Signatures of a quantum diffusion limited hydrogen atom tunneling reaction

Abstract

We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH₂) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH₃OH) isolated in solid pH₂. Short-term irradiation of CH₃OH at 1.8 K readily produces CH₂O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH₃O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH₂OH growth. The CH₂OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH₃O with the pH₂ host, (ii) H atom reactions with the CH₂O photofragment, and (iii) long-range migration of H atoms and reaction with CH₃OH. We assign the rapid CH₂OH growth to the following CH₃O + H₂ → CH₃OH + H → CH₂OH + H₂ two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD₃OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH₂ quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

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1. Introduction

Hydrogen atom (H atom) adsorption and diffusion are important in many chemical environments such as heterogeneous catalysis,¹ condensed phase astrochemistry,^2–4 and hydrogen storage materials.⁵ There are a variety of H atom diffusion regimes based on the corrugation of the translational potential energy surface and the temperature at which diffusion occurs. Our interest lies in the regime of homogeneous periodic potential corrugations and extreme low temperatures where the diffusion of the H atom is inherently quantum mechanical. Specifically, we are studying the quantum diffusion of H atoms in solid parahydrogen (pH₂) in the temperature range between 1.7 and 4.3 K. In this temperature range we have observed new types of chemical behavior for reactions that involve H atoms. The basic premise of our work is that the H atom diffusion mechanism in solid pH₂ is somewhat unique and thus should lead to new types of diffusion limited reaction kinetics. In some cases we have observed tunneling reactions that only occur with appreciable yields below a certain critical temperature.^6–8 For reactions of H atoms with formic acid conducted in solid pH₂ at low temperature^7,8 we observed qualitatively different reaction products than the analogous reactions conducted in rare gas matrix studies⁹ at slightly higher temperatures suggesting the tunneling reactions in solid pH₂ are occurring under a different diffusional regime. A deeper understanding of the mesoscopic diffusion of H atoms in solid pH₂ is needed to unify a variety of seemingly disparate experimental observations. Further, understanding H atom quantum diffusion limited chemistry in solid pH₂ at a predictive level may also allow us to control a variety of low temperature H atom diffusion phenomena.

It is believed^10–19 that H atoms tunnel between adjacent lattice sites in solid pH₂ by a chemical mechanism that is based on the simplest chemical reaction, H + H₂ → H₂ + H. Given that the activation barrier²⁰ for this chemical reaction is 9.60 kcal mol⁻¹ (3360 cm⁻¹), at low temperature the only way the H atom can “quantum diffuse” is by repeated tunneling jumps through the reaction barrier. From a chemistry perspective, this means that H atom reactions with chemical dopants in solid pH₂ can continue to occur even at the lowest achievable temperatures because the H atom retains its mobility through quantum effects (tunneling). Evidence of quantum diffusion in surface studies is usually provided by the observation of temperature independent diffusion rates.²¹ The transition at low temperature from classical thermally activated hopping (Arrhenius-type temperature dependence) to quantum tunneling (temperature independent) typically occurs in the range of 60–140 K for H atoms on metal surfaces.²² Observation over such a large temperature range is not possible in solid pH₂ where the solid starts to rapidly sublime at temperatures above 5 K. Similarly, H atom reaction studies conducted in rare gas matrices can only be conducted over limited temperature ranges, but usually the H atoms only diffuse at appreciable rates in the classical thermal hopping range.⁹ The chemical physics in the quantum diffusion range should be distinct from the thermal hopping regime because the diffusion is governed by quantum mechanical phenomena. We therefore expect that quantum diffusion limited chemistry of H atoms with other chemical species in solid pH₂ will show both interesting temperature effects and reaction products. Indeed, we have now documented a series of H atom reactions with N₂O, HCOOH, and NO that show novel temperature effects and products.^6–8,23

In this study we focus on investigating reactions of H atoms with methanol (CH₃OH). The photochemistry and low temperature surface reactions of this chemical system (H + CO) have been well studied due the abundance of CH₃OH in a variety of astronomical environments.^4,24 To do this we rely on the 193 nm in situ photochemistry of methanol (CH₃OH) in solid pH₂ to generate H atoms. At this photon energy there are five open dissociation channels, namely,^25,26

CH₃OH + hν(193 nm) → CH₃O + H (1a)

→ CH₂OH + H (1b)

→ CH₃ + OH (1c)

→ CH₂ + H₂O (1d)

→ CH₂O + H₂ (1e)

However, gas phase photolysis at 193 nm results primarily in O–H bond fission via channel (1a) with an absolute quantum yield²⁵ of Φ = 0.86 ± 0.10. If channel (1a) is also dominant for the in situ photolysis in solid pH₂, then photolysis should produce both CH₃O and H atoms. We expect that since the cage effect in solid pH₂ is extremely weak,^14,19,27 the condensed phase photochemistry should only be weakly perturbed from the gas phase dynamics. Our basic experimental approach is to photolyze the CH₃OH/pH₂ sample for a short period of time to generate H atoms, and then we study the ensuing reaction kinetics for the reaction of H atoms with mainly CH₃OH. However, it turns out that the other product of this photolysis channel, namely the methoxy radical (CH₃O), can react directly with the pH₂ host via a two-step tunneling reaction scheme. Shown in Fig. 1(a) is the proposed reaction energy level diagram (electronic + vibrational zero point) calculated previously by Carvalho et al. from their best estimate results based on CCSD(T) electronic structure calculations.²⁸ Based on the reaction scheme shown in Fig. 1(a), when CH₃O is produced in the 193 nm photolysis of CH₃OH, the following two-step sequential tunneling mechanism becomes feasible,

CH₃O + H₂ → CH₃OH + H → CH₂OH + H₂ (2)

The reaction of CH₃O with the pH₂ host (step 1) has a high barrier (∼4440 cm⁻¹) and is suspected to be slightly exothermic (−280 cm⁻¹) to form the CH₃OH + H products.²⁸ At this point the H atom can diffuse away from the CH₃OH reaction partner or undergo another tunneling reaction (step 2) to form CH₂OH + H₂. The back reaction to reform CH₃O + H₂ is not possible under these low temperature conditions (T ≤ 4.3 K) because it would require an input of energy on the order of 280 cm⁻¹ (∼400 K). Indeed, we will show formation of CH₂OH follows this two-step tunneling mechanism. This reaction scheme is also consistent with recent studies of CH₃O trapped in solid pH₂ by Lee and co-workers.^29,30 In this previous study they produced CH₃O via the in situ 355 nm photodissociation of CH₃ONO and observed that the CH₃O species decayed with a time constant τ = 1/k = 2.2(1) min at 3.2 K.³⁰ By conducting additional studies on CD₃O, they were able to show that the dominant decay mechanism involves this two-step tunneling mechanism and not unimolecular isomerization of CD₃O → CD₂OD. Importantly, because they detect CH₃O using direct IR absorption, it means the fully equilibrated CH₃O fragment is reacting with the pH₂ host. These researchers also showed that there was no effect of IR irradiation from the FTIR source,³⁰ and thus the CH₃O is reacting with ground vibrational state pH₂. We will be able to explore this reaction mechanism further in the present study.

Fig. 1 Potential energy level diagram (electronic and zero point) for the reactions of (a) CH₃O with the pH₂ host and (b) H atoms with CH₂O. Note that the first step in (a) CH₃O + H₂ → CH₃OH + H is calculated to be slightly exothermic and is followed by a second step to form CH₂OH. See text for details.

Our interest in the 193 nm in situ photochemistry of CH₃OH in solid pH₂ is motivated by our desire to study the H + CH₃OH → CH₂OH + H₂ tunneling reaction.^28,31 As discussed, if photochannel (1a) is dominant, along with the generation of CH₃O is the production of H atoms. Further, because some of the primary photolysis products (CH₃O and CH₂OH) are also photolabile at 193 nm, there can be additional H atom production from secondary photolysis events. We can test for the presence of H atoms using the tunneling reaction of H atoms with CH₃OH to produce CH₂OH. By conducting these photolysis experiments such that CH₃OH is the most concentrated species after photolysis, repeated FTIR scans after photolysis can be used to indirectly monitor the H atom concentration via the tunneling reaction with CH₃OH. We can study the reaction kinetics as a function of temperature over the experimental range (1.7 to 4.3 K) to further explore the details of H atom quantum diffusion. That is, because the H + CH₃OH reaction is a bimolecular reaction that requires both reactants to be in adjacent lattice sites to react, the reaction kinetics are likely controlled by how fast and to what extent the two reaction partners diffuse next to each other. As we will show, reactions that rely on H atom quantum diffusion to occur can display anomalous temperature effects. Specifically, this type of reaction may only occur at low temperature and not at high temperature over this small range. This can be the result of changes in the microscopic details of H atom quantum diffusion over this small temperature range. Specifically, non-resonant tunneling jumps can be accommodated by one- and two-phonon processes that might steer the H atom differently towards a potential reaction partner.^32–34 This is still an active area of research and in these studies we will show evidence for H atom reactions with CH₃OH that only occur at 1.8 K, and not 4.3 K.

2. Experimental details

Our experimental apparatus is described in detail elsewhere;³⁵ briefly, we grow millimeters thick, chemically doped pH₂ crystals via co-deposition of independent gas streams of dopant (CH₃OH) and pH₂ host onto a BaF₂ optical substrate maintained at approximately 2.5 K inside a liquid helium bath cryostat. The pH₂ host in these studies is enriched to 99.97% pH₂ levels using a variable temperature ortho/para catalytic converter operated near 14.0 K. FTIR spectroscopy is performed on the sample using a normal incidence transmission optical setup. The measured integrated intensities of specific solid pH₂ IR absorptions^36–38 allow us to determine the IR path length through the sample, which permits the concentration of different species within the crystal to be determined using the Beer's Law expression,where [X] is the mole fraction of species X in parts per million (ppm), ε is the gas phase integrated absorption coefficient, d is the IR path length, and V₀ = 23.16 cm³ mol⁻¹ is the molar volume³⁹ of solid pH₂. The dopant, anhydrous 99.8% CH₃OH (Sigma-Aldrich) and fully deuterated CD₃OD (Sigma-Aldrich, 99.5% D) were used as received after several freeze–pump–thaw cycles. The concentrations of the various chemical species studied in this work are determined using eqn (3) and the integrated absorption coefficients listed in Table S1 provided in the ESI.† The accuracy of the determined absolute concentrations varies for each molecule studied due primarily to uncertainties in the integrated absorption coefficient, but we estimate the errors in the determined concentrations to be on the order of ±20%.

Photolysis is achieved using the 193 nm output of an ArF excimer laser (Gam Laser EX5) configured to pass through the sample at an angle of 45° with respect to substrate surface normal. This optical setup permits FTIR spectra to be recorded within the photolyzed region of the crystal either during or immediately after 193 nm irradiation. The typical experimental procedure is to photolyze a CH₃OH/pH₂ sample at a specified temperature for a short period of time and then record repeated FTIR spectra with short acquisition times to measure the ensuing low temperature kinetics. In this study we used two different FTIR configurations. To characterize the as-deposited sample we used a liquid nitrogen cooled InSb detector to record the spectrum from 1800–5000 cm⁻¹ at 0.05 cm⁻¹ resolution. To characterize the kinetics, we used a liquid nitrogen cooled HgCdTe detector for the range from 600 to 4900 cm⁻¹ at a resolution of 0.05 cm⁻¹ with a 5500 cm⁻¹ low pass filter in the IR beam. In this study we did not explicitly check for the effects of the FTIR beam on the measured kinetics; however, previous studies have shown that the decay of CH₃O is not induced by IR irradiation.³⁰ The time resolution of the FTIR spectra used to map out the kinetics therefore is controlled by how many scans are averaged together and the resolution. For example, the methanol system required a time resolution of 41.3 s (4 co-added scans at 0.05 cm⁻¹ resolution) for one of the fastest post-photolysis reactions measured in this study.

We employed the GAUSSIAN 09 program⁴⁰ to perform geometry and harmonic vibrational calculations on CH₂OH for all possible hydrogen and deuterium isotopomers. We conducted both MP2 and density functional calculations with Dunning's correlation-consistent polarized-valence triple-zeta (cc-pVTZ or aug-cc-pVTZ) basis sets.^41,42 These data are presented in the ESI,† in Tables S2–S10.

3. Results and discussion

One of the first steps in any photolysis study is the spectroscopic assignment of all the various species involved, and most importantly the photolysis products that may be unstable otherwise. In this case, we had published spectra for a variety of the species involved (CH₃OH, CO, CHO)^7,43–45 but needed assigned peaks for all possible deuterium isotopomers of CH₂OH, CH₃OH and CH₂O. For convenience we list the various peaks used to determine species concentrations in Table S1 (ESI†). All the initial vibrational assignments of CH₂OH were carried out by comparison to B3LYP harmonic vibrational frequency and intensity calculations, gas phase literature values where available,^46,47 and Ar matrix isolation studies.^48,49 During the course of this work Lee and co-workers published^29,30 vibrational assignments for CH₂OH and CD₂OH isolated in solid pH₂ at 3.2 K. Note this previous work did not report observation of CD₂OD and the reasons for this will become clear in this study. We present all the peaks assigned to CH₂OH, CD₂OD, and CD₂OH in Tables S11–S13 (ESI†) along with representative spectra of CH₂OH in Fig. S2 in the ESI.†

3.1 Photolysis studies of CH₃OH/pH₂

In total four separate photolysis experiments were conducted on as-deposited CH₃OH/pH₂ samples at ∼1.8 K with initial CH₃OH concentrations ranging from 75 to 120 ppm. Representative FTIR spectra of CH₃OH, CH₂OH, CH₂O, CHO, and CO are presented in Fig. S3 in the ESI† at different stages of the photolysis experiment (Expt. #4). The full kinetic data for all four low temperature photolysis experiments is shown in Fig. S4 in the ESI.† The kinetic data for the photolysis experiment (Expt. #4) recorded with the highest time resolution is shown in Fig. 2. The grey vertical bar in Fig. 2 represents the timing and duration of the 193 nm photolysis exposure. After deposition is complete, FTIR spectra are recorded to characterize the CH₃OH concentration prior to photolysis (117(1) ppm indicated by dashed red line in Fig. 2). What is clear from Fig. 2 is that even after the photolysis laser is shut off, a variety of chemical reactions continue to occur even at 1.84(1) K.

Fig. 2 Kinetic plots for a 193 nm photolysis experiment (Expt. #4) conducted on a CH₃OH/pH₂ sample at 1.84(1) K. The photolysis exposure (3 min, 80 Hz, 19 mW cm⁻²) is indicated by the grey vertical bar. The data are represented by dotted circles, and the lines are the results of least-squares fits of the data to eqn (4) or (5), except the CH₂OH data that is fit to the sum of three first-order processes (see text for details).

We will first characterize the photolysis step. In the four photolysis experiments performed in this study the general findings are (1) the CH₃OH photolysis follows first-order kinetics with a quantum yield of Φ = 0.14(1), (2) the major photolysis products are CO and CH₂O in a concentration ratio of [CO]/[CH₂O] = 1.1(1) and (3) there is a 13(9)% systematic overestimation in the concentration of the photoproducts (CO + CH₂O) compared to the decay in the CH₃OH precursor concentration. Using the published cross section⁵⁰ for CH₃OH at 193 nm and the measured UV fluence and exposure time, the determined quantum yield is consistent with the photolysis quantum yields of other small molecules measured by this lab^27,51 (see Fig. S5, ESI† for analysis) and illustrates the weak cage effect of solid pH₂. The photo-induced production of CO indicates a significant amount of secondary photolysis is occurring under these conditions as none of the primary photochannels produce CO (see eqn (1)). We note that in addition to CO and CH₂O there is minor production (<10%) of CH₄ which can arise from CH₂ production (CH₂ + H₂ → CH₄). Given the uncertainties in the measured concentrations of each species, getting the concentrations to agree to within ±20% is an adequate level of agreement. We point out that the CH₃OH concentration is determined using the ν₁ OH stretching vibration. This CH₃OH feature has a complicated lineshape (see Fig. S3, ESI†) thereby making systematic errors in the CH₃OH concentration likely larger. In the experiment shown in Fig. 2 we observe only minor photoproduction of H₂O (<1 ppm), however, H₂O is difficult to characterize because H₂O is present in the vacuum gas surrounding the crystal. Examination of Fig. S4 (ESI†) shows that for most experiments there is zero-order growth in the H₂O concentration due to continued deposition of gas phase H₂O. However, we find no evidence of H₂O satellite peaks^52,53 or ortho-H₂O immediately⁵⁴ after the photolysis laser is stopped indicating that H₂O is not produced at significant levels by the in situ photolysis of CH₃OH. The negligible H₂O production is consistent with the gas phase photochemistry that shows channel (1d) is a minor channel and experiments conducted on CD₃OD (to be shown) which display only minor production of D₂O.

What is striking about the kinetic traces in Fig. 2 is the amount of chemistry that occurs well after the photolysis laser is shut off. For example, the CH₃OH concentration continues to decrease by 7.0(3)% over the full post-photolysis reaction period (approximately 500 minutes). This post-photolysis behavior in the CH₃OH concentration can be quantified by fitting the data to a single exponential decay function,

[X] = [X]_∞ + A exp(−kt) (4)

and the results of the fit to the CH₃OH data are shown as a red line in Fig. 2 with the fitted constants reported in Table S14 (ESI†). The decay of CH₃OH after photolysis proceeds with an average (averaged over the four low temperature experiments) first-order rate constant k_AVG = 6.1(10) × 10⁻³ min⁻¹. This behavior is indicative of H atom reactions which can continue to occur well after the laser is stopped because the H atom can undergo long-range quantum diffusion.^6–8,23 At this low temperature (e.g., 1.84(1) K), only H atoms are mobile while all the other species are essentially immobilized. As we will show, this post-photolysis chemistry can be rationalized by a combination of (1) reactions of photochemical intermediate (CH₃O) with the pH₂ host and (2) H atom reactions with stable chemical species (CH₃OH, CH₂O) present in the crystal.

For the two major photoproducts CO and CH₂O, the kinetic behavior after photolysis is qualitatively different. Surprisingly, a clear decrease in the CO concentration after photolysis is not observed. The fitted line in Fig. 2 for the CO data is just the equation of a straight line (y = mx + b) and it shows almost no change in the CO concentration (a slight decrease). In contrast, the CH₂O concentration decays immediately after photolysis with a first-order decay constant. The CH₂O data are fit to eqn (4) and the extracted parameters are shown in Table S15 (ESI†). CH₂O decays with a significantly greater average rate constant (k_AVG = 1.8(4) × 10⁻² min⁻¹) than CH₃OH. However, we believe the CH₂O decays for the same reason as CH₃OH, reactions with H atoms. We will discuss the CH₂O decay in more detail, but we assert it is faster because it involves local migration of H atoms to photo-produced CH₂O.

The two species that continue to grow after photolysis are CHO and CH₂OH. The CHO growth after photolysis is fit to the following expression,

[X] = [X]₀ + A[1 − exp(−kt)] (5)

and the results of the fit are shown as a black line in Fig. 2 with the fitted parameters reported in Table S16 (ESI†). The CHO concentration rapidly increases with an average first-order rate constant of k_AVG = 2.3(9) × 10⁻² min⁻¹ right after photolysis is stopped. We know^7,8 that CHO trapped in solid pH₂ is photodissociated at 193 nm and thus the concentration of CHO can only start to grow after the photolysis laser is stopped. Based on the close agreement for the rate constants extracted for CHO growth and CH₂O decay, we speculate that CHO is produced by the tunneling reaction,

H + CH₂O → H₂ + CHO (6a)

→ CH₂OH (6b)

When H atoms react with CH₂O they can either abstract a hydrogen atom to form CHO or add to CH₂O to form CH₂OH.⁵⁵ The potential energy diagram in Fig. 1(b) illustrates the energetics of both reactions (including zero point energies) using calculated values in the literature.^55,56 We will use this strategy of “matching” the extracted rate constants to work out the various chemical reaction mechanisms that are operative under these conditions. As already discussed, we do not measure a decrease in the CO concentration ruling out the possibility that the association reaction H + CO → HCO is readily occurring under these conditions. This lack of reaction with CO at first seems surprising given that H atom reactions with CO have been measured for surface reactions and in neon matrices at temperatures as low as 3 K.^4,57–60 One potential difference is that CO freely rotates^44,45 in solid pH₂ as evidenced by the rotational fine structure in FTIR spectrum (see Fig. S3, ESI†) of CO. The lack of the H + CO reaction underscores how low temperature tunneling reactions depend critically on the timescales for diffusion and reactive tunneling. Indeed, H atom hydrogenation reactions with CO show surface temperature, composition, and surface structure dependent effects.⁴ The studies by Pirim and Krim on hydrogenation reactions with CO show that the reaction environment or composition of the ice can have a dominant role on steering the low temperature tunneling reactions.^57–60

We will return to the discussion of why the rate constant for eqn (6) is significantly larger than the rate constant extracted from the CH₃OH data in the Discussion section. We want to point out that comparing first-order rate constants is not affected by systematic errors in the concentration determinations. Clearly, we check the proposed mechanisms by verifying that the amount of products equals the loss in reactants, but these comparisons are only as good as the determined absolute concentrations. By “matching” rate constants we provide a more reliable way to infer the elementary tunneling reaction steps that are occurring under these conditions. The proposed mechanism reported in eqn (6) thereby suggests that we might also measure a contribution to the growth of CH₂OH that has a first-order rate constant in the range measured for CH₂O decay. Examination of Fig. 1b shows that this reaction can occur by H atom addition to CH₂O (however with a higher reaction barrier).

By far the most complex kinetic behavior is displayed by the growth of the CH₂OH species. As shown in Fig. 2, right after photolysis there is rapid growth in the CH₂OH concentration that is right at the limit of the time resolution of the repeated FTIR spectra. Then the CH₂OH growth transitions into a slower increase that continues for the full length of the experiment. The high quality of the CH₂OH data allows us to fit the growth to an expression that contains three separate first-order rate expressions. The total fitted expression is shown as a blue line in Fig. 2 and the individual fitted components are shown in an expanded view in Fig. 3. There is a fast process with an average (excluding experiment #1 which was recorded with too slow a time resolution) rate constant k₁ = 0.35(1) min⁻¹ that happens right after the photolysis laser is stopped. The value of this extracted rate constant is very close to the rate constant determined by Lee and co-workers (k = 0.46(2) min⁻¹) for the decay in the CH₃O concentration after photolysis of CH₃ONO at 3.2 K.³⁰ Thus, we assign the fast component of the CH₂OH growth to reactions of CH₃O with the pH₂ host. The medium rate growth process has an average rate constant of k₂ = 1.7(6) × 10⁻² min⁻¹ and is assigned to reactions of H atoms with CH₂O according to eqn (6b). Finally, the slowest process that accounts for 74.1% of the post photolysis growth of CH₂OH occurs with an average rate constant k₃ = 4.0(5) × 10⁻³ min⁻¹. We assign this process to reactions of H atoms with CH₃OH because the k₃ rate constant is very close to the rate constant for the CH₃OH decay (k = 6.1(10) × 10⁻³ min⁻¹) as it must be if we are observing a single elementary step, i.e., H + CH₃OH → H₂ + CH₂OH. This reaction continues to occur over the full 500 min reaction time. We assert that the H + CH₃OH → H₂ + CH₂OH reaction is quantum diffusion limited. We point out that the extracted k₃ rate constant is very similar to the average rate constant (k = 4.9(7) × 10⁻³ min⁻¹) measured for the H + HCOOH → H₂ + HOCO reaction studied previously⁷ in solid pH₂ at 1.9 K that we also claim is quantum diffusion limited. As discussed previously, this slow process is the most interesting because we believe it occurs via long-range migration of H atoms.

Fig. 3 Expanded view of the early time growth kinetics of CH₂OH for the experiment depicted in Fig. 2. A fit to the data consisting of three first-order processes is shown as a solid blue line, the three individual first-order components to the CH₂OH growth are plotted as solid red lines (labeled by the rate constant and percent final concentration), and the residuals from the fit are plotted as a solid black line. See text for details.

We want to explore the fast growth in the CH₂OH concentration observed immediately after photolysis a little further. This reaction has been studied extensively theoretically due to its importance in methanol combustion chemistry.^31,61,62 Shown in Fig. 1(a) is the best ab initio estimates²⁸ for the reaction barriers (ΔV⁰₀) and enthalpy of reaction (ΔH⁰₀) at 0 K for the two reactions involved in the conversion of CH₃O to CH₂OH in solid pH₂. In the proposed tunneling mechanism, CH₃O reacts with a neighboring pH₂ molecule to form CH₃OH and an H atom. This reaction step involves tunneling through a 4440 cm⁻¹ barrier and is almost thermo-neutral depositing about 280 cm⁻¹ to the reaction products. Then because the two products are produced in adjacent lattice sites and solid pH₂ can efficiently dissipate the reaction energy, they undergo a second tunneling reaction (ΔV⁰₀ = 2870 cm⁻¹) to form CH₂OH and H₂. This two-step tunneling mechanism is relatively fast because the first tunneling reaction is for a dopant reacting with the pH₂ host and therefore the reaction does not require diffusion of the reactants to occur.

3.2 Photolysis studies of CD₃OD/pH₂

The assignment of the CH₂OH growth process with the fast rate constant (k₁) to the reaction of CH₃O with the pH₂ host is clearly speculative because we never observe CH₃O directly. We would likely have to alter the photolysis conditions significantly to observe CH₃O directly because CH₃O is only a minor product in the 193 nm in situ photolysis of CH₃OH in pH₂ and CH₃O does not have any strong absorptions (greatest ∼13.0 km mol⁻¹) in the infrared.³⁰ In the previous studies by Lee and co-workers that detected CH₃O,³⁰ they utilized 1000 ppm concentrations of the precursor (CH₃ONO) and irradiated the sample for 150 s and recorded the spectrum immediately after irradiation with acquisition times of ∼25 s. However, we can test this assignment using CD₃OD as a precursor. If we re-write reaction (2) starting with fully deuterated CD₃O,

CD₃O + H₂ → CD₃OH + H → CD₂OH + HD, (7)

we see that only the growth of CD₂OH can show this fast component. After the reaction of CD₃O with pH₂, the H atom can only abstract the deuterium atom attached to carbon because abstraction of the H atom attached to oxygen to reform CD₃O would require a significant input of energy. Therefore, in photolysis studies of CD₃OD we should still observe rapid growth in CD₂OH right after photolysis, but the only way to produce CD₂OD is through H atom reactions with fully deuterated methanol (CD₃OD) and we would expect this to happen at a much slower rate because the reaction is quantum diffusion limited.

To test our interpretations of the CH₂OH kinetic data we conducted three additional photolysis experiments using fully deuterated methanol (CD₃OD). First, we need to characterize the concentration of various deuterated methanol isotopomers to look for the possibility of isotopic scrambling prior to photolysis. We detect absorption features for the CD₃OD/pH₂ samples in both the O–D and O–H stretching regions, indicating that some scrambling has occurred for the hydroxyl deuterium atom. However, only minor scrambling (if any) of the methyl deuterium atoms was detected. Using Ar matrix infrared data⁶³ for the various deuterium isotopomers of methanol, we expect medium to strong infrared absorptions in the 2800 to 3000 cm⁻¹ region for various C–H stretching modes of CHD₂OH, CHD₂OD, CH₂DOH and CH₂DOD. As shown in Fig. S6 in the ESI,† if we examine this region for both the CH₃OH/pH₂ and CD₃OD/pH₂ samples, prominent C–H stretching peaks are only observed for the CH₃OH/pH₂ sample. For the CD₃OD/pH₂ sample, the only absorption in this region is due to the O–D stretching vibration of CD₃OD near 2709.65 cm⁻¹. Note that the absorption near 2612.76 cm⁻¹ in Fig. S6 (ESI†) is due to the hydrogen bonded O–D stretch of the CD₃OD dimer.⁶⁴ Even at 10 times the magnification, only very small absorptions are measured in the expected C–H stretching region. We take this as evidence that the only methanol isotopomers at appreciable concentrations prior to photolysis are CD₃OD and CD₃OH. This scrambling likely occurs in the metal sample holder attached to the dopant vacuum manifold prior to deposition.

We performed the first CD₃OD photolysis experiment in an analogous fashion as the CH₃OH/pH₂ photolysis experiments on a low temperature, as-deposited sample. We can monitor the growth of CD₂OH and CD₂OD separately using the corresponding CO stretch peaks near 1200 cm⁻¹ that are shown in Fig. S7 in the ESI.† The kinetic behavior of the CD₂OD and CD₂OH isotopomers are qualitatively different and provide further support for the mechanistic interpretations of the CH₂OH kinetic data. The full kinetic data for all species are shown in Fig. S8 in the ESI;† we present expanded views of the kinetic data after the first photolysis for CD₂OD and CD₂OH in Fig. 4. We fit both isotopomers to a sum of two first-order growth expressions and find clear differences between the two growth curves. For CD₂OH, we observe 45% production via a fast process and 55% via a slow process. Thus, as predicted by mechanism (7) we observe fast growth in CD₂OH after photolysis consistent with rapid tunneling reactions of CD₃O with the pH₂ host. In contrast, the importance of this fast growth process is much diminished in CD₂OD, although not completely absent. For CD₂OD, we observe 12% production via a fast process and 88% via a slow process. As we show in Fig. S8 (ESI†), in a second photolysis exposure of the same CD₃OD/pH₂ sample the amount of this fast process for CD₂OD was even more diminished. Further, for both species the rate constant extracted from the slow growth process quantitatively matches the rate constant extracted for the slow growth of CH₂OH. We take this as evidence that for all three hydroxymethyl isotopomers (CH₂OH, CD₂OH, CD₂OD) the slow growth is caused by reactions of mobile H atoms with the corresponding methanol isotopomers (CH₃OH, CD₃OH, CD₃OD). The reason the extracted rate constants are all approximately the same is because the rate is determined by the rate of H atom quantum diffusion to the reactive partner. We note that in these deuterated methanol experiments the photoproduction of CD₂O is much less (about a factor of two less) suggesting that H atom reactions with CD₂O should be less important to the CD₂OH kinetics and that is why the CD₂OH growth kinetics can be well fit with just two first-order rates.

Fig. 4 Kinetic plots for a 193 nm photolysis experiment conducted on a CD₃OD/pH₂ sample at 1.84(1) K. The photolysis exposure is indicated by the grey vertical bar. The data are represented by dotted circles, and the lines are the results of least-squares fits of the data to the sum of two first-order growth processes. Note that CD₂OH shows a significant fast growth process right after photolysis that is not present in the CD₂OD growth.

3.3 Temperature dependence of the photoinduced kinetics

We want to measure the temperature dependence of the observed photo-induced kinetics as a further test of which reactions are quantum diffusion limited. In Fig. 5 we show the results of two separate photolysis exposures conducted on the same CH₃OH/pH₂ sample. We deposit the CH₃OH/pH₂ sample as usual and then raise the temperature to 4.3 K prior to photolysis. We allow the sample to equilibrate at 4.34 K for approximately 10 min. As can be seen in Fig. 5, at 4.34 K we measure a decrease in the CH₃OH concentration with photolysis and production of CH₂O and CO similar to the photolysis experiments conducted at low temperature (∼1.8 K). The relative amounts of CO and CH₂O are slightly different from the low temperature photolysis, but we detect the same major photoproducts. However, the contribution to the growth of CH₂OH from the slow k₃ process is now completely absent and post-photolysis changes in the CH₂O and CHO products are not observed. The CH₂OH data after photolysis #1 can be fit to an expression that contains only two first-order rate constants. The results of this fit are shown in Fig. 5 as a black line and the fitted constants are shown in Table S17, Expt. #5 (ESI†). Under these high temperature conditions, 70% of the CH₂OH growth occurs due to reactions of CH₃O with the pH₂ host. This is what we expect because the reaction of CH₃O with the pH₂ host does not rely on H atom diffusion, and thus it should still readily occur at 4.34 K. The remaining 30% of the CH₂OH growth occurs with a rate constant of k₂ = 1.2(8) × 10⁻² min⁻¹ and we will explore the interpretation of this result in the Discussion section. Note that the difference in the CH₂OH post-photolysis growth at 4.3 K is also reflected in the kinetics of other species that rely on H atom quantum diffusion to occur.

Fig. 5 Kinetic plots for a 193 nm photolysis (3 min, 80 Hz, 208 μJ cm⁻²) experiment conducted on a CH₃OH/pH₂ sample at two different temperatures (Expt. #5). The first photolysis exposure (photo #1) is performed at 4.34(1) K (red dotted circles). The sample is then cooled to 1.74(2) K and photolyzed (blue dotted circles) for a second time (photo #2). The data clearly show that continued growth of CH₂OH and CHO after photolysis is only observed at the lower temperature. Fits to the data are shown as solid black lines.

We then lowered the temperature of the sample to 1.74 K and mark the first data point recorded at the lower temperature with an arrow in Fig. 5. We let the sample equilibrate and recorded four repeated FTIR spectra. We did not detect any significant changes in the concentration of any of the species implying that significant concentrations of H atoms are not present in the sample at this time. After the sample equilibrated at the lower temperature (1.74(1) K), we photolyzed the sample for a second time (photo #2) and recorded the ensuing kinetics. Consistent with our previous low temperature experiments, we observe the complicated CH₂OH growth kinetics that can be fit to the sum of three single exponential growth expressions. We find similar fitted parameters showing significant contributions to the growth of CH₂OH from the slow k₃ process. We also detect growth in the CHO concentration and decay in the CH₃OH and CH₂O concentrations that support our interpretation of the kinetics. We point out that for the two photolysis exposures at different temperatures, the amount of fast CH₂OH growth and the fitted k₁ rate constants are equal to within the fitted uncertainties. This supports our assignment of the fast process to reactions of the CH₃O with the pH₂ host. The photolysis conditions of both exposures are the same and therefore we produce comparable amounts of CH₃O during photolysis that then decay at the same rate. We expect the rate constant for reaction of the CH₃O photofragment with the pH₂ host to be independent of temperature over this range because it does not depend on H atom diffusion. Basically, this rate constant characterizes the pseudo first-order decay kinetics ([pH₂] ≫ [CH₃O]) of CH₃O in the pH₂ host; the two reactive species are in constant physical contact because the CH₃O is produced in solid pH₂. In contrast, a reaction of an H atom with CH₃OH requires these two species to be in close proximity and therefore depends on the details of H atom quantum diffusion. These results verify that H atom quantum diffusion is qualitatively different at these two temperatures and implies that only at the lower temperature does the H atom undergo long-range migration and reaction with CH₃OH.

We performed a similar temperature dependent photolysis experiment on a CD₃OD/pH₂ sample. The full kinetic data for this experiment is shown in Fig. S9 in the ESI† and in Fig. 6 we show the results for just CD₂OH and CD₂OD. We deposit the CD₃OD/pH₂ sample, raise the temperature to 4.36 K, and record four FTIR spectra prior to photolysis. As can be seen in Fig. 6, photolysis at 4.36 K produces around 0.35 ppm of CD₂OH and almost no CD₂OD as expected based on the high temperature CH₃OH/pH₂ photolysis results. That is, CD₂OH can still be produced by reactions of the CD₃O photofragment with the pH₂ host, but CD₂OD cannot be produced by this mechanism. These findings are also consistent with the work of Lee and co-workers who did not report³⁰ observation of the CD₂OD isotopomer in their photolysis experiments conducted at 3.2 K. This isotopomer can only be produced by H atom reactions with CD₃OD and these quantum diffusion limited reactions do not occur at higher temperatures (only at 1.8 K). Then the sample temperature is lowered (as marked with an arrow in Fig. 6) and after the sample equilibrates it is photolyzed for a second time. Photolysis at 1.67(1) K clearly shows the qualitatively different kinetics for CD₂OH and CD₂OD. The CD₂OH shows significant contributions from two first-order processes with rate constants that match the previously recorded k₁ and k₃ rate constants. Note the CD₂OD kinetics only show a minor medium rate constant component (∼4%) with greater than 96% coming from the slow k₃ component. In this case, the different post-photolysis kinetics for CD₂OH and CD₂OD is even more evident than in Fig. 4. Furthermore, the different temperature behaviors of the CD₂OD/CD₂OH kinetic traces are consistent with the temperature dependence measured in the 193 nm photolysis of CH₃OH/pH₂. We note for completeness, that we performed another experiment on a CD₃OD/pH₂ sample where we conducted the temperature dependent photolysis in the reverse order (e.g., low and high) and rigorously found the same behavior (see Fig. S10 and Tables S18 and S19, ESI†).

Fig. 6 Kinetic data for the 193 nm photolysis (3 min, 80 Hz, 17 mW cm⁻²) of a CD₃OD/pH₂ sample at two different temperatures (Expt. #7). The first photolysis exposure (photo #1) is performed at 4.34 K (red dotted circles). The sample is then cooled to 1.74(2) K and photolyzed (blue dotted circles) for a second time (photo #2). The data clearly show that continued growth in CD₂OH and CD₂OD after photolysis is only observed at the lower temperature. Fits to the data are shown as solid black lines.

4. Discussion

4.1 Understanding the CH₂OH (CD₂OH) growth kinetics

One of the features of the complex CH₂OH (CD₂OH) growth kinetics that initially confused us was why it separated into three distinct first-order processes. We show in Fig. 7 pseudo first-order plots of all the extracted rate constants based on the assigned reaction mechanisms. For example, for the CH₃O + H₂ reaction we plot in Fig. 7(a) the extracted k₁ rate constant measured from the CH₂OH growth curve as a function of the initial CH₃O concentration (also estimated from the fit). Based on the assigned mechanism, the rate law for the production of CH₂OH via the fast k₁ reaction should be, Rate = k₁[pH₂][CH₃O], but since the pH₂ concentration is constant, it can be written in a pseudo first-order form as Rate = k^eff₁[CH₃O] where k^eff₁ = k₁[pH₂]. As expected, the extracted rate constant shows no dependence on the initial CH₃O concentration and gives a precise average rate constant of k₁ = 0.36(1) min⁻¹. The fact that this fast first-order process can be separated from the other two CH₂OH growth processes immediately implies that the fast process is occurring by a different reaction mechanism than the other two. This is consistent with assigning this fast rate process of the CH₂OH growth to reaction mechanism (2) that does not involve H atom reactants. Similarly, we extract a comparable fast rate constant (see Fig. 7(a)) from the CD₂OH growth for a lower initial CD₃O concentration consistent with the rate limited tunneling step being abstraction of an H atom from a nearby pH₂ molecule.

Fig. 7 Plots of the extracted H atom reaction rate constants (k₁–k₃) versus the initial concentration of the reaction partner. None of the rate constants show the expected pseudo first-order linear dependence on reaction partner concentration. Note that blue symbols signify rate constants extracted from CH₂OH concentrations, black from CH₃OH, red from CHO, green from CH₂O, cyan from CD₂OH, and brown from CD₂OD. The indicated errors are from the fit.

We can roughly estimate the timescale for the first tunneling reaction step as follows. If we model the reaction as tunneling through a square barrier, we can calculate the probability or rate constant (s⁻¹) using the following expression,

where ν₀ is the translational zero point frequency of CH₃O in a single substitutional site in solid pH₂, a is the width of the barrier, m is the mass of the tunneling particle, and E_a is the height of the barrier. For this simple estimate, we use the zero point energy for CH₃O in a 1-dimensional particle-in-a-box with length equal to 3.8 Å (ν₀ = 0.37 cm⁻¹ = 1.1 × 10¹⁰ s⁻¹), E_a = 4442 cm⁻¹ based on the barrier to the reaction, m = m_H, and we vary the value of a to match the measured tunneling rate of k₁ = 0.36(1) min⁻¹. A value of a = 0.867 Å reproduces the tunneling rate and seems plausible. For comparison, we measured a decay rate of k_tun = 1.9(5) min⁻¹ for ortho-NH₂ that was produced in 193 nm photolysis studies⁶⁵ of NH₃ in solid pH₂. Similar to CH₃O, we assigned the rapid decay of ortho-NH₂ to a tunneling reaction with the pH₂ host (NH₂ + H₂ → NH₃ + H) where the barrier to reaction in this case was 3966 cm⁻¹. For the slightly smaller barrier we would expect a faster tunneling rate, and if we just change the barrier height and use the same parameters used above and eqn (8) to calculate the tunneling rate constant for ortho-NH₂ we get k_tun = 1.7 min⁻¹. This level of agreement is probably largely fortuitous, but it does illustrate that the proposed tunneling mechanism is plausible. In general, reactions of photogenerated species with the pH₂ host should be relatively fast for hydrogen abstraction reactions and the tunneling rate should be nearly independent of temperature because these reactions do not require H atom quantum diffusion. We also note that the analogous photochemical studies conducted in solid ortho-deuterium should show significantly reduced decay rates.

We assign both the medium (k₂) and slow (k₃) rate constants for CH₂OH growth at low temperature to reactions with mobile H atoms. These H atom quantum diffusion reactions are different from reactions of a chemical species with the pH₂ host because they require the H atoms to both quantum diffuse and react. The reason we can separate the fast growth of CH₂OH from these other first-order growth processes is because the fast reaction is occurring by a different reaction mechanism than the H atom quantum diffusion reactions, i.e., reactions of CH₃O with the pH₂ host. However, why the medium and slow CH₂OH growth processes can be separated into two different “types” of first-order H atom quantum diffusion reactions is not so immediately apparent. Assuming that all H atoms quantum diffuse at the same rate and react with different dopant species at different rates depending on the barrier to reaction, then you should only measure one effective rate constant that equals the sum of all the first-order rate constants. To better illustrate this idea examine Fig. 3. Only a small percentage (9.4%) of the H atoms react with a medium rate constant. The majority of H atoms (74.1%) react with a much slower rate constant. How can this be that the medium rate constant reaction does not use up all the H atom reactants? Clearly, H atom reactions with CH₂O should continue to occur given that the CH₂O concentration is still non-zero (see Fig. 2). But, indeed this is not what we observe. The ability to decompose these two CH₂OH growth processes into two first-order reactions immediately suggests that there are different “types” of H atoms.

Another indication that quantum diffusion can be selective such that H atoms only diffuse next to certain species is given in the pseudo first-order rate constant plots shown in Fig. 7. For both the medium (k₂) and slow rate (k₃) coefficients that we have assigned to H atom reactions that involve quantum diffusion, we observe that the effective rate constant extracted from the fits does not scale linearly with the concentration of the H atom reaction partner. For example, take the reaction of H atoms with CH₂O that produces CHO which are shown as green circles in Fig. 7(b). Given that this is an elementary step we can immediately write the rate law as Rate = k[CH₂O][H]. Assuming that the CH₂O concentration does not change much, we can rewrite the rate law as Rate = k^eff[H], where k^eff = k[CH₂O]. This implies that the effective pseudo first-order rate constant k^eff should scale linearly with the CH₂O concentration. Examination of Fig. 7(b) shows that this is not the case, instead, the measured k₂ rate constant remains constant for changes in the initial CH₂O concentration of more than a factor of 2 (e.g., 4 ppm to 10 ppm). We have now observed this behavior for a variety of H atom quantum diffusion reactions that we have studied to date.^7,23 We observe the same behavior for the H + CH₃OH → H₂ + CH₂OH reaction with the slowest rate constant where the measured rate constant does not scale linearly with the initial CH₃OH concentration (see Fig. 7(c)). Further, we measure the same rate constant for the growth of CD₂OD (brown circles) or CD₂OH (cyan circles). We take this as evidence that the reaction is not “diffusion limited” in the normally defined sense. As we have shown previously for the H + NO reaction,²³ because the H atom continues to be mobile due to quantum diffusion the bimolecular reaction kinetics are intrinsically first-order (the rate does not depend on the CH₃OH concentration over the 75 to 120 ppm range) and the H atom decay kinetics reflect the H atom quantum diffusion rate, not the tunneling reaction rate of H atoms with CH₃OH.

We speculate that the two different rates for the H atom quantum diffusion reactions are caused by both short- and long-range diffusion mechanisms. That is, the reactions that occur with a faster first-order time constant represent reactions of H atoms with other photofragment species that are nearby. Under these conditions where the CH₃OH concentrations is the largest, but still rather dilute (<100 ppm), the dominant H atom decay channel is the reaction of H atoms with CH₃OH. Only this reaction continues to occur over the full length of the experiment and constitutes proportionally the greatest amount of H atom decay. This implies that the H atom reactions with CH₂O only occur for H atoms that are generated in near proximity to the CH₂O photofragment. This explains why the amount of H atoms that decay via the medium rate (k₂) tunneling reactions with CH₂O is always small; only a subset of the generated H atoms is produced near another chemical impurity. In addition, these H atoms may be the result of secondary photolysis and be in regions of the crystal that are damaged or strained. One possible example is an H atom created in an interstitial site close to a CH₂O photofragment. However, H atoms that quantum diffuse through the solid over longer distances only react with the CH₃OH molecule. Thus, the two “types” of H atoms that are formed during the in situ CH₃OH photolysis step are H atoms in close proximity to other photofragments, and well isolated H atoms. By well-isolated we mean H atoms produced in substitutional sites far removed from other chemical impurities. The smaller fraction of H atoms that react on a faster timescale do so because they have smaller distances to quantum diffuse and react. These short-range H atoms diffuse differently because the quantum diffusion is perturbed by the presence of a nearby chemical dopant or because the H atom is produced in a region that is strained. Once these H atoms are consumed, these reactions stop occurring and now the only H atom reactions possible involve long-range quantum diffusion through the pH₂ solid and the reaction with CH₃OH. Clearly this interpretation of the data is speculative and more experiments are needed to refine our understanding. However, two features measured in this study provide important clues as to the details of this chemistry. First, the H atom reactions do not obey pseudo first-order kinetics and second they can be separated into two different first-order processes.

4.2 Signatures of H atom quantum diffusion reactions

Another important signature of an H atom quantum diffusion reaction is that because the reaction kinetics reflects the H atom diffusion rate and not the tunneling reaction rate with specific chemical dopants, the H atoms do not necessarily decay by the tunneling reaction with the lowest reaction barrier. For example, Fig. 1(b) shows the reaction barriers for the three exothermic reactions of an H atom with CH₂O. We assign the dominant H atom decay channel to the H + CH₂O → CH₂OH reaction which has the highest barrier. Now it could also be occurring via the reaction that produces the CH₃O intermediate, but we also observe CHO growth that we assign to reactions of H + CH₂O that has the intermediate barrier. This points to an important working hypothesis; the decay dynamics and kinetics are controlled by H atom quantum diffusion, not the individual reaction tunneling rates. This goes against conventional wisdom in low temperature tunneling reactions and is a ramification of the somewhat unique reaction conditions that exist in low temperature solid pH₂ where the H atom continues to quantum diffuse even at the lowest temperatures. Take for example the lack of H atom reactions with CO that we observe under these conditions. This reaction has a very low barrier to reaction (E_a = 1590 ± 50 cm⁻¹).⁶⁶ This implies that the H atom has a much greater probability of diffusing next to a CH₂O or CH₃OH molecule compared to CO. The requirement that the two species diffuse next to each other restrains the chemistry that can occur. Quantum diffusion limited chemistry likely depends solely on the probability that the H atoms diffuse to a nearest neighbor site of a potential reactant. The presence and type of chemical impurity can also likely steer the trajectory of the incoming H atom such that the probability an H atom tunnels next to certain impurities is very low or high.

Another important signature of H atom quantum diffusion limited chemistry is the strong temperature dependence these reactions show. The H atom decay channels and rates depend on the details of how an H atom diffuses next to a chemical impurity and this differs from the quantum diffusion rates in pure pH₂. H atom quantum diffusion in a perfect pH₂ crystal proceeds via a resonant tunneling mechanism H + H₂ → H₂ + H where the initial and final lattice positions of the H atom have exactly the same energy due to the translational symmetry of the crystal.^16–18 The presence of crystal imperfections (e.g., chemical dopants) breaks this translational symmetry and causes a mismatch in the zero point energies of the H atom in for example second nearest and nearest neighbor lattice sites which greatly reduces the tunneling rate from the resonant value. This level mismatch can be compensated for by one- and two-phonon processes, which leads to a strong temperature dependence of the H atom quantum diffusion rate close to crystal imperfections.³² Not only is the rate changed, but the two different phonon assisted mechanisms lead to qualitatively different diffusion trajectories.³² For attraction between the reaction partners, diffusion towards the reaction partner is accompanied by spontaneous emission of phonons. The rate of spontaneous emission is proportional to ω³ (ω is the phonon emission frequency) and thus the most probable quantum diffusion jump is along the energy gradient (toward the chemical impurity).³² This mechanism would be operative only at the last stages of pairing when the intermolecular forces with the chemical dopant are the strongest. This mechanism is also independent of temperature. In contrast, the two-phonon mechanism where a thermal phonon inelastically scatters off the H atom–pH₂ pair can either result in positive or negative energy mismatch jumps. Because it requires the presence of phonons, this mechanism becomes more important at higher temperatures. For the two-phonon mechanism, the most facile tunneling trajectory is along small energy mismatches.³² This mechanism therefore leads to H atom trajectories that avoid chemical dopants. This combination of resonant, one- and two-phonon mechanisms can lead to temperature dependent H atom quantum diffusion where the different diffusional mechanisms compete with each other. While the details of how H atom quantum diffusion towards chemical impurities still need to be worked out, this work and others from this laboratory^6,7,23 show that H atom quantum diffusion reactions typically show a strong temperature dependence over the 1.7 to 4.3 K temperature range.

5. Summary

We show in this work that CH₃OH is readily photodissociated in solid pH₂ using 193 nm laser radiation. We identify CH₂O and CO as the major photolysis products and that they are produced in comparable amounts under these conditions. Through detailed kinetic studies of the sample after photodissociation, we assert that CH₃O is also produced during photolysis but can readily react via tunneling reactions with the pH₂ host to ultimately produce CH₂OH. While we do not observe the CH₃O intermediate directly, the fast growth in the CH₂OH concentration right after photolysis is assigned to CH₃O reactions with the pH₂ host. This mechanism is supported using similar photolysis studies of CD₃OD where we demonstrate the kinetics of CD₂OD and CD₂OH are consistent with reactions with the pH₂ host and not unimolecular isomerization (CH₃O → CH₂OH). Indeed, the measured fast CH₂OH rate constant is also comparable to the literature value³⁰ for the CH₃O decay rate in solid pH₂. This indicates that pH₂ matrix isolation cannot be used to store the CH₃O radical for long periods of time.

One of the major experimental observations of this study is that the H + CH₃OH → H₂ + CH₂OH reaction continues to occur long after the photolysis laser is shut off when the sample is maintained at 1.8 K. In fact, detailed analysis of the CH₂OH growth kinetics after photolysis indicate that at least three separate tunneling reactions are contributing to the CH₂OH growth; (i) the fast initial growth is due to reactions of the photoproduced CH₃O with the pH₂ host, (ii) the medium rate growth is due to H atom reactions with the CH₂O photofragment that are likely produced in close proximity, and (iii) the slowest and largest contribution to the growth is due to long-range migration of H atoms and reaction with CH₃OH. The different mechanisms of CH₂OH growth are confirmed via simultaneous kinetic measurements on CH₃OH and CH₂O. The reason the tunneling reaction of CH₃O with the pH₂ host represents the fastest CH₂OH growth mechanism is because the two reagents are in constant physical contact. Tunneling reactions of a photogenerated species with the pH₂ host can be relatively improbable (have large reaction barriers), but still represent the fastest decay channel because the two species do not need to diffuse to come in contact with each other to react. In contrast, reactions between an H atom and another dopant species require the two species to be in neighboring lattice sites, and this relies strongly on the basic transport mechanism of the H atom. Therefore, typically H atom reactions with other dopants are much slower than reactions with the pH₂ host and can be said to be quantum diffusion limited.

The second major finding of this work is that the H + CH₃OH reaction shows anomalous temperature dependence. Namely, this reaction readily occurs at 1.8 K while at 4.3 K it does not. This is the third example measured in this laboratory of an H atom reaction in solid pH₂ that more readily occurs at low temperature.^6–8 As we discuss in this paper, we believe the anomalous temperature dependence is related to the details of H atom quantum diffusion. We show in this paper that the expected dependence on reaction partner concentration for the pseudo first-order H atom reaction kinetics is not observed implying that the rate limiting step is not diffusion limited in the normal sense. H atom quantum diffusion limited reactions in solid pH₂ is still not fully understood and deserves further investigation. For example, not all H atom reactions with chemical dopants show this same anomalous temperature dependence. We note that the H + NO → HNO/NOH association reaction has a rate constant that increases with temperature over the 1.7 K to 4.3 K temperature range in an Arrhenius-type fashion, but yet also does not show pseudo-first order kinetics.²³

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We want to thank undergraduate Kylie A. Kufeld for conducting the first set of experiments in this project. The authors thank the National Science Foundation for its generous support through Grant CHE 08-48330 and CHE 13-62497.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp05064j

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