Quantum Diffusion-Controlled Chemistry: Reactions of Atomic

Article pubs.acs.org/JPCA

Quantum Diffusion-Controlled Chemistry: Reactions of Atomic Hydrogen with Nitric Oxide in Solid Parahydrogen Mahmut Ruzi and David T. Anderson* Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071, United States S Supporting Information *

ABSTRACT: Our group has been working to develop parahydrogen (pH2) matrix isolation spectroscopy as a method to study low-temperature condensedphase reactions of atomic hydrogen with various reaction partners. Guided by the well-defined studies of cold atom chemistry in rare-gas solids, the special properties of quantum hosts such as solid pH2 afford new opportunities to study the analogous chemical reactions under quantum diffusion conditions in hopes of discovering new types of chemical reaction mechanisms. In this study, we present Fourier transform infrared spectroscopic studies of the 193 nm photoinduced chemistry of nitric oxide (NO) isolated in solid pH2 over the 1.8 to 4.3 K temperature range. Upon short-term in situ irradiation the NO readily undergoes photolysis to yield HNO, NOH, NH, NH3, H2O, and H atoms. We map the postphotolysis reactions of mobile H atoms with NO and document first-order growth in HNO and NOH reaction products for up to 5 h after photolysis. We perform three experiments at 4.3 K and one at 1.8 K to permit the temperature dependence of the reaction kinetics to be quantified. We observe Arrhenius-type behavior with a pre-exponential factor of A = 0.036(2) min−1 and Ea = 2.39(1) cm−1. This is in sharp contrast to previous H atom reactions we have studied in solid pH2 that display definitively non-Arrhenius behavior. The contrasting temperature dependence measured for the H + NO reaction is likely related to the details of H atom quantum diffusion in solid pH2 and deserves further study.

1. INTRODUCTION The technique of matrix isolation spectroscopy is one of the most widely used methods to spectroscopically characterize highly reactive species such as radicals, especially in the IR region.1,2 Most matrix isolation studies utilize a low-temperature rare-gas matrix to immobilize the species of interest and prevent it from reacting with itself or other reagents within the matrix. Typically, the reactive species are generated by in situ photolysis of a precursor molecule or by passing a precursor gas stream through a microwave discharge during deposition. However, from the beginning it was realized that small atoms (N, O, F, and S) can be thermally mobilized in rare-gas matrices at cryogenic temperatures.3−6 This thermally induced mobility therefore introduces a third strategy,7 to use bimolecular reactions in the matrix to generate the species of interest. The application of matrix isolation spectroscopy therefore depends critically on the process of atomic and molecular diffusion through the matrix. However, the ability to “store” reactive species in a rare-gas matrix requires the reactive species to have a sufficiently small diffusion coefficient. In contrast, if a bimolecular reaction is required to generate the radical of interest, then the time scale of the radical’s production depends on how fast the reactants can diffuse within the matrix. In this latter case one wants one of the reactants to diffuse readily. To greater exploit these two competing synthetic strategies there was a burst of activity in the 1990s aimed at quantifying the diffusion process of atoms in rare-gas matrices over the © 2015 American Chemical Society

accessible cryogenic temperature range where the matrix remains solid. Some of the first studies focused on long-range migration of F atoms following photodissociation of F2 and led to the development of solid-state excimer lasers.8−10 The chemistry of translationally hot F atoms produced from the photodissociation of F2 is typically different from translationally cold atom chemistry initiated by thermally activated diffusion of the F atoms in the lattice.11 The hot atom chemistry promotes abstraction reactions that produce radicals, while the cold atom chemistry usually leads to insertion products. The O atom system has been extensively studied as well and shows small but measurable diffusion coefficients for O atoms in Xe,3 first-order O atom decay kinetics in the O + O recombination reaction consistent with long-range migration (>300 Å),4 and diffusionlimited geminate recombination of O + O2 in solid Xe.5 More recent studies have exploited O atom diffusion to study complexes of O atoms with other species (e.g., H2O−O).6,7 In our opinion, studies of H atom mobility are the most interesting because these are the lightest atoms and thus should display the most pronounced quantum effects at low temperature. Most H atom diffusion studies in rare-gas solids rely on photolysis to create the H atoms and a controlled increase in Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics Received: July 2, 2015 Revised: August 21, 2015 Published: August 28, 2015 12270

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The Journal of Physical Chemistry A temperature to induce mobility.12−18 For example,12,13 H atoms are stable for days in Xe at low temperature (T = 10 K) but readily decay at 40 K presumably by various recombination reactions. H atom mobility studies in Ar and Kr show similar behavior, with the major difference being the H atoms start to diffuse at 16 and 24 K, respectively.15 The mean H atom trapping time in Kr and Xe shows an Arrhenius-type temperature behavior that is characteristic of the matrix host.17 In more recent studies, the recovery kinetics of xenon hydrides (e.g., HXeSH and HXeH) after IR and visible photolysis are fit to first-order kinetics with stretched exponentials to take into account dispersion in the barrier heights encountered by the H atom.19 Through combined electron spin resonance (ESR) and IR measurements, Feldman et al. found the formation of XeH2 is the major trapping site (70%) for thermally mobile H atoms in a Xe matrix, with hydrogen abstraction from the butane precursor less important, and recovery of the precursor due to the H + R• reaction is negligible.18 On the basis of these studies of H atom diffusion in rare-gas solids, we expect the details of the diffusion process to greatly influence the observed chemistry. Now with quantum hosts such as para-hydrogen (pH2), we can explore cold atom chemistry under new diffusion regimes, that is, quantum diffusion. Initial studies by Apkarian and coworkers on O atoms in solid normal D2 showed the thermally induced recombination reaction (T > 5.5 K) to be catastrophic, accompanied by thermal runaway and material loss.4,20 However, H atom diffusion in nuclear spin enriched solid pH2 displays a qualitatively different behavior that indicates the H atom diffusion is never fully quenched, even at the lowest temperatures. Studied almost exclusively using ESR spectroscopy, it is believed that H atom diffusion through solid pH2 occurs via reactive tunneling.21,22 Thus, a good picture of this tunneling process is the H atom “hops” from one lattice site to the next by reacting with one of its nearest neighbor pH2 molecules. The probability that the H atom tunnels to a specific lattice site depends on the energetics of the H atom in the initial and final states of the hop. The H + H2 → H2 + H exchange reaction has a barrier of ∼10 kcal mol−1.21,22 Therefore, at the experimentally accessible temperature range (1.7 to 5 K) the tunneling is said to be in the deep tunneling range, well below the crossover temperature.23 Under these conditions the tunneling is most facile if the initial and final H atom sites are isoenergetic.24,25 If for example the H atom tries to tunnel to a site next to a chemical impurity, the tunneling probability depends strongly on the sign and magnitude of this energy difference. We therefore expect bimolecular reactions of an H atom with another chemical species to be very different in this quantum diffusion regime. Most importantly this may lead to highly selective radical chemistry that is governed by longrange intermolecular forces but also may occur under completely different kinetic mechanisms than thermally induced H atom reactions in rare-gas solids. Specifically, we can investigate bimolecular chemistry at much lower temperatures than in rare-gas solids simply because the diffusion mechanisms are so different. Our group recently decided to reinvestigate the H + NO reaction in solid pH2 that was originally studied by Momose and co-workers as an H atom diffusion-limited reaction.26 As described in this earlier work, the rate constant for the H + NO → HNO reaction is likely diffusion-limited and therefore directly related to the H atom diffusion coefficient. That is, because this reaction is calculated to be barrierless,27,28 the

measured rate constant for the production of HNO should reflect the H atom diffusion coefficient. However, the diffusion rate extracted from the H + NO reaction measurements26 did not agree with the H atom diffusion rate measured by ESR spectroscopy.29 Further, the experiments of Momose only investigated the reaction kinetics at one temperature (T = 5.2 K). Therefore, we decided to reinvestigate this system at two different temperatures, 1.8 and 4.3 K, respectively, to measure the effect of temperature on the reaction rate. Another reason to revisit this system is the anomalous results we have recently measured30−32 for other H atom reactions in solid pH2. For example, in the case of the H + N2O → cis-HNNO reaction we observed a very strange temperature dependence.30 This reaction only begins to occur at temperatures below ∼2.4 K, and at higher temperatures the reaction does not occur. We therefore wanted to quantify the temperature dependence of the H + NO reaction for comparison with these other H atom reaction studies. The final reason for our interest in this reaction is the fact that H atom mobility in solid pH2 has not been studied as extensively as in rare-gas solids. Quantitative studies are needed to characterize H atom quantum diffusion in solid pH2, especially solid pH2 that contains other chemical impurities. We expect very different H atom chemistry in solid pH2 compared to rare-gas solids due to the qualitatively different operative diffusion mechanisms and because we can study these reactions at much lower temperatures in solid pH2.

2. EXPERIMENTAL SECTION The nitric oxide (NO) doped pH2 crystals are prepared using the rapid vapor deposition method of Fajardo and Tam.33,34 The crystal is grown by codeposition of independent gas flows of NO and pH2 onto a precooled BaF2 optical substrate held at ∼2.5 K within a sample-in-vacuum liquid-He cryostat. The pH2 solids are prepared by enriching normal-H2 gas to greater than 99.97% pH2 enrichment levels using a variable-temperature ortho/para converter operated near 14.0 K. The orthohydrogen (oH2) concentration in the sample can be checked using the integrated intensity of the oH2-induced Q1(0) feature and the measured crystal thickness.34−36 The temperature of the sample is measured using two silicon diode sensors; one is mounted (TA) to the cold tip of the helium cryostat, and the other (TB) is mounted to the Au-plated oxygen-free-high-conductivity Cu substrate holder at the point furthest from the cold tip. All the reported temperatures are using TB. The H atoms are generated as byproducts of the 193 nm in situ photolysis of the NO precursor. The unfocused 193 nm output of a broadband ArF excimer laser (Gam Laser EX5) with 8 ns pulse duration is directed at an angle of 45° with respect to the surface normal of the BaF2 optical substrate. The Fourier transform infrared (FTIR) beam is focused with 8″ offaxis parabolic mirrors through the sample at normal incidence to the BaF2 optical substrate in a transmission optical setup. This optical setup permits FTIR spectra to be recorded within the photolysis region either during or immediately after 193 nm irradiation. The laser fluences in these experiments, measured with a power meter after an adjustable iris located in front of the photolysis window on the cryostat, range from 50 to 300 μJ cm−2 pulse−1. High-resolution rapid scan FTIR spectroscopy (e.g., acquisitions times of 290 s for 16 coadded scans at 0.03 cm−1 resolution) is performed on the sample using a FTIR spectrometer (Bruker IFS 120HR) equipped with a glowbar source and Ge-coated KBr beamsplitter. For all the kinetic 12271

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we assign the R(1/2) and P(3/2) transitions that also display sharp (fwhm ≈ 0.1 cm−1) line shapes. We present all the peak positions of the observed NO molecules in Table S2 in the Supporting Information. We are currently preparing a separate manuscript focused on the rovibrational spectroscopy of NO isolated in solid pH2. However, for the purposes of this work, we only want to point out that the FTIR spectroscopy indicates the NO molecule freely rotates and that we can use this IR spectrum to measure the concentration of NO monomers. Each spectral trace in Figure 1 is labeled on the right-hand side by the extracted NO concentration in parts per million. As can be seen in Figure 1, the 193 nm photolysis of the sample results in a 28% decrease in the NO concentration from 32.4 to 23.3 ppm, and more importantly, the NO concentration continues to decrease well after the photolysis laser is stopped as seen by comparing traces (b) and (c). As we will show, the continued decrease in the NO concentration after photolysis is caused by reactions of NO with mobile H atoms. Further, under these experimental conditions the only change in the NO spectrum caused by 193 nm photolysis or reactions with H atoms is an overall decrease in intensity, not any changes in line shape. The major 193 nm in situ photoproducts of NO trapped in solid pH2 are NH3, NH, and H2O. We show in Figure 2 FTIR

measurements we use a liquid nitrogen cooled HgCdTe detector to record spectra from 700 to 4500 cm−1. The concentrations of NO, NH, NH3, H2O, HNO, NOH, tHNOH, and NH2OH are measured from the integrated intensity of the various peaks using the integration protocols listed in Table S1 in the Supporting Information. Note that the largest contributions to errors in the reported concentrations likely involve uncertainties in the integrated absorption coefficients. We try to use experimental values when possible; for many species these values are not available, and we must resort to theoretical calculations of the integrated absorption coefficients. We calculate the concentration in units of parts per million (ppm) using the following equation. 2.303 ∫ log10(I0/I )dν ̃

V0(1 × 106) (1) εl where X is the species of interest, ε is the integrated absorption coefficient for the transition used, l is the IR path length through the crystal, and V0 is the molar volume of solid pH2 at liquid helium temperatures (23.16 cm3 mol−1).37 The value of l is determined for each sample using the IR spectroscopic method developed by Fajardo.35,36 [X] =

3. RESULTS AND ANALYSIS A. Infrared Spectroscopy. Figure 1 shows FTIR spectra of the v = 1 ← 0 fundamental of NO recorded at different stages

Figure 2. FTIR absorption spectra in the ν2 NH3 and ν3 H2O spectral regions showing the photoproduction of these species for the same spectra described in Figure 1. Figure 1. FTIR absorption spectra in the region of the NO fundamental recorded at different stages of a NO/pH2 photolysis experiment conducted at 4.3 K. The three traces are shown at different steps in the experiment; (a) before 193 nm irradiation, (b) 1.8 min after irradiation, and (c) 332.6 min after irradiation (see text for details). The NO concentration (ppm) determined from each spectrum is indicated of the right-hand side next to the trace.

spectra in the region of the ν2 and ν3 fundamentals of NH3 and H2O, respectively, for the same spectra shown in Figure 1. Detailed assignments of the NH3 and H2O FTIR spectra have been presented elsewhere,38−40 and here we show expanded views to illustrate the type of information that can be extracted. Trace (a) in Figure 2 shows that the concentrations of orthoNH3 and para-H2O (both the lowest energy nuclear spin states) are negligible before photolysis. The small R(0) peak for paraH2O in trace (a) originates from H2O molecules that deposit in the pH2 matrix from the surrounding vacuum gas. Immediately after photolysis we observe a number of peaks in both spectral regions that provide clues as to how the 193 nm photolysis of NO leads to the production of NH3 and H2O. For NH3 we observe the S1 and S2 satellite peaks (see Figure 2) that indicate a significant fraction of the nascent NH3 is produced in a metastable solvation site.38 Specifically, we have shown previously that the in situ photolysis of NH3 in solid pH2 produces ortho-NH3 in a double substitution site as evinced by the S1 and S2 satellite peaks.38 We speculate that NH3 is produced in this higher-energy double substitution site by

of a NO/pH2 photolysis experiment conducted at 4.3 K. Trace (a) is recorded just prior to photolysis, trace (b) is recorded immediately after photolysis, and trace (c) is recorded 330.8 min after trace (b), while the sample is held at a constant temperature of 4.3 K. The spectrum of NO isolated in solid pH2 shows evidence for rotational fine structure; there is a sharp central feature with additional peaks arranged symmetrically around this absorption. If NO freely rotates in solid pH2, at a temperature of 4.3 K, we expect the two lowest rotational states of the 2Π1/2 NO rotor (J = 1/2, 3/2) to be thermally populated. Accordingly, we assign the central peak at 1873.53 cm−1 to the Q(1/2) transition, which is shifted 2.55 cm−1 to lower energy than the analogous gas-phase transition. Similarly, 12272

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The Journal of Physical Chemistry A reactions of NH2 fragments with an adjacent pH2 molecule leaving behind an H atom that diffuses away producing NH3 next to a vacancy. After the photolysis laser is stopped, the intensity of these two satellite features steadily decrease, and the intensity of the aR(0,0) peak increases as the pH2 host reorganizes around the nascent NH3 molecule. Thus, the spectra shown in Figure 2 indicate the in situ photolysis of NO also produces NH3 in these same double substitution sites (satellite peaks) that then convert slowly into single substitution sites (aR(0,0) peak) after the laser is stopped. We also do not observe significant photoproduction of paraNH3 (the higher-energy nuclear spin state) under these conditions.41 For the experiment shown in Figure 2, we detect ∼0.1 ppm of para-NH3 immediately after the photolysis laser is stopped, which is only 2.2% of the total NH3 produced. However, the concentration of para-NH3 rapidly decays in solid pH2 with a half-life of t1/2 = 370(30) s due to nuclear spin conversion.41 In contrast, for H2O we observe significant photoproduction of ortho-H2O, and almost no para-H2O is produced in a metastable solvation site. As shown in Figure 2, immediately after photolysis we observe significant intensity in the P(1) and R(1) rovibrational transitions of ortho-H2O. The intensity of these two rovibrational features then decrease, while the intensity of the R(0) transition increases as the higher-energy ortho-H2O molecules nuclear spin convert to the lower-energy para-H2O nuclear spin state. Analogously to NH3, if the paraH2O molecule is produced in a double substitution site then we should observe S1 and S2 satellite peaks close to the H2O R(0) transition.39,40 While it is difficult to see on the scale of Figure 2, we do detect these H2O satellite peaks, but they are very weak. Thus, it appears that the series of elementary reaction steps that lead to the production of H2O produce significant amounts of ortho-H2O in single substitution sites. The opposite is observed for NH3, in this case the lower-energy nuclear spin isomer is produced in double substitution sites, and almost none of the higher-energy nuclear spin isomer is produced. We will explore these differences further when we present the reaction kinetics in the next section. Now let us describe the IR spectroscopy of the major H atom reaction products. The vibrational assignment of the IR absorptions of HNO, NOH, and trans-HNOH (t-HNOH) is straightforward because the IR spectra of HNO and t-HNOH have been observed previously42 in solid normal hydrogen (nH2), and the IR spectrum of NOH has been measured in solid Ar.43 Shown in Figure 3 are spectra of the three fundamental transitions of HNO for a fully reacted sample that is then cooled to 1.8 K. In Table 1 we compare our measured frequencies with the peak frequencies reported42 for HNO isolated in solid nH2 at 3 K and the original peaks positions assigned by Jacox and Milligan to HNO trapped in an Ar matrix.44 As can be seen in Figure 3, each fundamental shows fine structure that we believe represents the remnants of free rotation of a near-prolate asymmetric top (JKaKc). We assume HNO only populates the lowest rotational state (000), and therefore we should observe both a-type (101 ← 000) and b-type (111 ← 000) rovibrational transitions from this ground rotational state to the extent the HNO freely rotates in solid pH2. The HNO molecule is a closed-shell, near-prolate asymmetric top with A = 18.48 cm−1 and (B+C)/2 = 1.36 cm−1 in the ground vibrational state.45 In the free rotor limit the splitting between the a-type (101 ← 000) and b-type (111 ← 000) rovibrational transitions should be approximately (A′ −

Figure 3. FTIR absorption spectrum of the three fundamentals of HNO for a fully reacted NO/pH2 sample recorded at 1.8 K. In each spectral region we label the a-type and b-type rovibrational transitions and indicate with red lines the measured splittings (see text for details). Note that the absorption intensity in the ν2 and ν3 regions has been multiplied by four.

Table 1. Peak Positions of the Observed Transitions of HNO, NOH, t-HNOH, and NH2OH Isolated in Solid pH2 species HNO HNO HNO HNO HNO HNO HNO HNO HNO HNO HNO HNO NOH NOH NOH t-HNOH t-HNOH t-HNOH t-HNOH t-HNOH NH2OH a

assignment ν1 ν1 ν1 ν2 ν2 ν2 ν3 ν3 ν3 ν2 ν2 ν2 ν1 ν1 ν3 ν1 ν1 ν2 ν4 ν5 ν5

pH2, 1.8 K

A′ N−H str A′ N−H str A′ N−H str A′ N−O str A′ N−O str A′ N−O str A′ bend A′ bend A′ bend + ν3 + ν3 + ν3 A′ OH str a-type A′ OH str b-type A′ bend OH stretch a-type OH stretch b-type NH stretch cis bend NO stretch NH2 wag b

c

2694.29 2694.53 2695.08 1500.42 1500.93 1501.49 1562.80 1563.34 1563.88 2991.11 2991.57 2992.14 3475.85 3488.80 1098.84 3582.67 3590.29 3244.77 1241.66 1063.26 1117.04

nH2, 3 K

Ar matrix

2697.7a

2717.0b

1503.3a

1505.0b

1563.8a

1563.5b

3467.2c 1095.6c (3643.5)d (3268.3)d 1241.7a 1063.6a 1115.47e d

Reference 42. Reference 44. Reference 43. Peaks not observed, DFT calculated values. eReference 47.

B′). Given that the inertial a-axis falls closely along the N−O bond, we expect to observe a-type transitions near the vibrational origin and b-type transitions ∼17 cm−1 higher in energy. In the gas phase45 this splitting for the bend and NH stretch vibrational modes is 17.18 and 16.25 cm−1, while for HNO isolated in solid pH2 the measured splittings are 8.71 and 9.04 cm−1, respectively. In Figure 3 we highlight the peak positions used to calculate these splittings with red lines. The fact that the measured splittings are ∼50% of the gas-phase values are evidence that rotation around the a-axis, which involves primarily H atom motion, is approximately preserved in the pH2 matrix. In the free rotor limit the relative intensities between the a-type and b-type transitions reflect the projection of the transition moment for each mode along the inertial axes of the molecule, but in our case these relative intensities are strongly modified by the perturbed HNO rotational motion in 12273

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frequencies in Table 1. The ν4 and ν5 peak frequencies observed in this work match very closely the previous measurements42 of t-HNOH isolated in solid nH2. However, we did observe two absorption features not reported previously. We observe a weak peak at 3244.77 cm−1 that we assign to the NH stretching mode, and we observe peaks at 3582.67 and 3590.28 cm−1 that we assign to the a-type and b-type rovibrational transitions of the OH stretching mode of tHNOH. Observation of both the a-type and b-type rovibrational transitions implies that K-rotation around the a-axis is nearly preserved for t-HNOH isolated in solid pH2. Finally, we did assign one feature at 1117.04 cm−1 to NH2OH. This assignment is only tentative, however, because this was the only feature we could observe for NH2OH. The one assigned feature corresponds to the NH2 wagging vibration (ν5) that is the strongest NH2OH fundamental absorption (135 km mol−1).47 The spectrum of the assigned NH2OH feature is shown in Figure S5 in the Supporting Information. B. Photoinduced Kinetics. The full kinetic data for one of the experiments conducted at 4.3 K is shown in Figure 5. The

solid pH2. Complicating more detailed assignments, both the aand b-type transitions display additional fine structure not present in the gas phase that can be caused by the perturbed rotational motion and/or different solvation sites. We report this additional fine structure for HNO in Table 1 to guide future studies. The ν2+ν3 combination band spectrum of HNO is shown in Figure S1 in the Supporting Information. The general picture that emerges is one where the (B+C)/2 rotational motion of HNO is likely strongly perturbed or quenched; however, there are still remnants of free rotation around the a-axis. We expect the spectrum of NOH trapped in solid pH2 to be somewhat similar to HNO except for the important difference that NOH is thought to have a triplet ground electronic state.27,28 Shown in Figure 4 is the spectrum of NOH recorded

Figure 4. FTIR absorption spectrum of the two fundamentals of NOH for a fully reacted NO/pH2 sample recorded at 1.8 K. In each spectral region we label the a-type and b-type rovibrational transitions and indicate with red lines the measured splittings (see text for details). Note that the absorption intensity in the ν1 region has been multiplied by three.

for a fully reacted sample cooled to 1.8 K. Analogous to previous Ar matrix studies of this molecule,43 we only observe peaks due to the ν3 bend and ν1 OH stretch; the ν2 NO stretch feature is too weak and not observed. For the ν1 OH stretch we observe what appears to be both a-type and b-type transitions where the b-type transition is significantly broadened. The measured splitting is 12.77 cm−1, while ab initio rotational constants46 predict 20.3 cm−1. The peak frequencies and relative intensities measured for NOH agree well with the Ar matrix results.43 Further, from the comparison between the observed IR spectrum (peak positions and intensities) and ab initio calculations of the IR spectrum of singlet and triplet NOH, it is clear we observe the triplet state of NOH.46 This comparison is shown in Figure S2 in the Supporting Information. Further, we note that both NOH absorption features show similar fine structure for the a-type transition. It is difficult to see on the scale of Figure 4, but both a-type features consist of a central peak of maximum intensity with peaks symmetrically distributed around this central feature. For expanded views of the two a-type transitions assigned to triplet NOH see Figure S3 in the Supporting Information. The origins of this fine structure are still unclear. However, the agreement between ab initio theory46 and experiment clearly identify triplet NOH as the carrier. The IR spectroscopy of t-HNOH isolated in solid nH2 has already been presented in the literature.42 We show the four absorption features assigned in this work to t-HNOH in Figure S4 in the Supporting Information and report the peak

Figure 5. Kinetics plots for a 193 nm photolysis (3.2 min, 250 Hz, 308 μJ cm−2 pulse−1) experiment on a NO/pH2 sample at 4.3 K. The photolysis exposure is indicated by the gray vertical bar. The data are represented by dotted circles, and the lines are the result of leastsquares fits of the data to eq 2 or 3. Note that the final three data points (not included in the fits) were measured after cooling the reacted sample to 1.7 K.

gray vertical bar in Figure 5 represents the time and duration of the 193 nm photolysis exposure. The Q-branch of the NO fundamental is saturated in the spectrum of the as-deposited sample recorded at 1.8 K, the first NO data point in Figure 5, and therefore this data point (−81 min, 40.8 ppm) is inaccurate. After deposition we raise the temperature of the sample to 4.3 K and record four spectra (346 s acquisition times) as the sample equilibrates. The NO fundamental rovibrational peaks broaden at this higher temperature, and all the peak intensities come on scale at 4.3 K. In addition, the NO spectrum shows the effects of annealing at this higher 12274

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and the results of the fits are shown as lines in Figure 5 with the fitted constants reported in Table S3. The fitted rate constants (Expt. 1) for defect-NH3 and ortho-NH3 are comparable as they must be for a unimolecular conversion of defect-NH3 → ortho-NH3. Note also that the change in concentration of defect-NH3 and ortho-NH3 after photolysis agree to within ±0.1 ppm. As discussed in the previous section, the amount of para-NH3 produced by the in situ NO photochemistry is negligible and therefore is not shown in Figure 5. In terms of the oxygen-containing photoproducts, only H2O is detected. We have never been able to observe the OH radical in solid pH2, presumably because OH reacts too quickly with the pH2 matrix to be detected with our modest temporal resolution of ∼1 min.39,40 However, we see evidence for the photoproduction of ortho-H2O, the higher-energy nuclear spin state. The results of fits of the ortho-H2O and para-H2O data to eq 2 and 3 are shown as solid lines in Figure 5, and the fitted constants are reported in Table S4 in the Supporting Information. We have discussed the IR spectroscopy of H2O in the previous section and elsewhere.39,40 Here we note that ∼33% of the H2O produced during photolysis is in the form of ortho-H2O. Careful examination of the para-H2O data in Figure 5 shows evidence for more complicated kinetics than single exponential. One of the processes that produce para-H2O is nuclear spin conversion of the photoproduced ortho-H2O. However, another source is the nearly constant deposition from gas phase H2O in the vacuum shroud. Accordingly, the paraH2O data are fit to a modified version of eq 3 that contains a zero-order term (+Ct). The ortho-H2O produced in solid pH2 during photolysis immediately starts decaying to para-H2O with a single exponential time constant measured49 to be τ = 1900(100) s at 2.4 K. For the data presented in Figure 5, taking the average rate constant for ortho- and para-H2O we find a comparable time constant (τ = 1670(50) s) and single exponential kinetics. Therefore, in the series of photoinduced reaction steps that produce H2O there is significant production of ortho-H2O and very small amounts of defect-H2O produced. This is in contrast to the 193 nm in situ photolysis of formic acid, which produced mostly defect-H2O and very little orthoH2O.31,32 These differences provide clues as to the series of elementary reaction steps that ultimately lead to the production of H2O. C. Hydrogen Atom Reaction Kinetics. Now we turn to the main focus of this study, namely, the reaction kinetics that produce HNO and NOH well after the photolysis laser is stopped. As can be seen in Figure 5, some HNO and NOH are produced during photolysis, but the concentrations of these two species continue to increase significantly after the laser is turned off. As we will see, both of these species photodissociate upon exposure to the 193 nm radiation, and thus the concentrations of these two species can only steadily increase after the laser is turned off. We observe single exponential growth of HNO and NOH after the photolysis exposure. In addition, we observe the complementary single exponential decay in the concentration of the NO reagent. We can fit the NO data to eq 2 and the HNO/NOH data to eq 3, and the results of these fits are shown as solid lines in Figure 5; the fitted constants are reported in Tables 2 and 3. Given the proposed photochemical mechanism, we expect H atoms produced during photolysis to be mobile under these reaction conditions. We interpret the growth curves of HNO and NOH as due to reactions of H atoms with NO. For the 23 ppm concentration of NO after photolysis, we estimate the average

temperature, and this is why the NO concentration appears to increase right before photolysis. The sample is photolyzed at 4.3 K, and three FTIR scans (51 s acquisition times) are recorded during photolysis. Typically, the first scan recorded during photolysis shows an increased NO concentration as NO clusters (e.g., NO dimer) are broken up by the photolysis laser. With all these uncertainties in the initial NO concentration, we estimate photolysis reduces the NO concentration by 9.1 ppm or 30%. As discussed previously,26 the energy of a 193 nm photon is slightly less than the NO bond dissociation energy, and yet in an Ar matrix the 193 nm photolysis of NO results in the formation of isolated N(4S) atoms.48 To organize the discussion of the photochemistry, we present the following possible photoinduced reactions. NO + hν(193nm) → N( 4S) + O(3P)

(R1)

N( 4S) + H 2 → NH + H

(R2)

NH + H 2 → NH 2 + H

(R3)

NH 2 + H 2 → NH3 + H

(R4)

O(3P) + H 2 → OH + H

(R5)

OH + H 2 → H 2O + H

(R6)

Given the reaction stoichiometry of R1, we would expect the decrease in the NO concentration produced by photolysis to equal both the increases in the concentrations of the nitrogen and oxygen containing photoproducts. For the experiment depicted in Figure 5, we measure a 9.1 ppm decrease in NO and observe increases in the HNO (+0.6 ppm), NOH (+1.1 ppm), NH (+2.2 ppm), NH3 (+4.4 ppm), and H2O (+12 ppm) concentrations. Therefore, subtracting the total amount of HNO and NOH from the NO decrease gives 7.4 ppm, which compares favorably with the 6.6 ppm of nitrogen containing photoproducts. This gives some indication of the accuracy of the measured concentrations in this study. However, as stated in the Experimental Section, errors in the integrated absorption coefficients can lead to significant errors in the absolute concentrations, and these errors can vary from species to species. We have studied the 193 nm photochemistry of NH3 in solid parahydrogen previously,38 and therefore we know that if NH is produced it does not react via R3 with the pH2 matrix. However, if NH2 is formed it reacts quickly with the pH2 matrix to form defect-NH3. The reaction of NH2 with an adjacent pH2 molecule leads to the production of NH3 in a defect solvation site. That is, the NH3 finds itself in a double substitution site instead of its lower-energy single substitution site.38 We can distinguish defect-NH3 from the normal solvation site of orthoNH3 using IR spectroscopy; defect-NH3 shows two satellite peaks in the vicinity of the single aR(0,0) ortho-NH3 peak. As can be seen in Figure 5, defect-NH3 is produced only during the in situ photolysis and immediately starts to relax back to the lower-energy solvation site after the laser is stopped. The data for defect-NH3 and ortho-NH3 are fit to the corresponding first-order rate expressions [X] = [X]∞ + A exp(−kt )

(2)

[X] = [X]0 + A(1 − exp(−kt ))

(3) 12275

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The other two species plotted in Figure 5 are t-HNOH and NH2OH. From expanded views of the growth curves of these two species at short reaction times, we observe inflection points consistent with consecutive first-order reaction kinetics. However, the data are not of high enough quality to consistently fit the data to these more complex functional forms. Therefore, we fit both the t-HNOH and NH2OH kinetic data to eq 3 analogous to the HNO/NOH data. The results of the fits are summarized in Table S5 in the Supporting Information and shown as solid lines in Figure 5. Consistent with the limiting reagent being H atoms, the growth curves of tHNOH and NH2OH also level off at around the 250 min mark. Thus, it seems the H atoms can also react with HNO/NOH to produce t-HNOH and with t-HNOH to produce NH2OH. They all react with a similar first-order rate constant that reflects the sum of all first-order decay reactions. This would seem to imply that there is no selectivity to the H atom reactions under these conditions. The only requirement is that the reaction be exothermic so that it can occur at such low temperatures via a tunneling mechanism. However, even though the H + NH reaction leads to the production of NH2 and is exothermic, we do not observe significant decay in the concentration of the NH radical over the same reaction interval (see Figure 5). This implies that H atom reactions with NH are somehow inhibited under these conditions. The H atoms cannot react with either NH3 or H2O because there are no exothermic reactions with these two species. The next experiment was designed to examine the temperature dependence of the reaction kinetics. Accordingly, the kinetic experiment was repeated with a comparable NO concentration and photolysis conditions; however, this time the sample was photolyzed at 1.8 K, and the reaction kinetics was measured at 1.8 K. Shown in Figure 6 are the full kinetics results for this experiment. The first data point in Figure 6 was recorded for the as-deposited sample at 1.8 K. Then three repeated FTIR spectra were recorded prior to any photolysis exposure. The sample was photolyzed as before, and three scans were recorded during photolysis. After the photolysis laser was stopped, the kinetics are measured at 4 min intervals for ∼379 min. As can be seen in Figure 6, at 1.8 K the reaction that forms HNO and NOH has drastically slowed, and the production of these two species is much less. Note that the conversion of defect-NH3 to ortho-NH3 has also slowed. At 4.3 K the average rate constant for defect-NH3 → ortho-NH3 is k = 4.8(4) × 10−2 min−1, while at 1.8 K it is 1.21(3) × 10−2 min−1. In contrast, the H2O NSC rate constant has not changed significantly; however, less ortho-H2O is produced during photolysis at this lower temperature. One could argue that fewer H atoms are produced during the photolysis of NO at this lower temperature; indeed the percent decrease in NO is smaller, and the amounts of NH, NH3 and H2O are all a factor

Table 2. Kinetics Parameters for the Decay of NO after Photolysisa expt 1

expt 2

expt 3

parameter

4.3 K

1.8 K

4.3 K

expt 4 4.3 K

[NO]∞ A k, 1 × 10−2 min−1 R2

16.82(3) 6.81(5) 1.51(3) 0.997 996

29.84(2) 2.4(2) 0.6(1) 0.903 743

26.87(3) 10.60(7) 1.48(2) 0.998 624

46.23(6) 11.1(2) 1.56(4) 0.993 578

a

All concentrations in parts per million. The uncertainties represent the 1σ values from least-squares fits to eq 2.

distance between NO molecules is ∼74 Å. Assuming a homogeneous distribution of H atoms and NO molecules, this means that on average the H atom must travel 19 lattice constants to encounter an NO molecule. We believe that, for short 193 nm exposures (3.2 min), most of the H atoms are generated from the photoinduced chemistry of excited NO molecules with the pH2 host, and thus the H atoms and NO molecules are not preferentially created next to each other. One of the observations that we initially found surprising is that the branching between HNO and NOH is almost exactly the same even though there is a significant barrier for the reaction that produces NOH, while the reaction that produces HNO is thought to be barrierless.27,28 As we will see, the reason the branching is nearly equal is because the reaction is proceeding at the quantum diffusion limit, and thus the branching between products is determined by the H atom diffusion rate, not the reaction rate. For the data shown in Figure 5, the kinetics parameters are determined from fits of the data collected after photolysis and up to around the 332.6 min mark, while the sample is held at a constant temperature of 4.3 K. Examination of Table 3 shows that both the fitted rate constants for HNO and NOH agree to within the fitted uncertainties; however, the increase in the HNO concentration is slightly larger than the NOH increase. We believe the total amounts of HNO and NOH produced are limited by the number of H atoms produced during photolysis. Thus, after ∼250 min both growth curves level off as the number of H atoms decays to near zero. After the kinetics is measured, we lower the sample temperature to 1.8 K and record three more spectra (the last three data points in each plot in Figure 5). To a first approximation, all concentrations remain constant as the temperature is lowered. Note that only the concentrations of HNO, NOH, and NO appear to change slightly at these lower temperatures. These small concentration changes are artifacts caused by the sharpening of the specific transitions for these three species at low temperature. Therefore, after the reaction kinetics has stopped, no additional changes in concentration are observed as the temperature of the sample is lowered.

Table 3. Kinetics Parameters for the Growth of HNO and NOH after Photolysisa expt 1

expt 2

4.3 K

a

expt 3

1.8 K

expt 4

4.3 K

4.3 K

parameter

HNO

NOH

HNO

NOH

HNO

NOH

HNO

NOH

[X]0 A k, 1 × 10−2 min R2

0.56(4) 2.54(4) 1.72(6) 0.992 454

1.10(1) 2.05(1) 1.67(3) 0.998 575

0.47(3) 1.10(6) 0.60(9) 0.948 532

0.23(1) 0.65(4) 0.43(6) 0.973 772

0.97(5) 3.90(4) 1.64(4) 0.995 973

1.91(2) 3.16(2) 1.59(2) 0.998 455

1.18(8) 3.98(8) 1.73(7) 0.987 327

2.32(3) 3.19(3) 1.79(3) 0.997 716

All concentrations in parts per million. The uncertainties represent the 1σ values from least-squares fits to eq 3. 12276

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production of HNO and NOH. In this case, we deposited a sample with an NO concentration of 57 ppm and anneal the sample at 4.3 K before photolysis. The kinetics data for this experiment are shown in Figure 7. Once again the NO

Figure 6. Kinetics plots for a 193 nm photolysis (3.2 min, 250 Hz, 312 μJ cm−2 pulse−1) experiment on a NO/pH2 sample at 1.8 K. The photolysis exposure is indicated by the gray vertical bar. The data are represented by dotted circles, and the lines are the result of leastsquares fits of the data to eq 2 or 3. Note the five data points after the arrow were measured after raising the temperature to 4.3 K, and the last two data points were measured after recooling to 1.8 K.

Figure 7. Kinetics plots for a 193 nm photolysis experiment on a NO/ pH2 sample at 4.3 K. The two separate photolysis exposures (both 3.2 min, 250 Hz, 312 μJ cm−2 pulse−1) are indicated by the gray vertical bars. The data are represented by dotted circles, and the lines are the result of least-squares fits of the data to eq 2 or 3

of ∼2 less. However, after the kinetics was measured and at ∼391.9 min, we raised the temperature of the sample to 4.3 K and recorded five FTIR spectra. As soon as the temperature was raised the concentration of HNO rapidly increased (first scan at 4.3 K had a 346 s acquisition time) suggesting that H atoms were still present in the sample at this point in the experiment. Similarly, we measured a decrease in the NO concentration. After several spectra were recorded at 4.3 K, we again lowered the temperature to 1.6 K and recorded two spectra (last two data points in Figure 6). The concentration of HNO did not change once the temperature was lowered implying the thermally induced changes are irreversible. Interestingly, the concentration of NOH did not increase significantly when the sample temperature was first raised to 4.3 K. We interpret this experiment in the following way. At low temperature the H atom diffusion rate is significantly smaller, and therefore we see less reaction in the same amount of time. However, the H atom concentration does not decay to near zero as long as the temperature of the sample is maintained at 1.8 K. Then the first time the temperature is raised to 4.3 K large scale changes in the sample morphology are induced by annealing. During this annealing process H atoms can diffuse long distances and react to form HNO. However, the H atom diffusion induced by annealing is different from H atom diffusion at 4.3 K for a fully annealed sample. This difference in the H atom diffusion mechanism is signaled by the different branching ratios between HNO and NOH. This also shows that H atoms were produced by the photolysis of NO at 1.8 K, and that the slower rate constant was not caused by very small concentrations of H atoms. The next experiment was conducted at 4.3 K but with a slightly higher NO concentration in an attempt to optimize the

concentration before raising the sample temperature to 4.3 K is likely distorted because the spectrum of NO contains saturated lines. Nonetheless, as before we measure photoproduction of NH3 and H2O during photolysis, followed by growth in the concentration of HNO and NOH after the photolysis laser is stopped. The kinetics fits to the NH3 and H2O data show similar agreement to the previous 4.3 K measurements. Once again the HNO and NOH growth curves level off at ∼250 min, and the data are well-fit by single exponential expressions. In this experiment, at approximately the 360 min mark, we photolyzed the sample for a second time. As can be seen in Figure 7, the concentrations of HNO and NOH rapidly decrease during this second photolysis step showing that both species are photolabile at 193 nm. The behavior of the other monitored species during this second photolysis of the same sample is as expected. The NO concentration decreases, the H2O and NH concentrations increase, the NH3 concentrations change because the NH3 is photodissociated, and the concentration of t-HNOH and NH2OH also rapidly decrease. In this case, some of the growth of HNO and NOH could be due to geminate recombination for the second photolysis (HNO or NOH). However, the extracted rate constants agree to within experimental uncertainty with the rate constants extracted from the first photolysis implying a similar reaction mechanism after both photolysis exposures. This also implies that longer photolysis exposures could be used to study the reaction mechanism without changing from homogeneous reaction kinetics to geminate recombination. 12277

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designed to ensure that the initial H atom spatial distribution is random to permit us to study homogeneous kinetics and not geminate recombination. We operate under very dilute conditions and produce the H atoms as the result of side reactions with the pH2 host. Thus, H atoms are generated far removed from potential NO reaction partners, and we know the NO exists as isolated monomer species from the IR spectroscopy. We also perform the UV photochemistry in very short exposures where the HNO/NOH concentration is minimal. If instead we started with an HNO-doped pH2 sample, we would expect the importance of geminate recombination to possibly increase. Geminate recombination can yield first-order kinetics.5 However, even under this hypothetical scenario it is not clear if we would study geminate recombination because the pH2 cage effect for photodissociation is so weak even in situ photolysis of HNO results in well-separated reaction partners. We interpret the measured first-order reaction kinetics as evidence of long-range H atom migration. This interpretation of the data follows a similar kinetics argument used to explain the rate law for thermally induced nongeminate recombination of O atoms trapped in crystalline Kr and Xe.4 In this model we specify two types of H atoms, H and H* as trapped and mobile H atoms, respectively. The idea is that thermal excitations in the form of phonons can promote H atoms to tunnel from one lattice site to the next.24,25 The tunneling barrier in the lattice is by definition periodic, and therefore mobile H atoms can retrap. We represent this in terms of a reaction mechanism.

The last kinetics experiment was performed four months after these initial three experiments, and the ArF laser was delivering significantly lower laser fluences (factor of 3). To compensate, we photolyzed the sample with a longer exposure and kept the NO concentration at ∼62 ppm. The kinetics data for this experiment are shown in Figure 8. Again we produce

k1

k −1

(4)

H → H* ⎯→ ⎯ H Figure 8. Kinetics plots for a 193 nm photolysis experiment (6 min, 250 Hz, 38.4 μJ cm−2 pulse−1) on a NO/pH2 sample at 4.3 K. The photolysis exposure is indicated by the gray vertical bar. The data are represented by dotted circles, and the lines are the result of leastsquares fits of the data to eq 2 or 3. Note last three data points were recorded at 1.9, 4.4, and 1.8 K, respectively.

At any given time, only a small number of H atoms are expected to make jumps, and therefore, the bimolecular reaction should be dominated by the encounter of mobile H atoms with the NO molecule. k2

(5)

H* + NO → HNO

NH3 and H2O and can follow them via the various unimolecular transformations that occur after the photolysis laser is stopped. Note that at these lower fluences, the amounts of defect-NH3 and ortho-H2O are less. We measure growth of both HNO and NOH, and the fitted kinetics parameters match quantitatively those for the NO decrease. We measure the largest concentrations of HNO and NOH in this experiment, and again the kinetics level off at the 250 min mark. Similar to previous experiments, after the kinetics have been measured at 4.3 K, we lower the temperature to 1.8 K and record a spectrum, raise the temperature to 4.3 K and record a spectrum, and finally lower the temperature back to 1.8 K and record a final spectrum. As can be seen in Figure 8, these three spectra show reversible changes in the NO concentration. This is an artifact caused by the saturation of the NO fundamental at low temperature. The small changes in the HNO and NOH concentrations give some indication of the precision in these measurements at different temperatures.

Making the steady-state assumption in H*, the growth of HNO can be expressed as d[HNO] [H][NO] = k1·k 2· dt (k −1 + k 2[NO])

(6)

which reduces to a first-order rate only if k2[NO] ≫ k−1. Therefore, under conditions where the rate of finding an NO molecule is much larger than the retrapping rate constant, the reaction should proceed with a first-order rate law. This is roughly equivalent to the statement that first-order kinetics will arise if H* undergoes long-range migration. The specific requirement is that the volume swept by H* prior to retrapping is V = k2/k−1 ≫ 1/[NO]. At an NO concentration of 20 ppm, this condition implies that the swept volume is larger than 1 × 10−18 cm3 or, equivalently, a migration range larger than 100 Å. As the NO concentration decreases due to reaction, the kinetics should switch from first-order to second-order. However, under the current reaction conditions, the NO concentration never drops below 15 ppm, and therefore we do not observe this switch. This also implies that we could test this hypothesis by photolyzing the sample longer to reach lower final NO concentrations. Further support for long-range migration of the H atoms is provided by a pseudo-first-order analysis of the kinetics data. If instead of modeling the kinetics with two types of H atoms we

4. DISCUSSION A. Implications of First-Order Kinetics. A microscopic understanding of H atom quantum diffusion in solid pH2 doped with chemical impurities is our chief aim. The main experimental observable in this respect is our measurement that bimolecular reactions (H+NO) that lead to formation of HNO/NOH follow first-order kinetics. The experiment is 12278

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bimolecular chemical reactions of H atoms with NO. We can use these data to construct Arrhenius plots (k = A exp(−Ea/ kT)) for the three processes and extract both activation energies (Ea) and pre-exponential factors (A). Shown in Figure 10 are Arrhenius plots for solvent reorganization around NH3

use the kinetics equations developed for reactions in solution,50,51 we can model the reaction as k1

k −1

H + NO → H−−−NO ⎯→ ⎯ H + NO k2

H−−−NO → HNO

(7) (8)

where H---NO is the encounter complex between the two reagents. In our case this encounter complex is when the H atom and NO molecule occupy adjacent lattice sites. Again, if we assume a steady-state treatment for the encounter complex, the rate law is d[HNO] [H][NO] = k1·k 2· dt (k − 1 + k 2 )

(9)

As postulated previously for the H+NO → HNO reaction in solid pH2, if k2 ≫ k−1, then the rate law simplifies to the “diffusion limited” case and Rate = k1[H][NO]. Given our experimental conditions where [NO] ≫ [H], if this is the operative rate law then we would expect to measure pseudofirst-order kinetics, where Rate = k2′[H] and k2′ = k2[NO]. In addition, the measured k2′ rate constant should scale linearly with the NO concentration. Using the data in Table 2, we can accurately determine the initial NO concentration right after photolysis. Shown in Figure 9 is a plot of the fitted rate 26

Figure 10. Arrhenius plots for pH2 solvent reorganization around NH3 (red), H2O NSC (green), and the H + NO reaction (blue ○ HNO, □ NOH, and △ NO). The lines are the results of least-squares fits of an Arrhenius expression to the data.

(red), H2O NSC (green), and the reaction of H atoms with NO (blue) where we plot the rate constants extracted from the kinetics of HNO, NOH, and NO. The fitted parameters are presented in Table 4. First, we can see from Figure 10 that two Table 4. Arrhenius Parameters for Fits of the Measured Rate Constantsa parameter −1

A, min Ea, cm−1 a

pH2 solvent reorganization

H2O NSC

H + NO

0.10(1) 2.7(2)

0.045(4) 0.5(2)

0.036(2) 2.39(1)

The uncertainties represent the 1σ values from the least-squares fits.

of the processes show clear “activated” Arrhenius-type behavior, while H2O NSC does not. The rate constant for H2O NSC is almost temperature-independent over this range. Once the nuclear spins of the protons in H2O flip the molecule originally in a 101 rotational state must relax to the 000 state requiring the dissipation of quite a bit of rotational energy (23.79 cm−1 in the gas phase).52 This process of intramolecular NSC is very different from the other two processes studied here. The conversion of defect-NH3 → ortho-NH3 shows the largest pre-exponential factor and Ea = 2.7(2) cm−1. We believe this activation energy is related to the pH 2 solvent reorganization around the NH3 molecule. We have previously assigned defect-NH3 to an ortho-NH3 molecule that sits in a single substitution site next to a vacancy created by the reaction of NH2 with the pH2 host. Thus, we picture this conversion process as a pH2 molecule moves one lattice site to displace a vacancy from one of the nearest neighbor sites of the NH3 impurity. This process is an activated process, but not in the normal sense of activation over a barrier. The potential barrier to solvent reorganization is very much higher than the extracted activation energy, and thus this represents an activated tunneling process. For the pH2 to move next to the NH3 molecule and complete the first solvation shell around the NH3 it must physically translocate to the vacant site. This tunneling process is therefore likely promoted by phonons. The translational tunneling behavior of a single vacancy in a pure pH2 crystal is likely more facile when the position of the

Figure 9. A plot of the measured rate constants (blue, HNO, red, NOH, and green, NO) as a function of the initial NO concentration right after photolysis. Note the measured rate constants do not scale linearly with the increasing NO concentration.

constants as a function of the NO concentration after photolysis. Clearly, for the three high-temperature kinetics experiments, the fitted rate constant does not show a strong dependence on the NO concentration. We interpret this as another piece of evidence that the rate law governing the H atom reaction kinetics indicate the H atom undergoes longrange migration. Further, this process is intrinsically a firstorder process (the rate does not depend on NO concentration), and thus we cannot use the extracted rate constant and the NO concentration to calculate the H atom diffusion coefficient. While this may seem like a subtle point, it is an important distinction. For NO concentrations in the range of 20 to 60 ppm, the concentration of H atoms decays via a firstorder rate law that is related to the H atom quantum diffusion rate, not the reaction rate of the H atom with NO. B. Activated Tunneling. In this study we measured the rate constants for three distinct processes at both low and high temperatures. We studied solvent reorganization around NH3 molecules produced in the in situ photolysis of NO, intramolecular H2O nuclear spin conversion (NSC), and 12279

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different from thermally activated diffusion in rare-gas solids. Quantum diffusion of H atoms in solid pH2 is relatively slow but continues even to extreme low temperatures. Thus, we predict that quantum diffusion-limited chemistry in solid pH2 is very different from the chemistry observed in rare-gas matrices where the H atoms are imparted mobility by activation over the barrier to translation. In the experiment depicted in Figure 6 we see signs that this prediction is correct. After the lowtemperature kinetics was measured we raised the temperature to 4.3 K and annealed the sample. We observe rapid growth in the HNO signal but almost no growth in the NOH concentration. This implies that the diffusion-limited chemistry is qualitatively different in these two regimes. We also noted differences in the chemistry for the H + HCOOH reaction in solid pH2 and solid Kr where again we observe different reaction products than are observed in solid Kr.31,32 C. Quantum Diffusion Controlled Chemistry. The major finding of this work is that the H + NO reaction shows temperature-activated chemistry over the range between 1.8 and 4.3 K. This immediately suggests that if the chemistry could be performed at even lower temperatures, it can essentially be stopped. For example, to achieve a first-order time constant of 1000 min would require lowering the temperature to just 1 K. The reason we find this behavior so intriguing is because in all the other H atom reactions that we have studied to date we observe a qualitatively different temperature behavior. For example, in the H + HCOOH → H2 + HOCO reaction we observe that the reaction only starts to occur below a temperature of approximately 2.7 K.31,32 Similarly, for the reaction H + N2O → cis-HNNO we observe the reaction only proceeds at temperatures below 2.4 K.30 We speculated that this non-Arrhenius behavior (negative activation barrier) is related to the energetics of the pre-reactive complex between the H atom and the N2O molecule. The results for the H + NO reaction presented here point out a qualitatively different low-temperature behavior. One possible reason for the different low-temperature behaviors could be related to the details of H atom quantum diffusion. As discussed in this paper, the H atom moves by repeated tunneling jumps through the H + H2 → H2 + H reaction barrier. The probability of making a tunneling jump is necessarily a many-body quantum mechanical problem that is largely impacted by the energies before and after the jump. The tunneling rate is largest when the energies of the H atom in the two lattice sites are isoenergetic. However, once chemical impurities are added to the pH2 matrix, they break the translational symmetry of the crystal and introduce energy differences. If the approach of the H atom to the chemical impurity is slightly uphill, then the most likely tunneling process involves phonon-assisted jumps whereby the energy mismatch (δE = Einitial − Efinal = negative) is compensated for by inelastic scattering of phonons.24,25 If δE/k ≫ T, these so-called two-phonon processes will show activated behavior where the most probable jump is to the site with the smallest |δE|. In contrast, if the approach of the H atom toward the impurity is downhill, the most probable tunneling jump is accompanied by spontaneous emission of a phonon (δE = hωphonon > 0).24,25 Interestingly, because the probability of spontaneous emission goes as frequency to the third power, now the most probable tunneling jumps are for the greatest energy differences (δE). Further, for this type of quantum diffusion the motion occurs in irreversible jumps along the largest energy gradient.24,25 These two types of quantum diffusion processes therefore should

vacancy in two adjacent lattice sites are isoenergetic. However, if the vacancy sits next to a chemical impurity, then the solvation energies of the vacancy in the first solvation shell and the second solvation shell of the chemical impurity are no longer isoenergetic, and for the vacancy to tunnel from one lattice site to the next it needs a mechanism to account for this energy difference. One proposed mechanism is that a phonon inelastically scatters off the vacancy such that the difference in solvation energies is taken up by the energy difference between the incoming and outgoing phonons.24,25 Thus, the measured activation energy is likely related to the phonon activation energy and is not a measure of the potential barrier separating the vacancy between the two sites. The pre-exponential factor also illustrates how slow these processes are on the molecular time scale, that is, even at the high temperature limit the solvent reorganization occurs with a time constant of 10 min. We are more interested in the Arrhenius parameters for the H + NO reaction. The extracted activation energy Ea = 2.39(1) cm−1 is comparable to the activation energy extracted for the pH2 solvent reorganization around ortho-NH3. This is likely not a coincidence because both processes are similar. The activation energy is too small to be related to over the barrier activation but rather, as discussed before, is related to the energy difference between the before and after configurations. The extracted activation energy for the H + NO reaction reflects the translational motion of the H atom through the pH2 solid and its approach to the NO impurity. We know that the H atom migrates by repeated tunneling jumps through the H + H2 → H2 + H reaction barrier. Analogous to the movement of a vacancy through the pH2 solid, the energetics of the solvation energies of the H atom in two adjacent lattice sites must be accounted for in the tunneling jump between these two sites. At a first approximation the two activation energies are very similar, but the H + NO value is the smaller of the two. This suggests that the translational motion of a vacancy produces larger perturbations (greater energy shifts) than the motion of an H atom. The pre-exponential parameter for this process is also informative. If we convert this to a time constant (τ = 1/A) we get a value of 28(1) min, which is ∼3 times larger than the time constant for the pH2 solvent reorganization around NH3. This in some sense represents the collision frequency between the H atom and the NO molecule. The fact that A is so small reflects the fact that it is a bimolecular process even though it follows first-order kinetics. In contrast, the pre-exponential factor for the solvent reorganization around NH3 is a unimolecular process of decay from a higher energy configuration. Such a small pre-exponential factor for H + NO is also related to the residence time of the H atom in a given lattice site. If on average the H atom sits next to the NO impurity for a time long with respect to the two possible tunneling reactions that lead irreversibly to HNO and NOH, then the branching between products should be equal even if one reaction has a significant barrier. That is, even though the H + NO → HNO reaction is barrierless on the singlet surface, it is only barrierless if sampled with the correct orientation of reactants.27,28 The NO molecule in solid pH2 is in a J = 1/2 rotational state and therefore only samples this one pathway with some constant probability (rotationally averaged). Thus, since at these temperatures the reaction dynamics can occur by tunneling through even sizable barriers we observe comparable branching between the HNO and NOH products. The other point to make is that the dynamics of H atom translation via quantum diffusion are very 12280

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the measured rate constants cannot be easily converted to diffusion coefficients to compare with previous studies. This possibly explains why measurements of the H atom diffusion coefficient differ by 2 orders of magnitude for measurements based on ESR spectroscopy of H atoms and IR measurements of the H + NO reaction kinetics.26,29 The most important finding of this study is the H + NO reaction kinetics show activated Arrhenius behavior over this small temperature range of 1.8 to 4.3 K. This temperature behavior is qualitatively different than the kinetics of the H + HCOOH and H + N2O reactions that our group has also studied using the same apparatus. For these two reactions, we observe definitive non-Arrhenius behavior whereby the reactions only proceed at low temperature. By adding the new information acquired on the temperature dependence of the H + NO reaction, the identified contrasting kinetic behaviors indicates the low-temperature H atom chemistry in solid pH2 is quite rich and deserves further study. We hope that these measurements motivate other research groups to study this interesting chemistry in hopes of developing a quantitative understanding of quantum diffusion-limited H atom chemistry.

show different temperature dependencies and provide mechanisms for how the diffusion is not random but directional. We speculate that the first quantum diffusion process is responsible for the H+NO chemistry described in this work. Specifically, if the energy mismatches are small in the approach of the H atom to the NO molecules, then the first mechanism is likely operative, and the kinetics should display activated Arrhenius behavior. For this mechanism the energy mismatch can be positive or negative, and the H atom jumps most probably perpendicular to the energy gradient.24,25 Since the energy differences are small, these kinetics should be closer to the quantum diffusion of an H atom through a pure pH2 crystal. In contrast, for the reactions that only occur at low temperature the other mechanism is operative, and the H atom is irreversibly drawn to the chemical impurity. However, this type of quantum diffusion while directed toward the impurity involves spontaneous emission of phonons and is therefore slower. Clearly further work is needed to test some of the more speculative aspects of this work. We are working on performing additional kinetics measurements on the H + NO reaction at intermediate temperatures to further quantify the temperature dependence. However, we are excited about the possibility to study H atom reactions under qualitatively new experimental conditions not possible in the gas phase or in rare-gas matrices. The idea that the chemistry is controlled by small energy differences in the solvation energies of the H atom at different lattice sites instead of the heights and widths of chemical reaction barriers offers the possibility of exploring new types of chemistry. Further, the chemistry can be controlled by a single easily varied physical variable, temperature, which makes these experiments easy to implement.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b06356. Table of integrated absorption coefficients and integration limits used to determine concentrations, table of NO peak positions, the ν2+ν3 combination band spectrum of HNO near 3000 cm−1, a comparison between the measured NOH peak positions and intensities with ab initio calculations of the lowest energy triplet and singlet states of NOH, an expanded view of the NOH a-type transitions, spectra of the four t-HNOH absorption features measured in this work, spectrum of the one NH2OH absorption peak observed in this work, table of the kinetic parameters for defect-NH3 and ortho-NH3, table of the kinetic parameters for ortho-H2O and paraH2O, and table of the kinetics parameters for t-HNOH and NH2OH. (PDF)

5. SUMMARY We present FTIR-based spectroscopic measurements of the kinetics of low-temperature tunneling reactions of H atoms with NO in solid pH2. The first part of the paper is focused on presenting the detailed IR spectroscopy and assignments used to study the kinetics. The reactions are initiated by the 193 nm in situ photolysis of NO. We observe the photoproduction of HNO, NOH, NH, NH3, and H2O during photolysis and thereby speculate that H atoms are also generated during photolysis by side reactions of the photoproducts with the pH2 host. After photolysis is stopped, we monitor the ensuing “dark” reaction kinetics using rapid scan FTIR spectroscopy for up to 5 h at a constant temperature of either 1.8 or 4.3 K. We detect first-order growth in HNO, NOH, t-HNOH, and NH2OH during this period that we assign to H atom reactions with NO, HNO/NOH, and t-HNOH, respectively. By measuring the reaction kinetics at two different temperatures we can fit the measured rate constants to an Arrhenius expression to extract pre-exponential factors and activation energies for the processes studied. We find the rate coefficient for H2O NSC is temperature-independent, but that pH2 solvent reorganization around NH3 and the H + NO reaction are both activated processes with small activation energies. A chief goal in this work is to develop a microscopic understanding of H atom quantum diffusion in chemically doped pH2 solids. By using different kinetics mechanisms we show that the measured H + NO reaction kinetics are consistent with long-range migration of the H atoms. This is an important point because the bimolecular reaction kinetics are intrinsically first-order under these conditions, and therefore

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AUTHOR INFORMATION

Corresponding Author

*Phone: 307-766-2775. E-mail: [email protected]. Present Address

Department of Chemistry and Physics, LaTrobe Institute for Molecular Science, LaTrobe University, Melbourne, Victoria Australia, 3083. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge support from the National Science Foundation (CHE-1362497). REFERENCES

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