Reaction kinetics and isotope e ff ect of water formation by the surface reaction of solid H 2 O 2 with H atoms at low temperatures

We performed laboratory experiments on the formation of water and its isotopologues by surface reactions of hydrogen peroxide (H2O2) with hydrogen (H) atoms and their deuterated counterparts (D2O2, D) at 10–30 K. High-purity H2O2 (>95%) was prepared in situ by the codeposition of molecular oxygen and H atoms at relatively high temperatures (45–50 K). We determined that the high-purity H2O2 solid reacts with both H and deuterium (D) atoms at 10–30 K despite the large activation barriers ( 2000 K). Moreover, the reaction rate for H atoms is approximately 45 times faster than that for D atoms at 15 K. Thus, the observed large isotope effect indicates that these reactions occurred through quantum tunneling. We propose that the observed HDO/H2O ratio in molecular clouds might be a good tool for the estimation of the atomic D/H ratio in those environments.


Introduction
Water (H 2 O) is the predominant solid constituent of icy layers of submicron-sized interstellar grains.Because of the potential importance of H 2 O for chemical evolution in molecular clouds (MCs), elucidating the formation mechanism of H 2 O in those environments is important.Although H 2 O formation is possible by gas phase reactions at low temperatures, 1 the observed large abundance of H 2 O cannot be explained only by the gas-phase synthesis. 2Therefore, it is generally accepted that grain-surface reactions are crucial for producing H 2 O in MCs.
Tielens and Hagen 3 proposed that H 2 O formation is initiated by hydrogenation of atomic oxygen (O), molecular oxygen (O 2 ), and ozone (O 3 ), and is completed by the following reactions: Since reaction ( 1) is a radical-radical reaction, it should proceed immediately once reactants encounter each other on the surface.5][6][7] In contrast to reaction (1), reactions (2) and (3) have large activation barriers (>2000 K) in the gas phase. 8,9However, despite such a large barrier, these two reactions were proposed to contribute signicantly to H 2 O formation in dense MCs. 10 Since reactions having such large barriers do not occur thermally in MCs, reactions (2) and (3) require quantum tunneling.The quantum tunneling rate k q is expressed by the following equation, assuming a rectangular activation barrier with a height E a and width a: where n 0 and m represent the frequency of harmonic motion and the mass of the reaction, respectively.Since temperature is not included in the equation, k q does not depend on the reaction temperature.][13][14] We have recently studied reaction (2) experimentally by the codeposition of nonenergetic OH with H 2 and isotopologues such as OD, HD, and D 2 on a substrate and determined that the reactions occur at 10 K. 14 In addition, significant isotope effects were observed, and reactions of OH and OD abstracting a D atom from HD and D 2 were approximately ten times slower than those abstracting an H atom from H 2 and HD.This isotope effect can be explained by the difference in the effective mass of tunneling reactions. 14 number of research studies have been conducted on reaction (3).In these previous studies, O 2 was used as an initial reactant rather than hydrogen peroxide (H 2 O 2 ), which was produced by the successive hydrogenation of O 2 as follows: For example, Miyauchi et al. 15 exposed solid O 2 layers to H or D atoms at 10 K and determined that (i) the rate of O 2 hydrogenation (reaction (5)) is equal to that of O 2 deuteration, (ii) the rate of reaction (3) is slower than that of reaction (5), and (iii) the rate of reaction (3) is eight times faster than that of the following isotopically substituted reaction (7): Miyauchi et al. considered that the rate difference between reactions (3) and ( 7) would be due to the isotope effect of quantum tunneling. 15However, in the O 2 hydrogenation experiments, the formation of both H 2 O 2 and H 2 O occurs in the sample solid.Furthermore, the parent O 2 molecule is IR-inactive.Thus, multiparameter ttings, which oen cause signicant errors, are necessary to obtain the rates for reactions (3) and (5).Moreover, recent studies suggested that H 2 O may form by another exothermic reaction in typical experimental conditions for O 2 hydrogenation: 16,17 OH + OH / H 2 O + O. (8)   In addition to reaction (3), OH is expected to form by the following pathway: where H 2 O 2 * is a reaction intermediate.The reaction of two OH also yields H 2 O 2 on the surface: The branching ratio of barrierless reactions ( 8) to (10) was determined experimentally 17 to be 1 to 4 at 40 K and theoretically 18 to be 1 to 9 on a cold substrate.In any case, reactions ( 8) and ( 10) may compete during O 2 hydrogenation experiments to some extent, making it more difficult to obtain reliable kinetic parameters for reaction (3).0][21][22][23] However, additional experiments using H 2 CO as an initial reactant have enabled us to better understand the reaction kinetics and isotope effects of CO and H 2 CO hydrogenation. 13,24Similarly, the use of H 2 O 2 as an initial reactant is desirable for studying the kinetics and isotope effects of reaction (3).However, because of difficulty in using pure H 2 O 2 , to date such an experiment has not been performed.
In the present study, we performed experimental studies on the formation of H 2 O via reaction (3) and its isotope effect using high-purity (>95%) solid H 2 O 2 and D 2 O 2 .

Apparatus and experimental conditions for water formation
All experiments were performed using the Apparatus for SUrface Reaction in Astrophysics (ASURA) system.The ASURA primarily comprises a main chamber and an atomic source.An aluminum (Al) substrate was mounted at the center of the main chamber and all reactions were performed on the substrate at 10-30 K. Hydrogen (H) and deuterium (D) atoms were produced by the dissociation of H 2 and D 2 molecules, respectively, in a microwave discharge plasma, and were cooled by multiple interactions with the inner wall of the aluminum pipe, which was cooled to 100 K.We conrmed that the formed H and D atoms were well thermalized to the pipe temperature. 25Further details of the ASURA have been described elsewhere. 25,26he uxes of H and D atoms were not directly measured in the present experimental setup; they were estimated by comparing the effective rates of CO hydrogenation and deuteration with those reported by Hidaka et al., 27 which were obtained under the same experimental conditions.Briey, amorphous H 2 O ice (a-H 2 O) with a thickness of approximately ten monolayers (ML; $10 15 molecules cm À2 ) was produced by vapor deposition on the substrate at 15 K, followed by the deposition of CO with a thickness of $0.8 ML.The column density of H 2 O and CO was calculated from the peak area and the previously published band strengths, as described by Hidaka et al. 27 The band strengths for the CO stretching of CO and OH stretching of H 2 O are 2.0 Â 10 À16 and 1.1 Â 10 À17 cm molecules À1 , respectively. 28he obtained effective rates were 1.4 and 0.21 min À1 for the hydrogenation and deuteration of CO, respectively (see Results section below for the determination of effective rate constants).These values are a factor of 3.3 and 6.4 larger than the effective rates of CO hydrogenation and deuteration, respectively, compared to those reported by Hidaka et al., 27 whose uxes of both H and D atoms were 2.6 Â 10 14 atoms cm À2 s À1 .Assuming that the surface density of H and D atoms correlates linearly with their uxes, the uxes of H and D atoms in the present study were estimated to be 8.7 Â 10 14 and 1.7 Â 10 15 atoms cm À2 s À1 , respectively, which corresponds to a D and H atom ux ratio of $2.The variations in the H and D uxes are expected to be less than 10% during and between each experiment.
Approximately 1 ML of solid H 2 O 2 or its deuterated counterpart D 2 O 2 was produced on the substrate by the procedures shown in the next section.H 2 O 2 and D 2 O 2 were exposed to H (D) atoms at 10-30 K. Reaction products were monitored in situ by a reection absorption Fourier Transform Infrared (FTIR) spectrometer with a resolution of 4 cm À1 in the spectral range from 700 to 4000 cm À1 .The column density of H 2 O 2 and D 2 O 2 was calculated from the peak area and previously published band strengths. 15The band strengths used were 2.1 Â 10 À17 and 1.5 Â 10 À17 cm molecule À1 for the OH and OD bending bands at 1385 and 1039 cm À1 , respectively.
Experiments were also performed on an amorphous D 2 O ice (a-D 2 O; $30 ML) vapor-deposited at 10 K.The band strength used was 1.3Â 10 À16 cm molecule À1 for the OD stretching band. 15eparation of high-purity solid hydrogen peroxide In previous studies, 29,30 high-purity H 2 O 2 (>97%) has been prepared by distilling commercially available H 2 O 2 solution under vacuum.The distilled H 2 O 2 was introduced into a reaction substrate through a transfer line made with nonreactive materials such as glass to avoid the catalytic decomposition of H 2 O 2 on metal surfaces.However, in a typical apparatus, which comprises a stainless steel chamber and gas lines, it is not easy to obtain pure H 2 O 2 using this procedure without signicant modication.
Thus, we produced high-purity solid H 2 O 2 in situ by the codeposition of H atoms with O 2 molecules on a substrate at relatively high temperatures.In our previous study, we determined that H 2 O 2 -rich ice tends to form by the O 2 /H codeposition at high temperatures (>30 K) and with an increasing proportion of O 2 relative to H atoms. 31 For example, when O 2 and H were codeposited with an O 2 /H ratio of $2 Â 10 À3 at 20 K, the main product was H 2 O with a small amount of H 2 O 2 (H 2 O/H 2 O 2 $ 5).When the same experiment was performed with an O 2 /H ratio of $9 Â 10 À3 at 40 K, the main product was H 2 O 2 with $15% contamination of H 2 O.We further extended this experiment for the production of solid H 2 O 2 with higher purity suitable for studying the kinetics and the isotope effect of reaction (3).One of the major advantages of this sample preparation method is that it is possible to study the isotope effect of reaction (3) using different isotopes (i.e., H and D), which was not possible in previous studies. 15,32aseous O 2 was introduced into the main chamber through a capillary plate.From the pressure inside the main chamber, the O 2 ux was estimated to be 1.0 Â 10 14 molecules cm À2 s À1 , which is two to four orders of magnitude larger than that used by Oba et al. 31 The H atoms were codeposited with O 2 onto the substrate at 45-50 K.In the present experiments, pure H 2 O 2 solid and the solid on a-D 2 O were used as reactants.The amount of solid H 2 O 2 was $1 ML.Aer the formation of solid H 2 O 2 , the microwave was switched off, the supply of all gases (H 2 and O 2 ) was stopped, and the substrate temperature was raised to 70 K to remove residual O 2 from the sample solid.H 2 O contamination in the solid H 2 O 2 was <5%, which was conrmed by the IR spectrum of the product (Figure 1a).We believe that this small amount of contamination does not signicantly impact the kinetics of reaction (3).We conrmed this by a temperature-programmed desorption experiment wherein little O 2 remained on the substrate aer the sample treatment.The produced H 2 O 2 was then cooled to the desired temperatures (10-30 K) for hydrogenation or deuteration experiments.Moreover, when D atoms were used, high-purity D 2 O 2 was formed (Figure 1b).

H 2 O 2 + H and H 2 O 2 + D
Figure 2 shows IR absorption spectra of solid H 2 O 2 (top) and H 2 O (bottom) for comparison and the difference spectra of 1 ML pure solid H 2 O 2 aer H atom exposure for up to 10 min at 15 K (middle).In the difference spectra, the peaks below and above the baseline represent decreases of initial reactant and increase of reaction products, respectively.With increasing H atom uence, the peak intensity for the OH bending of H 2 O 2 at 1385 cm À1 decreased, and new peaks appeared at 3000-3600, 2850, and 1660 cm À1 .The peak at 1660 cm À1 is attributable to the OH bending of H 2 O formed by reaction (3).Based on the peak position of OH stretching bands of solid H 2 O 2 and H 2 O (Figure 2), the H 2 O band at 3000-3600 cm À1 has a substantial overlap with that of H 2 O 2 , and the peak shape would be attributable to the sum of H 2 O 2 decrease and H 2 O increase.In addition, H 2 O 2 has another strong peak at 2827 cm À1 , which is oen assigned to the n 2 + n 6 combination band. 33If the amount of H 2 O 2 decreases aer H atom exposure, the intensity of the peak should also decrease.However, a peak was observed slightly above the baseline at 2850 cm À1 aer H atom exposure, unlike other peaks at $3300 and 1385 cm À1 (Figure 2).These apparently contradictory observations will be discussed later in the Discussion section.Two small peaks This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
appeared at 3697 and 3721 cm À1 aer H atom exposure (Figure 2), which are attributed to the 3-and 2-coordinated water molecules, respectively. 34igure 3 shows the difference spectra of 1 ML H 2 O 2 aer D atom exposure for up to 120 min at 15 K.If H 2 O 2 reacts with D atoms, HDO is expected to form as a main product by the following reaction: Aer D atom exposure to H 2 O 2 , the peak area for OH stretching and bending bands decreased.New peaks appeared at 3490, 2527, and 1492 cm À1 , which are   typically observed for solid HDO at low temperatures. 35,36This result clearly indicates that HDO was formed by reaction (11) at 15 K.Although the peak area for OH stretching and bending bands decreased aer D atom exposure, the n 2 + n 6 combination band at 2860 cm À1 increased slightly.Very small peaks appeared at 2722 and 3693 cm À1 aer D atom exposure (Figure 3), the former of which is probably derived from the dangling OD bond of HDO. 37The latter peak could be the dangling OH bond of HDO; however, the assignment is uncertain because of low S/N. Figure 4 plots variations in the column density of solid H 2 O 2 normalized to the unexposed initial amount aer exposure to H or D atoms.We tted the plots in Figure 4 to the following single-exponential decay function to obtain the kinetic parameters for reactions (3) and (11): where A is a saturation value, t is the H or D atom exposure time, k n is the rate constant of reaction (n), and [X] is the number density of X atoms (X ¼ H or D) on the surface.Unfortunately, it is difficult to measure [X] in the present experiment; thus, the product k n [X] is obtained as a tting parameter for equation (12).Hereaer, k n [X] is denoted as the effective rate constant k n 0 in the present study.
We assume that during exposure, [X] is independent of time and is governed mainly by the balance between the ux of X atoms, the sticking coefficient of the impinging atoms, and the loss of atoms by X-X recombination.We obtained k 3 0 ¼ 7.2 Â 10 À1 and k 11 0 ¼ 3.2 Â 10 À2 min À1 at 15 K, and the k 3 0 /k 11 0 ratio was 23.
In the present study, we do not determine the absolute yields of reaction products with the decrease in the column density of reactants, because the band strengths of the products (H 2 O or HDO) have been reported only for a transmission method.Using these reported values may cause a large error (<50%) 31 when those band strengths are used in a reection method.However, it does not affect the values of effective rate constants because the term of band strength is not included in equation (12).In addition, a portion of the reaction products could desorb from the substrate upon formation, 38,39 making the interpretation of the yields of products more difficult.
Figure 5 shows variations in the difference spectra of pure solid D 2 O 2 aer exposure to H atoms on the Al substrate at 15 K.With increasing D atom uence, the peak intensity of OD stretching and bending bands at 2467 and 1045 cm À1 , respectively, decreased, and new peaks appeared at 3455, 2587, and 1477 cm À1 .By comparing the peak positions with those given in the literature, 36 we determined that these new peaks are attributable to HDO, indicating that solid D 2 O 2 reacted with H atoms to yield HDO at 15 K: The peak intensity of the n 2 + n 6 combination band for D 2 O 2 (2126 cm À1 ) 33 increased slightly, which is opposite to the behavior that would be observed if D 2 O 2 was consumed by reaction (13).The dangling OH band of HDO was observed at 3694 cm À1 while the dangling OD band was not conrmed probably due to low S/N (Figure 5).
Figure 6 shows variations in the difference spectra aer D atom exposure to D 2 O 2 for up to 120 min at 15 K.This experiment was performed to study reaction (7): This reaction has been studied in previous O 2 deuteration experiments. 15,32In the present study, with increasing D atom uence, new peaks appeared at 2562 and    À0.2 aer a few minutes.In contrast, the decrease of D 2 O 2 by reaction (7) was much slower, reaching the almost same saturation value aer 150 min.By tting the plots in Figure 7 into single exponential decay function (12) where [H 2 O 2 ] is replaced with [D 2 O 2 ], we obtained k 13 0 ¼ 8.9 Â 10 À1 and k 7 0 ¼ 2.3 Â 10 À2 min À1 , and the k 13 0 /k 7 0 ratio was 38.

Reactions on amorphous D 2 O ice
Hydrogenation and deuteration of solid H 2 O 2 and D 2 O 2 were also performed on vapor-deposited a-D 2 O with a thickness of $30 ML at 15 K. Figure 8 shows an IR spectrum of 1 ML solid H 2 O 2 produced on a-D 2 O and the difference spectra aer H atom exposure for up to 5 min.The peak area of the n 2 + n 6 combination band before H atom exposure was larger by a factor of two than that on the Al substrate, although the peak area of other bands (OH stretching and bending) was almost equal.
With increasing H atom uence, the intensities of peaks at 3233, 2852, and 1392 cm À1 decreased and new peaks appeared at 3422 and 1635 cm À1 .These observations clearly indicate that H 2 O was formed by reaction (13).Notably, the peak intensity for the n 2 + n 6 combination band at 2852 cm À1 decreased aer H atom exposure.This behavior is straightforward since H 2 O 2 was consumed by reaction (13); however, interestingly, this is opposite to the result for the same reactions of pure H 2 O 2 on the Al substrate described above.In addition to reaction (13), we conrmed in separate experiments that reactions (11), (13), and ( 7) occur on a-D 2 O at 15 K. Two small peaks appeared at 3697 and 3719 cm À1 aer exposure to H atoms (Figure 8), which are attributed to the 3-and 2-coordinated dangling OH bands, respectively. 34e determined the effective rate constants with statistical errors for each reaction (Table 1) by tting the attenuation of H 2 O 2 and D 2 O 2 into a single exponential decay function (12).As a general trend, values of k 0 are larger for reactions on a-D 2 O.The column densities of H 2 O formed on the Al and a-D 2 O by reaction (3) were calculated using the band strength of the OH-bending at 1635 cm À1 (1.2 Â 10 À17 cm molecule À1 ). 28We determined that the H 2 O yield on a-D 2 O was approximately two orders of magnitude larger than that on the Al at the same H uence, although the amount of H 2 O 2 consumption on H atom exposure was identical for a-D 2 O and Al (Figure 9).

Temperature dependence of reaction kinetics
Reaction (3) was studied using pure H 2 O 2 at 10, 20, and 30 K as well as at 15 K. Reaction (3) occurred at all temperatures.We obtained kinetic parameters for reaction (3) (k 3 0 ) at each temperature following the procedures described above.
Figure 10 shows variations in the relative abundance of pure H 2 O 2 aer H atom exposure at 10-30 K.The temperature dependence shows that the saturation value of H 2 O 2 becomes larger with increasing temperature up to 20 K; however, at 30 K, the reaction is very slow and the saturation value is much less than that below 20 K.The effective rate constant is the largest at 10 K and decreases with increasing temperature.These features were also obtained for reactions on a-D 2 O ice (Figure 11).

Discussion
Quantum tunneling and isotope effect The reaction of H 2 O 2 with H atoms and that of their deuterated counterparts has a large activation barrier (>2000 K) in the gas phase. 9,40,41Therefore, these reactions are expected to proceed through quantum tunneling at 10-30 K even on the surface, as mentioned earlier.A tunneling reaction strongly depends on the transmission mass of the activation barrier of reaction, as can be seen in equation (4).Theoretical studies proposed that H 2 O formation by reaction (3) initiates from the formation of an intermediate by H atom addition to one O atom in H 2 O 2 , followed by the cleavage of the O-O bond. 9,41In general, the tunneling mass in the two-body addition reaction is described by the reduced mass m. 12,13 As shown in In the present study, if we compare the P 3 /P 11 ratio with the k 3 /k 11 and the P 13 /P 7 ratio with the k 13 /k 7 , we obtain k 3 /k 11 ¼ $2 Â P 3 /P 11 and k 13 /k 7 ¼ $3 Â P 13 /P 7 .These differences are not surprising because the tunneling probability is signicantly affected by the shape of the potential barrier, and it is very difficult to determine the tunneling rate with an accurate barrier for surface reactions.In fact, Taquet et al. 40 noted that, although the Eckart model provides a signicant improvement over square barriers, which were typically used for this type of calculation, the tunneling probabilities of some reactions at low temperatures can be underestimated (or overestimated).We obtained the k 3 /k 7 ratios of 61 and 88 for pure Thus, we believe that our calculated value of k 3 /k 7 is more reliable than that obtained in O 2 hydrogenation/deuteration experiments.Next, we compare the rates of reactions ( 3) and ( 5).The k 5 /k 3 ratio in the O 2 hydrogenation experiment was reported to be 3.3. 15Based on the fact that reaction ( 5) is barrierless and reaction (3) has a large barrier (>2000 K), 9 the value obtained by Miyauchi et al. seems to be rather small.Subsequently, we calculated the k 5 /k 3 ratio using k 3 0 obtained in the present study.The value of k 5 0 reported by Miyauchi et al. (12.8 min À1 ) 15 was not used for this calculation because their conditions such as atom uxes and sample amounts were signicantly different from ours.Instead, we used the value of k 5 0 (5.2 min À1 ) obtained in the following experiment: solid O 2 ($3 ML) on an amorphous D 2 O ice (30 ML) was exposed to H atoms (ux: 2 Â 10 14 atoms cm À2 s À1 ) at 10 K. 42 Aer the correction of the ux difference, we obtained the k 5 /k 3 ratio of $15, which is approximately ve times larger than that reported by Miyauchi et al. 15 Although the sample compositions and the uxes of H atoms in these two experiments do not exactly match, we believe that the present result would better represent the k 5 /k 3 ratio compared to previous studies.Notably, the observed isotope effect in the hydrogen/deuterium addition to H 2 O 2 (k 3 /k 11 ) is much larger than that for one of the astrochemically-important tunneling surface reactions: the hydrogenation/deuteration of CO.Hidaka et al. 27 reported that the rate of CO hydrogenation (k H ) was larger than CO deuteration (k D ), with a k H /k D ratio of 12.5.This isotope effect is approximately four times smaller than that of the hydrogenation/deuteration of H 2 O 2 observed in the present study.This large difference is rather surprising because the barrier height for the hydrogenation/deuteration of H 2 O 2 is similar to that of CO. 40,43 We believe that the difference might have been due to accumulation of multiple factors such as differences in residence time of H/D atoms on H 2 O 2 and CO and the shape of the potential barriers.
As mentioned previously, we assume that the surface density of H atoms is the same as that of D atoms when the ux is equal.However, in a series of experiments under high H and D ux conditions, this may not always be true.Even under the same ux conditions for H and D atoms, the surface density of D atoms ([D]) may become larger than that of H atoms ([H]).Since H atoms can diffuse faster on the surface than D atoms, the recombination probability for H atoms is higher than that for D atoms, 12 resulting in a lower value of [H] than that of [D] even under the same uxes.In that case, the ratio of [H]/[D] becomes smaller than 0.5, yielding larger values of k 3 /k 11 and k 13 /k 7 than those reported in the present study.Further studies related to the surface densities of H and D atoms are necessary.

Dependence of reaction efficiency on temperature and type of substrate
The effective rate constants for reaction (3) decrease with increasing substrate temperature (Figure 11).This is opposite to the typical Arrhenius-type behavior where the reaction rate has a positive correlation with temperature.In addition, because reaction (3) occurred through quantum tunneling, the reaction rate should have lesser dependence on the surface temperatures.The decrease of the effective rate can be explained well by the decrease in the number density of H atoms on the surface with increasing temperature because the effective rate k The difference of the effective rate constant between reactions of pure H 2 O 2 and H 2 O 2 on a-D 2 O is the largest at 10 K and decreases with increasing temperature (Figure 11).The large difference observed at lower temperatures (<15 K) may be explained by the difference in the number density of H atoms on the surface because a-D 2 O would have a much larger surface area compared to planar Al substrate, as reported for CO hydrogenation by Hidaka et al. 44 who determined that the surface area for a-H 2 O with thickness equivalent to $17 ML is approximately nine times larger than that for crystalline H 2 O.In contrast, at elevated temperatures where the residence time of H atoms on the surface is very short even on a-D 2 O, the difference could little be affected by the density of H atoms, which can lead to similar effective rate constant values under both conditions (Figure 11).
In Figure 9, H 2 O yield for the sample of pure H 2 O 2 on Al substrate is lower than that for H 2 O 2 on a-D 2 O, although the decrease of H 2 O 2 is approximately the same for both samples.This difference may be partly explained by immediate desorption of H 2 O formed as a product at the reaction preferentially occurred on the Al substrate.This behavior is also observed in O 2 + D experiments on amorphous silicates and a-H 2 O, where the yield of D 2 O is higher for reactions on a-H 2 O. 39 The heat of reaction (3) (285 kJ mol À1 ¼ 2.9 eV) is partly partitioned to the reaction product H 2 O and OH.This energy would be sufficient for H 2 O to desorb from the substrate (Al or a-D 2 O).For the H 2 O 2 on a-D 2 O sample, interaction of H 2 O 2 and H 2 O product with the a-D 2 O surface is much stronger than that with the Al surface because of hydrogen bonding.Therefore, the reaction heat can dissipate into a-D 2 O more easily, and desorption at the reaction surface may be reduced.Furthermore, since a-D 2 O has a large surface area because of pores and cracks, the desorbed H 2 O can be retrapped on the surface of a-D 2 O.This type of H 2 O relaxation and trap has been demonstrated both experimentally [45][46][47] and theoretically 48,49 to occur during the photodesorption of H 2 O from bulk a-H 2 O.In addition to H 2 O, OH should also form by reaction (3) and can be the source of another H 2 O formation.Accordingly, H 2 O and OH trapped on the surface of a-D 2 O may explain the larger column density of the formed H 2 O than that on the Al substrate (Figure 9).
As shown in Figure 1, solid H 2 O 2 produced on the Al substrate has representative strong absorptions at three positions: 1385 (n 2 ), 2827 (n 2 + n 6 ), and 3326 cm À1 (n 1 ). 33Similarly, for solid H 2 O 2 on a-D 2 O, these three peaks are slightly shied on the spectrum at 1392, 2852, and 3233 cm À1 (Figure 8).The difference in the peak position for each band is not very large (<25 cm À1 ).However, the peak area of the n 2 + n 6 combination band was larger by a factor of two for the sample on a-D 2 O, although the peak area of other bands (n 1 and n 2 ) was identical on both substrates.A relatively strong peak at $2850 cm À1 for solid H 2 O 2 is typically assigned to the n 2 + n 6 combination band; 33,50 however, some studies considered that this assignment is disputable. 51,52Ignatov et al. 51 proposed that this peak is attributable to an OH valence band of the H 2 O 2 molecule placed in the unusual surface environment.The present results imply that the peak intensity at $2850 cm À1 might correlate with the conguration of H 2 O 2 on the substrate.In addition, the fact that H 2 O 2 forms hydrogen bonds more on a-D 2 O than on Al could result in the different IR features at $2850 cm À1 .In other words, the number of hydrogen bonds between H 2 O 2 and surrounding H 2 O may constrain the peak intensity at $2850 cm À1 .If this is the case, it could explain the contradictory behavior of the peak intensity aer exposure to atoms (e.g.Figures 2 and 8).More detailed experimental and theoretical studies are necessary for the precise peak assignment.Thus, we propose that care should be taken when this IR peak is used for quantication of solid H 2 O 2 in various environments.

Dangling OH (OD) bands of reaction products
We conrmed that the formed solid H 2 O and its isotopologues (HDO and D 2 O) show the dangling OH (OD) bands (e.g., Figure 2).The presence of dangling OH bands in the IR spectrum of solid H 2 O typically indicates that it is amorphous and has a microporous structure. 34However, we have reported that dangling OH bands are not observed in solid H 2 O formed by codeposition of O 2 and H atoms at 10 K and that the formed ice is amorphous but has a compact structure. 31These different results suggest that the formed ice structure depends on experimental conditions and that the properties of the reaction products are strikingly different between each study (multilayers with O 2 contaminants vs. very thin layers with little contaminants).

Astrophysical implication
4][55][56][57] In contrast, deuterated water was not clearly identied in the solid phase; only the upper limit of HDO was determined (HDO/H 2 O < 0.2%-2%). 58,59espite the detection of deuterated water in the gas phase only, it is reasonable to consider that deuterated water is also produced by surface reactions on interstellar grains at very low temperatures.
The following reactions are possible to yield water isotopologues from H 2 O 2 and its isotopologues: HDO 2 + H / HDO + OH, (14a) HDO 2 + D / HDO + OD, (15a) We did not study reactions ( 14) and ( 15) because of difficulty in producing high-purity HDO 2 .Two types of reaction products are possible for reactions (14)  and (15).Since the reduced mass of a reaction to produce the intermediate does not depend on the type of products, we expect that reactions (14a) and (14b) occur to the same extent statistically.In fact, the tunneling probability for reaction (14a) is calculated to be identical with that of reaction (14b). 40The same is true for reactions (15a) and (15b).Thus, for simplicity, we made a rough assumption based on the obtained results that H atom addition reactions such as reactions (3) and ( 13) occur faster by a factor of 50 than D atom addition reactions such as reactions ( 7) and (11).In addition, we assume that the atomic D/H ratio is constant and the surface diffusion rates of H and D atoms are the same.Under these assumptions, we determined that the HDO/H 2 O ratio was almost identical to the atomic D/H ratio, while the D 2 O formation was negligible ($10 À6 that of H 2 O).On the other hand, assuming no isotope effect on the reactions, the HDO/ H 2 O ratio becomes twice as large as the atomic D/H ratio; thus, quantum tunneling would cause a decrease of the HDO/H 2 O ratio in this reaction pathway.In other words, if quantum tunneling corrections are not included in a chemical model, the obtained result should overestimate the value of the HDO/H 2 O ratio.
We extend this discussion to other water formation pathways, i.e., reactions (1) (OH + H / H 2 O) and (2) (OH + H 2 / H 2 O + H).For reaction (2), we have experimentally determined the relative efficiency of reactions for all possible isotopologues; 14 H atom abstraction reactions are approximately ten times more efficient than D atom abstraction reactions.Assuming that OH and OD are formed by surface reactions O + H and O + D, respectively, HD/H 2 ratio is 10 À5 , and no D 2 is present, the HDO/H 2 O ratio was very much consistent with the atomic D/H ratio.
In contrast to the former two reaction pathways, the reactions of OH or OD with H or D atoms do not have an activation barrier.Thus, the product ratio would strongly depend on the atomic D/H ratio.Since there are two possible reactions to yield HDO (OH + D / HDO and OD + H / HDO), statistically the HDO/H 2 O ratio is twice as large as the atomic D/H ratio.With regard to the formation of D 2 O, this reaction pathway is the most favorable among the three reaction pathways; the D 2 O/H 2 O ratio is statistically the square of the value of the D/H ratio.For example, the D 2 O/H 2 O ratio is 10 À4 if the atomic D/H is 10 À2 .This value is two to four orders of magnitude higher than that estimated by other pathways under the same assumptions.Therefore, the OD + D reaction is the only possible pathway to effectively yield D 2 O in MCs.
Moreover, it is important to note that, on grain surfaces, the deuterium fractionation of water occurs only during the formation by surface reactions at the typical temperature of MCs ($10 K).This is supported by the fact that H 2 O does not react with D atoms at <15 K 60 and thermal H-D exchange does not occur at <100 K, 61 which prevents the D-enrichment by H-D substitution with other deuterium-enriched species aer the formation of H 2 O on the grains.The reactivity of water with D atoms at low temperatures differs from that of organic species such as CH 3 OH, 25,60 H 2 CO, 13,27 and CH 3 NH 2 62 where H-D exchange occurs for these molecules by reacting with D atoms at temperatures as low as 10 K.
Based on the present and previous experimental results for water formation, we suggest that the HDO/H 2 O ratio might be a key parameter to estimate the atomic D/H ratio during the formation of water.Namely, the following relationship is roughly derived from experimental studies: (D/H) atom # (HDO/H 2 O) # 2(D/ H) atom or 1/2(HDO/H 2 O) # (D/H) atom # (HDO/H 2 O), where (D/H) atom and (HDO/ H 2 O) represent the atomic D/H on grains and the HDO/H 2 O ratio formed by surface reactions, respectively.Note that these relationships were derived with reference to experimental studies for surface reactions.In addition to surface reactions, deuterium fractionation of water by gas phase reactions may also be possible. 63Moreover, energetic processes induced by UV and cosmic rays might cause hydrogen isotopic fractionation of water during its decomposition and interactions with other ice components, both of which may modify the HDO/H 2 O ratio.Therefore, we propose that further collaborative theoretical and experimental studies on surface and gas phase chemistries are necessary to construct a complete chemical model regarding the evolution of the water D/H ratio in MCs.

Fig. 2
Fig. 2 FTIR spectra of H 2 O 2 (top) and pure H 2 O (bottom) and the variations in the difference spectra of H 2 O 2 after exposure to H atoms for up to 10 min at 15 K (middle).

Fig. 3
Fig. 3 Variations in the difference spectra of H 2 O 2 after exposure to D atoms for up to 120 min at 15 K.

Fig. 4
Fig. 4 Variations in the column density of H 2 O 2 normalized to the initial amount as a function of exposure time of H or D atoms at 15 K. Solid lines are single-exponential decay fits to the plots.

Fig. 5
Fig. 5 Variations in the difference spectra of D 2 O 2 after exposure to H atoms for up to 10 min at 15 K.

Figure 7
shows variations in the column density of solid D 2 O 2 normalized to the unexposed initial amount aer H or D atom exposure at 15 K.The relative abundance of D 2 O 2 by reaction (13) reaches a saturation value of approximately

Fig. 6
Fig. 6 Variations in the difference spectra of D 2 O 2 after exposure to D atoms for up to 120 min at 15 K.

Fig. 7
Fig. 7 Variations in the column density of D 2 O 2 normalized to the initial amount as a function of H or D atom exposure times at 15 K. Solid lines are single-exponential decay fits to the plots.

Fig. 8
Fig. 8 Variations in the difference spectra of H 2 O 2 produced on a-D 2 O for up to 5 min at 15 K.

Fig. 10 Fig. 11
Fig. 10 Variations in the column density of pure H 2 O 2 normalized to the initial amount after exposure to H atoms at 10 (square), 15 (circle), 20 (triangle), and 30 (diamond) K. Lines are single-exponential decay fits to the plots.
H 2 O 2 /D 2 O 2 and H 2 O 2 /D 2 O 2 on a-D 2 O, respectively.These values are about one order of magnitude larger than those reported by Miyauchi et al., who determined the k 3 0 /k 7 0 ratio to be 8 in their O 2 hydrogenation/deuteration experiments at 10 K. Since the ux of H atoms was the same with that of D atoms in the previous experiment, 15 the k 3 0 /k 7 0 ratio is certainly equal to the k 3 /k 7 ratio on the assumption that the ratio of surface number densities between H and D atoms is same as that of the uxes.The large difference may arise for several reasons.First, multi-parameter ttings may cause signicant errors of k 3 and k 7 in their work.Second, H 2 O and D 2 O would form in O 2 hydrogenation/deuteration via separate pathways: OH + OH / H 2 O + O and OD + OD / D 2 O + O, respectively, which are both barrierless reactions.This would lead to an overestimation of the k 3 /k 7 ratio.In the present study, these uncertainties are removed because H 2 O 2 or D 2 O 2 are used as the initial reactants.

Table 1
Effective rate constants with statistical errors determined in the present study at 15 K Reaction Reaction number Substrate Effective rate (min À1 ) E a (K) a a Taquet et al. 40Fig.9 Variations in the column densities of H 2 O (circle) and H 2 O 2 (square) normalized to the initial H 2 O 2 amount obtained after H atom exposure to H 2 O 2 at 15 K. Open and filled symbols represent experimental results on a-D 2 O and Al substrate, respectively.

Table 1 ,
the mass dependence of the reaction rate is evident; the lighter mass results in a faster reaction rate.Thus, we conclude that the reactions of H 2 O 2 / D 2 O 2 with H/D atoms proceed by quantum tunneling.for pure H 2 O 2 and H 2 O 2 on a-D 2 O, respectively.Since the effective rate constant k n 0 is expressed as k n [X] where X ¼ H or D, the ratio of the effective rate constants is not equal to the ratio of the actual reaction rate constants if [H] s [D].Assuming that the value of [X] has a linear correlation with the ux of X atoms in the present experiment, the ratios of k 3 to k 11 (k 3 /k 11 ) become 44 and 48 for pure H 2 O 2 and H 2 O 2 on a-D 2 O, respectively, because the D atom ux is approximately twice that of the H atom ux.Similarly, the k 13 /k 7 ratio was calculated to be 75 and 81 for pure D 2 O 2 and D 2 O 2 on a-D 2 O, respectively.Taquet et al.
40calculated a tunneling probability P n through an Eckart potential barrier for reaction (n).