 K and 3.3×10¹⁵ cm^-3 at 118 K). A potential reason for the discrepancy with Vöhringer-Martinez et al.’s experiments is a direct consequence of the short time scale used by these authors (e.g., 80 μs at 77 K). To observe a decay of the LIF signal over several OH-lifetimes in that time scale high initial concentrations of acetaldehyde are needed. Their concentration range is more than 5 times higher than those used in this work. Employing high [CH₃CHO]₀, especially in the experiments without added H₂O, provokes the formation of acetaldehyde dimers, (CH₃CHO)2, as shown in Fig. 3 and discussed also by Blázquez et al.³² yielding curved k’ (or k’-k’₀) versus [CH₃CHO]₀ plots and a lower slope, implying a lower k _obs(T) when fitted to a straight line according to Eq. II. Blázquez et al.³² showed evidences that k _obs(T) obtained by Vöhringer- Martinez et al., in absence of water, were underestimated for that reason.

As mentioned above, the use of low [CH₃CHO]₀ ensures us to perform the kinetic study below the onset of acetaldehyde dimerization. As can be seen in Fig. 5, k _obs(T) reaches a roughly constant value at a certain [H₂O]₀. When [H₂O] → ∞, all CH₃CHO is converted into CH₃CHO(H₂O) complex (reaction 2) and then the OH-loss is dominated by reaction (3) in this limit condition.

$${\text{H}}_2{\text{O+CH}}_3\text{CHO}\to {\text{CH}}_3\text{CHO}\left({\text{H}}_2\text{O}\right)k_{complex}\left(T\right)$$ (2)

$${\text{OH+CH}}_3\text{CHO}\left({\text{H}}_2\text{O}\right)\to 2{\text{H}}_2{\text{O+CH}}_3\text{C}\left(\text{O}\right)k_{OH\_}\left(T\right)$$ (3)

Fig. 5.

Dependence of k_obs(T) with initial water concentration at different temperatures. The fitting lines represent the obtained result from the fit of the experimental data to Eq. (X). Uncertainties are ±1σ

To physically interpret the observed dependence of k _obs(T) with the water content, the time-dependence of [CH₃CHO] and [CH₃CHO(H₂O)] has to be taken into account to derive k’-k’0 and to further compare with Eq. IV. From the rate equation expressed as the OH loss by reaction with CH₃CHO and CH₃CHO(H₂O), k’-k’₀ is given by:

$$k^{\prime }-k_0^{\prime }=k( \text{T})\left[{\text{CH}}_3\text{CHO}\right]+k_{{\text{oH}}_{\text{c}}\text{omplex}}(\text{T})\left[{\text{CH}}_3\text{CHO}\left({\text{H}}_{2}0\right)\right]$$ (V)

In the presence of an excess of water, the destruction of acetaldehyde is essentially due to the association process (reaction 2) with a negligible contribution of the dimerization reaction (1). Hence the time-dependence expression of [CH₃CHO]_t can be simply approximated to:

$${\left[{\text{CH}}_3\text{CHO}\right]}_t={\left[{\text{CH}}_3\text{CHO}\right]}_0\exp \left(-k_{complex}\left(T\right){\left[{\text{H}}_2\text{O}\right]}_{0}t\right)$$ (VI)

On the other hand, [CH₃CHO(H₂O)]_t can be deduced considering the mass balance for CH₃CHO:

$${\left[{\text{CH}}_3\text{CHO}\right]}_0={\left[{\text{CH}}_3\text{CHO}\right]}_t+{\left[{\text{CH}}_3\text{CHO}\left({\text{H}}_2\text{O}\right)\right]}_t$$ (VII)

and that the rate of reaction (2) (k _complex(T)[CH₃CHO][H₂O]) is much higher than that for reaction (3) (k _{OH_complex}(T)[OH][CH₃CHO(H₂O)]) since [OH] is always several orders of magnitude smaller than the other involved concentrations. The resulting expression for [CH₃CHO(H₂O)]_t follows as:

$${\left[{\text{CH}}_3\text{CHO}\left({\text{H}}_2\text{O}\right)\right]}_t={\left[{\text{CH}}_3\text{CHO}\right]}_0\left\{1-\exp \left(-k_{complex}\left(T\right){\left[{\text{H}}_2\text{O}\right]}_{0}t\right)\right\}$$ (VIII)

Introducing equations (VI) and (VIII) into equation (V) leads to:

$$k\text{'}-k{\text{'}}_0={\left[{\text{CH}}_3\text{CHO}\right]}_0\left\{k_{OH\_complex}\left(T\right)+\left\{\left(k\left(T\right)-k_{OH\_complex}\left(T\right)\exp \left(-k_{complex}\left(T\right){\left[{\text{H}}_2\text{O}\right]}_{0}t\right)\right)\right\}\right\}$$ (IX)

Equation (IX) is comparable to equation (IV) when time t coincides with the experimental time t_hydro used to obtain the OH LIF decays which allowed the deduction of the first order rates k’-k’0 plotted in Fig. 4. As specified earlier, t _hydro is the time needed for molecules to flow from the nozzle exit to the extremity of the uniform flow concurring with the detection zone. Note that this time is flow dependent and its value is given is table V for each temperature condition employed in this work. From this, the observed rate coefficient can be expressed as:

$$k_{obs}\left(T\right)=k_{OH\_complex}\left(T\right)+\left\{\left(k\left(T\right)-k_{OH\_complex}\left(T\right)\right)\exp \left(-k_{complex}\left(T\right){\left[{\text{H}}_2\text{O}\right]}_0{t}_{hydro}\right)\right\}$$ (X)

Table V. Rate coefficients for the formation of the CH₃CHO(H₂O) complex as (k _complex(T)) and the hydrodynamic time as a function of temperature. Uncertainties are ±1σ statistical errors.

T / K	t hydro/μs	k(T) / 10-10 cm3 s-1	k complex(T) / 10-11 cm 3 s -1	k complex(T)/k(T
21.7±1.4	203	3.69±0.22	4.19±0.54	0.114±0.016
36.2±1.2	278	2.18±0.08	5.72±1.18	0.262±0.055
64.1±1.6	544	1.45±0.07	1.12±0.57	0.077±0.039
89.5±0.6	605	0.85±0.03	0.17±0.03	0.020±0.004
135.0±0.8	239	0.58±0.02

The k _obs(T) versus [H₂O]₀ curves presented in Fig. 5 are well-described by Eq. X. Therefore, since k(T) was experimentally obtained in the experiments performed without added water, k _complex(T) and k _{OH_complex}(T) were obtained from the fit of k _obs(T) versus [H₂O]₀. Table IV lists the rate coefficient for the water-assisted OH+CH₃CHO reaction and the kOH_complex(T)/k(T) ratios as a function of temperature. Clearly, the reaction of CH₃CHO(H₂O) with OH is slower than the water-free reaction, contrary to Vöhringer-Martinez et al.’s conclusions. The T-dependence of k _{OH_complex}(T) is well-described by the power relationship, k _{OH_complex}(T) = ATⁿ in the temperature range 20 -135 K (see Fig. 6). The fitted parameters are: A = (7.8±2.3)×10^-10 cm³ s^-1 and n = -(0.59±0.08), ±1σ statistical uncertainties. Regarding the k _{OH_complex}(T)/k(T) ratio, it slightly increases when temperature increases. In contrast, Iuga et al.¹⁷ calculated that k _{OH_complex}(T)/k(T) ratio decreases from 0.22 at 220 K to 5.3×10^-4 at 298 K. Uncertainties in k _{OH_complex}(T)/k(T) ratio is the result of the error propagation considering the uncertainties in k _{OH _complex}(T) and k(T).

Table IV. Rate coefficients^[a] for the water-free OH+CH₃CHO reaction (k(T)) and for the water-assisted OH+CH₃CHO reaction (k _{OH_complex}(T)) as a function of temperature.

T / K	k(T) / 10-10 cm3 s-1	k OH_complex(T) / 10 cm s	k OH_complex(T)/k(T)
21.7±1.4	3.69±0.22	1.22±0.11	0.33±0.04
36.2±1.2	2.18±0.08	0.97±0.06	0.44±0.03
64.1±1.6	1.45±0.07	0.76±0.05	0.52±0.04
89.5±0.6	0.85±0.03	0.45±0.03	0.53±0.04
135.0± 0.8	0.58±0.02	0.41±0.03	0.71±0.06

^[a]±1σ statistical uncertainties.

Fig. 6. Temperature dependence of the rate coefficient for the OH+CH₃CHO(H₂O) reaction, k _{OH_complex}(T).

Similarly, in Table V, the rate coefficients for the formation of CH₃CHO(H₂O) complex are presented as a function of temperature. As it can be seen, at the investigated ultra-low temperatures, the formation of CH₃CHO(H₂O) is around one order of magnitude slower than its reaction with OH radicals. In a general trend, k _complex(T) decreases at high temperatures as the association reactions are less favored. Uncertainties in k _complex(T)/k(T) ratio is the result of the error propagation considering the uncertainties in k _complex(T) and k(T).

V. Theoretical Results And Discussion

A. Equilibrium constants for the CH₃CHO(H₂O) and (CH₃CHO)2 complexes

Two geometries were found for the CH₃CHO(H₂O) complex (see Fig. S1 of the supporting information-SI). The most stable, at -4.77 kcal mol^-1 below the reactants, has the H₂O molecule spanning the CH₃ and acetyl O-atom, while the other complex, at -4.21 kcal mol^-1, bridges the CHO oxygen and H-atom. The equilibrium constant was calculated to be K_eq(20-300K) = 6.19×10^-26 (T/K)^0.19 exp(2488 K/T) cm³ molecule^-1, i.e. K_eq(100K) = 8.7×10^-15 cm³ molecule^-1 (see Fig. 7). Even at room temperature, the side-ways complex contributes 88 % of the complex population, and at the low temperatures in the experiments the complex will exist near-exclusively of this lowest-energy complex. The low equilibrium constant near room temperature reconfirms earlier reports^17,54 that water complexation cannot effectively catalyze acetaldehyde oxidation by OH in an atmospheric setting, due to the low incidence of H₂O-complexed CH₃CHO.

Fig. 7. Equilibrium constants for the CH₃CHO(H₂O) and (CH₃CHO)₂ complexes.

For the (CH₃CHO)₂ complex, 8 geometries were found, ranging stability from -4.3 to -1.8 kcal mol^-1 below the free constituents (see Fig. S1 of the SI). The most stable geometry is best described as an L- shaped structure, with the two acetaldehydes interacting with their aldehyde groups. The equilibrium constant was calculated to be K_eq(20-300K) = 7.30×10^-31 (T/K)^1.94 exp(2305 K/T) cm³ molecule^-1, i.e. K_eq(100K) = 4.9×10^-17 cm³ molecule^-1. As seen in Fig. 7, the equilibrium constant for the water complex is higher by at least one order of magnitude, and typically more, across the experimentally relevant temperatures. The preference for the water complex is driven both by its deeper energy well and by the entropic advantage of complexing a water molecule (low quantum state density for relative translation and rotation) compared to a CH₃CHO molecule (high state density). The higher equilibrium constant for H₂O implies that adding water to the reaction mixture will displace acetaldehyde from its dimer complexes and preferentially, if not exclusively, form water + acetaldehyde complexes.

B. Potential energy surfaces (PESs)

B.1. PES for the CH₃CHO + OH system

Figure 8 shows the PES for the reaction of OH radicals with CH₃CHO, which proceeds initially by the formation of a pre-reactive complex, for which 5 stable minima were found, with energies ranging from -4.7 to -0.1 kcal mol^-1 below the free reactants (see Fig. S2 of the SI). The most stable complex geometry has the OH radical bridging the acetaldehyde O-atom and CH₃ group, whereas the second-most stable complex, only 0.71 kcal mol^-1 higher in energy, complexes the OH radical across the CHO group. The remaining complexes are much less stable, > 3 kcal mol^-1 above the most stable complex, and correspond to van der Waals complexes without an H-bond. Figure SI-10 presents the energies and ball-and-stick depiction of the geometries of the complexes and transition states in the CH₃CHO+OH system.

The H-abstraction pathway involves two near-isoenergetic submerged transition states at -1.19 and -1.15 kcal mol^-1 below the free reactants. Our level of theory thus predicts a higher energy barrier than Vöhringer-Martinez et al. ²² (-2.4 kcal mol^-1) and Iuga et al. ¹⁷ (-1.28 and -1.72 kcal mol^-1). The lowest-energy pathway has a slightly non-planar TS geometry, and IRC calculations show it starts at the second-most stable H-bonded pre-reaction complex. The second TS geometry is fully planar, and its pathway initiates at a van der Waals reactant complex. We note that it is sometimes thought that the TS is submerged due to the pre-reaction H-bonding between the carbonyl group and the OH radical. In the TS geometries, however, the H-bond is fully broken, with ^•OH---O=C distances of ˜3.8 Å, and the submergence is due to van der Waals and dipole interactions.

Once the TS threshold is traversed, the reaction products, CH₃CO + H₂O, first form a post-reaction complex, for which we located 3 stable geometries at energies ranging from -32.0 to 30.3 kcal mol^-1. (see Fig. S2 of the SI). This complex readily dissociates to the free products at an energy of -28.6 kcal mol^-1.

The potential energy surface found here has the same essential features as determined in earlier theoretical works ^{17,22,55–57} and any difference can be attributed to our more detailed characterization of the complexation properties, at a higher level of theory.

B.2. PES of the OH + CH₃CHO(H₂O) system

Figure 8 also shows the PES for the reaction of OH radicals with the CH₃CHO(H₂O) complex; as already indicated, this reactant complex has two possible geometries, the most stable of which has the H₂O molecule complexed to the side of CH₃CHO. Adding OH allows for many distinct CH₃CHO(H₂O)(OH) complexes, where we have located 15 stable geometries spanning 5.6 kcal mol^-1 in relative energies, with the energetically lowest at -6.3 kcal mol^-1 below the reactants. In Fig.S3 of the SI, the energies and ball-and-stick depiction of the geometries of the complexes and transition states in the CH₃CHO(H₂O)+OH system are shown.

Two H-abstraction transition states were found, each with a pathway starting at a distinct CH₃CHO(H₂O) complex. The lowest-energy transition state, -4.9 kcal mol^-1 below the reactants, connects the OH radical, the H₂O molecule, and the aldehyde –CHO moiety in an H-bonded 7-membered ring. This barrier height is less submerged than found earlier by Vöhringer-Martinez et al. ²² (-6.3 kcal mol^-1) and Iuga et al. ¹⁷ (-8.8 and -9.5 kcal mol^-1). The geometry of the other TS resembles the CH₃CHO+OH transition state, but with a spectator H₂O molecule complexed on the side of CH₃CHO between the carbonyl O-atom and the methyl group; this TS is 3.72 kcal mol^-1 above the lower TS, owing to the absence of an H-bond on the abstracting OH radical, as in the CH₃CHO+OH PES. Once the TS is traversed, the reaction products, CH₃C^•O + 2 H₂O, first form a post-reaction complex, which readily dissociates to the free products at an energy of -23.8 kcal mol^-1.

C. Comparison of the reaction dynamics without and with H₂O

It is possible in principle to theoretically predict the temperature- and pressure-dependent rate coefficients for the CH₃CHO + OH and CH₃CHO + H₂O + OH reaction systems; we refer to our earlier work on CH₃OH + OH on the methodologies involved ³¹. Such rate coefficient calculations are typically accurate to a factor of 2 to 4, which unfortunately, in this case, is insufficient to discriminate between the reaction rate coefficients of the cases with and without water. As such, we have not performed these costly theoretical kinetic calculations. The available data, however, is still able to reveal interesting details on the reaction dynamics, and the effect of an H₂O catalyst.

C.1. Reaction dynamics of H-abstraction

The reaction of CH₃CHO + OH is fast, owing to its submerged H-abstraction TS. Its rate coefficient k(T) has a negative temperature-dependence, which is caused by two effects. Firstly, the initial complexation reaction is a barrierless reaction, which is known to show a slight negative temperature dependence. Secondly, at higher temperatures, the H-abstraction TS faces more competition from the energetically higher, but entropically more favorable redissociation of the complexes to the free reactants due to the increased energy in the nascent complexes, thus reducing the product formation efficiency of the overall reaction. This latter competition is more effective in the low-pressure regime when the complexes formed do not lose energy in collisions with the bath gas, and thus all have sufficient energy for redissociation. At high pressure, the complexes are instead thermalized within the pre-reaction complex energy well, and typically have insufficient energy to redissociate, leaving only H-abstraction as a viable reaction path, be it over the submerged barrier or by tunneling through this barrier.

C.2. The impact of water complexation

Comparing the potential energy surface with added water against that without a water molecule suggests at first sight that the CH₃CHO(H₂O) + OH reaction should be the faster reaction. Firstly, the pre-reaction complexes are more stable, and there are more complexation geometries possible, which typically leads to faster complexation. Furthermore, the H-abstraction TS is greatly reduced in energy, facilitating the H-abstraction and reducing redissociation of the complexes to the reactants. A more detailed comparison, however, reveals some surprising effects.

Firstly, the dipole moment of the CH₃CHO(H₂O) complex, 1.9 or 2.1 D depending on the complex geometry, is significantly smaller than that of the free CH₃CHO molecule, 2.9 D. The attractive force exerted on the OH radical at long distances is thus less for the water-complex, leading to a lower capture rate. This long-range interaction is important mostly at the lowest temperatures, as there the energies are lowest and the entropic bottleneck is located at the furthest distances. At higher energies, the kinetic bottleneck along the barrierless complexation pathway will tighten, shifting it to closer separations where the improved H-bonding synergies within the deeper water-complex energy well can be more effective. As already mentioned, we cannot theoretically quantify with sufficient accuracy to what internal energy the capture rate for the water-complex will remain below that of the free CH₃CHO reactant.

A second surprising observation is that H-abstraction from CH₃CHO(H₂O) is not all that favorable, despite the lowered barrier height. Specifically, the lowest abstraction TS has multiple H-bonds in a ring structure, making this TS very rigid and thus entropically unfavorable. To illustrate, we mention that for a Boltzmann distribution of the complexes at 300 K, the higher H-abstraction TS already contributes ˜25 % of the reaction flux, despite having a Boltzmann energy factor that is 620 times less favorable (3.72 kcal mol^-1 above the lowest TS). In the high-pressure regime, the lowest TS will remain the dominant pathway as the complexes are stabilized into the bottom of the energy well. In the low-pressure regime, however the complexes retain the full energy content of the reaction, and the reaction rate is no longer energy-limited but instead controlled by the unfavorable entropy, preventing the anticipated acceleration of H-abstraction This is illustrated in Fig. 9, showing the energy-specific rate coefficients for H-abstraction for the water-containing complexes, calculated using RRKM theory, including all conformers of reactants and transition states. The rate coefficient k(E) through the lowest TS reaches a maximum at internal CH₃CHO(H₂O)(OH) energies even less than those received in its formation, and reduces slightly at higher energies due to the faster increase of the state density of the many pre-reaction complexes compared to the TS. This is in stark contrast to the energy-specific rates intuitively expected when assuming similar rigidity for all TS structure. We illustrate this in Fig. 9 or a hypothetical TS at the same energy as the low TS, but entropically as loose as the high TS or as the CH₃CHO+OH TS; this hypothetical case leads to very fast H-abstraction rates. In reality, then, the nascent complexes may not necessarily always undergo H-abstraction despite the lower-energy TS, and redissociation to the reactants should be considered. At increasing internal energies, the less rigid higher-energy H-abstraction TS increases in importance and finally carries the largest reaction flux. The energy-specific k(E) for the water-free complexes are higher due to the lower state density for the CH₃CHO(OH) complexes compared to the CH₃CHO(H₂O)(OH) complexes.

Fig. 9.

Energy-specific rate coefficients for H-abstraction and redissociation in the pre-reaction complexes of the CH₃CHO + OH and CH₃CHO(H₂O) + OH reactions. H-abstraction rates are calculated directly from the quantum chemical data, while redissociation is estimated by inversion of the forward reaction rate using the equilibrium constant. The hypothetical transition state for H-abstraction is based on an intuitive interpretation of the PES ignoring the impact of entropy (see text).

C.3. Non-reactive redissociation of the OH-complexes

To judge the impact of redissociation on effective product formation, we need to estimate the redissociation reaction rate coefficients. Directly predicting the redissociation rates would require characterizing the barrierless pathways for all approaches to all complexes, which is computationally very costly. Furthermore, as already mentioned, the expected accuracy of the predictions would not be sufficient to unequivocally support the experimental observation that the rate coefficient is reduced by a factor of two in the case of added water. Still, to show that redissociation rate coefficients are in the correct order of magnitude, we should roughly estimate whether the entropic advantage of the redissociation is sufficient to overcome the 4.9 kcal mol^-1 energetic advantage of H-abstraction.

The redissociation rate coefficients can be estimated starting from the temperature-dependent equilibrium constants for OH-complexes. We find K _CH3CHO+OH(T)=2.53×10^-25 T ^-0.10 exp(2456 K/T) and K _{CH3CHO---H2O+OH}(T) = 2.31×10^-27 T ^0.47 exp(3302 K/T). Given that an equilibrium constant equals the ratio of the rate coefficients for the forward and reverse reaction, relying on the transition state theory expression for k(T), and assuming a rate coefficient of complexation k_complexation(T) similar to the experimental rate coefficient of ˜3×10^-10 cm³ molecule^-1 s^-1, we can then derive the T-dependent partition functions QTS(T) for the barrierless complexation/redissociation TS.

$$K_{\text{eq}}(\text{T})=\frac{k_{\text{complexation}}(\text{T})}{k_{\text{redissociation}}(\text{T})}$$ (XI)

$$k_{\text{redissociation}}(T)=\frac{k_{\text{complexation}}(T)}{{\text{K}}_{\text{eq}}(T)}=\frac{kT}{h}\frac{Q_{TS}(T)}{Q_{\text{complex}}(T)}\exp \left(\frac{-E_b}{kT}\right)$$ (XII)

we can then obtain k(E) for redissociation, where we integrate NTS(E) over energies 0 to E to obtain the sum of states GTS(E), and use the density of states N_complex(E) calculated for the ensemble of complexes using the Beyer-Swinehart-Stein-Rabinovitch algorithm. The resulting semi-quantitative k(E) for redissociation are highly approximate, with an anticipated uncertainty of an order of magnitude. They can be compared to the more reliable rate coefficient for H-abstraction, where we find that even for the hydrated case redissociation reaches parity with the H-abstraction rate coefficients with only ˜2 kcal mol^-1 excess energy in the reactants (see Fig. 9), and within the uncertainty redissociation is competitive against product formation. This is a counter-intuitive result, as one would normally not assume the H-abstraction TS to be so entropically hindered. Indeed, a hypothetical TS ignoring the rigidity of the lowest TS would not allow redissociation at all, as also illustrated in Fig. 9. Given the large uncertainty, we refrain from quantifying the fraction of redissociation, but conclude only that redissociation should not be discounted even in the water-catalyzed reaction despite the (deeply) submerged TS. The CH₃CHO(H₂O)(OH) complex can also dissociate to CH₃CHO(OH) + H₂O; this is isoenergetic to the OH loss, but as the cold CH₃CHO--OH complex formed will then undergo H-abstraction by tunneling this channel does not decrease the effective rate coefficient for product formation.

A critical condition of the above analysis is that the OH-complexes retain the full nascent energy of the reaction. As shown in Fig. 9, the energy-specific rates k(E) for dissociation are comparatively high in both systems, ≥ 4×10¹⁰ s^-1 even for the water complex. Hence, in the experimental conditions, both reactions are in the low-pressure regime, and even at 1 atm the reactions will still be in the low-pressure (CH₃CHO + OH) or fall-off regime (CH₃CHO(H₂O) + OH).

C.4. Temperature-dependence of effective product formation

The experimental data do not reveal which of the above two mechanistic effects, i.e. lower capture rate at low energies due to lower dipole moment, versus redissociation to the reactants due to the entropy of the H-abstraction TS, is the cause of the lower rate coefficient for CH₃CHO(H₂O) compared to CH₃CHO. The measurements do indicate that the redissociation fraction cannot be very high at the lowest temperatures as otherwise the rate coefficient would drop well below the collision limit, in disagreement with the observations. The experimentally observed decrease in the difference between the two cases with increasing temperature, starting at factor 3 at 21 K and disappearing above 135 K could have several reasons. Firstly, the difference in the capture rate between the two systems could decrease, as for higher energies the rate of reaction through barrierless complexation channels is determined increasingly by the OH-complex properties, and the effect on the long-range capture by the lower dipole moment of CH₃CHO(H₂O) compared to CH₃CHO would become less important. Secondly, the availability of a second H-abstraction channel in the CH₃CHO(H₂O)(OH) complex increases the total product formation rate at increasing internal energies faster than for CH₃CHO+OH (see Fig. 9). Higher temperatures could then allow the water complex to have a higher ratio of product formation to redissociation than the water-free reaction, increasing its apparent reaction rate. Likely, the observed trend is caused by a combination of these mechanisms. In principle, it should be possible to separate the effects by measurements in low-temperature but high-pressure gas-phase conditions, but we are not aware of an experimental setup that is capable of performing such measurements.

VI. Conclusions

In conclusion, we report that there is an anti-catalytic effect of water in the OH+CH₃CHO reaction at ultra-low temperatures (T=21.7-135.0 K). Increasing the water content in the jet converts, to a great extent, “free” CH₃CHO into a CH₃CHO(H₂O) complex, which enables to measure the impact of H₂O on its OH-rate coefficient in that temperature range. Our experimental results show that the water-assisted reaction is slower than the OH+CH₃CHO reaction at low temperatures, by a factor of ˜3 at 21.7 K and ˜2 at 36.2 – 89.5 K, while almost no effect of added H₂O was observed at 135.0 K. In agreement with Vöhringer-Martinez et al. ²², our theoretical calculations find that complexation of CH₃CHO with H₂O reduces the barrier to H-abstraction by 3.7 kcal mol^-1. The above experimental results thus appear in disagreement with the theoretical analysis, as intuitively one would instead expect a rate increase. However, the lower dipole moment of the CH₃CHO(H₂O) complex compared to free CH₃CHO reduces the long-range attraction to OH radicals, lowering the rate coefficient especially for the studied low temperatures where the rate is driven by long-range interaction. Furthermore, the hydrogen bonding with water strongly disadvantages the H-abstraction entropically. At the pressures used in the experiments (0.42 to 5.55 mbar), the nascent OH-complexes retain their full internal energy, and the entropic hindrance slows down the water-complexed reaction at those energies sufficiently to allow non-reactive redissociation towards the reactants to remain competitive against H-abstraction, to the same extent as for the water-free reaction.

The slight positive catalytic effect of a factor ˜2 previously described by Vohringer-Martinez et al. for the title reaction²² is attributed to a bias in these earlier measurements due to the short hydrodynamic time and high initial concentrations of CH₃CHO, which favors the formation of acetaldehyde dimers which have a lower reaction rate towards OH. We find that between 20 and 90 K, the formation of CH₃CHO(H₂O) is more favorable than (CH₃CHO)₂ and the present study provides an estimation of the association rate coefficient for the hydrated complex formation and of the rate coefficient for the OH + CH₃CHO(H₂O) reaction in this temperature range.

Data Availability

The data that supports the findings of this study are available within the article and its supplementary material. See Supplementary Material on energies and geometries of the CH₃CHO(H₂O) and (CH₃CHO)₂ complexes.