Quantum tunneling observed without itscharacteristic large kinetic isotope effectsTetsuya Hama1, Hirokazu Ueta2, Akira Kouchi, and Naoki Watanabe

Institute of Low Temperature Science, Hokkaido University, Sapporo 060–0819, Japan

Edited by Eric Herbst, University of Virginia, Charlottesville, VA, and accepted by the Editorial Board May 4, 2015 (received for review January 20, 2015)

Classical transition-state theory is fundamental to describing chem-ical kinetics; however, quantum tunneling is also important inexplaining the unexpectedly large reaction efficiencies observed inmany chemical systems. Tunneling is often indicated by anomalouslylarge kinetic isotope effects (KIEs), because a particle’s ability to tun-nel decreases significantly with its increasing mass. Here we exper-imentally demonstrate that cold hydrogen (H) and deuterium (D)atoms can add to solid benzene by tunneling; however, the observedH/D KIE was very small (1–1.5) despite the large intrinsic H/D KIE oftunneling (≳100). This strong reduction is due to the chemical kinet-ics being controlled not by tunneling but by the surface diffusion ofthe H/D atoms, a process not greatly affected by the isotope type.Because tunneling need not be accompanied by a large KIE in surfaceand interfacial chemical systems, it might be overlooked in othersystems such as aerosols or enzymes. Our results suggest that sur-face tunneling reactions on interstellar dust may contribute to thedeuteration of interstellar aromatic and aliphatic hydrocarbons, whichcould represent a major source of the deuterium enrichment ob-served in carbonaceous meteorites and interplanetary dust parti-cles. These findings could improve our understanding of interstellarphysicochemical processes, including those during the formation ofthe solar system.

quantum tunneling | kinetic isotope effect | heterogeneous reactions |reaction dynamics | astrochemistry

Tunneling arises from the wave nature of matter, allowingparticles to penetrate barriers that are impossible to over-

come classically. Because the de Broglie wavelength is inverselyproportional to particle momentum, tunneling becomes notice-able in small masses and at low temperatures. The de Brogliewavelengths for hydrogen (H, 9.8–1.8 Å) and deuterium (D, 6.9–1.3 Å) at 10–300 K exceed the scale of the typical widths ofactivation barriers in chemical reactions (∼1 Å), which invalid-ates a purely classical description of their motion in chemistry(1, 2). Hydrogen, including its ionic forms (H+ and H−), is presentin water and most organic compounds, and kinetic measurementshave established that tunneling occurs in reactions involving hy-drogen in gas (1), liquid (1, 3, 4), and solid phases (4). Tunnelinghas also been recognized as a significant factor in reactions onsurfaces and at interfaces; for example, proton transfer reactionsat the air/water interface (5) and enzyme catalysis (3, 6). More-over, tunneling reactions (e.g., CO + H or D) on interstellar dustare crucial in explaining the abundances of organic molecules suchas methanol and their deuterated isotopologues observed in coldand dense interstellar regions (≤100 K), such as molecular clouds,where thermally activated reactions rarely occur (2, 7).A particle’s ability to tunnel through a barrier decreases dras-

tically with its increasing mass. This means different isotopes of agiven element show very different tunneling behaviors, and largerkinetic isotope effects (KIEs) than those expected from semi-classical theory have been regarded as a reliable indicator of tun-neling (1). However, chemical reactions involving tunneling oncondensed phases are usually accompanied by other surface pro-cesses such as adsorption, diffusion, and desorption. These aregenerally thermal processes, and thus much less sensitive to thereactant isotope than tunneling is (2). Therefore, the observed

KIE can be much smaller than that intrinsically associated withtunneling in cases when the isotopically insensitive process de-termines the reaction rate. In other words, an observation of asmall KIE under a given condition does not necessarily excludetunneling, and tunneling may occur unrecognized in chemicalreactions on condensed phases.Using in situ IR reflection–absorption spectroscopy (Methods;

See also Supporting Information and Figs. S1–S3), we previouslyshowed that H atoms can add to an amorphous solid benzene(C6H6) surface by tunneling to form cyclohexane (C6H12) at 20 K(8). The present study investigates the KIEs associated with tun-neling in the following hydrogenation/deuteration reactions ofamorphous solid C6H6 over a wide temperature range (10–50 K):

C6H6 +HðDÞ→C6H7ðC6H6DÞ Ea = 18.2  kJ ·mol−1, [R1]

C6H7 +HðDÞ→C6H8ðC6H6D2Þ, [R2]

C6H8 +HðDÞ→C6H9ðC6H6D3Þ Ea = 6.3  kJ ·mol−1, [R3]

C6H9 +HðDÞ→C6H10ðC6H6D4Þ, [R4]

C6H10 +HðDÞ→C6H11ðC6H6D5Þ Ea = 10.5  kJ ·mol−1, [R5]

C6H11 +HðDÞ→C6H12ðC6H6D6Þ, [R6]

where Ea is the activation barrier for H-atom addition in the gasphase (9, 10). The radical recombination reactions R2, R4, andR6 are barrierless on the surface. We exposed amorphous C6H6

Significance

Quantum tunneling, an important phenomenon in many sur-face and interfacial chemical processes, is strongly dependenton the isotope of the tunneling atom. However, surface tun-neling during the hydrogenation/deuteration of solid benzeneat 15–25 K is accompanied by an almost semiclassical kineticisotope effect (KIE) of 1–1.5, which is much lower than thatintrinsic to tunneling (≳100), because isotopically insensitivesurface diffusion of the adsorbed atoms controls the chemicalkinetics. Our results suggest that tunneling has been unrec-ognized in studies of the chemistry of condensed phases, andsmall-KIE tunneling may account for the unexplained fast reac-tions of hydrogen and deuterium observed in surface/interfacechemical systems such as aerosols, enzymes, and interstellardust grains.

Author contributions: T.H., A.K., and N.W. designed research; T.H. performed research;T.H., H.U., A.K., and N.W. analyzed data; and T.H., H.U., A.K., and N.W. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. E.H. is a guest editor invited by the EditorialBoard.1To whom correspondence should be addressed. Email: hama@lowtem.hokudai.ac.jp.2Present address: National Institute for Materials Science, Tsukuba 305–0047, Japan.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1501328112/-/DCSupplemental.

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samples at 10–50 K to cold H or D atoms at 120 K. In situ IRspectroscopy revealed that cyclohexane or deuterated cyclohex-ane are efficiently formed by reactions R1–R6. Given the activa-tion barriers and low temperatures, these reactions proceededvia tunneling (8, 11); however, we observed only small KIEs. Theratio of the hydrogenation and deuteration rates (H/D) was 1–1.5at 15–25 K, whereas deuteration by tunneling typically occurs ata rate more than two orders of magnitude smaller than that ofthe comparable hydrogenation (11). This indicates that the iso-topically insensitive surface processes of the atoms physisorbedon solid C6H6 masked the tunneling KIE, despite tunneling’sproviding a classically anomalous reaction efficiency.The present study is also the first report to our knowledge of the

nonenergetic deuteration of aromatic hydrocarbons at low tem-perature. We discuss the importance of our findings for astro-chemistry and geochemistry in relation to the origin of deuteriumenrichment observed in extraterrestrial materials such as inter-stellar aromatic/aliphatic hydrocarbons, carbonaceous meteorites,and interplanetary dust particles (12–17), the chemistry of whichinfluences our understanding of interstellar physicochemical pro-cesses, including the formation of the solar system (18–20).

ResultsFig. 1A shows the IR spectra of amorphous C6H6 and C6H12 at20 K. The column density (the amount of a substance per unitarea integrated along a path perpendicular to the surface) wasestimated to be 6 × 1015 cm−2. For reference, the column densityof monolayer coverage of crystalline C6H6 is (6–8) × 1014 cm−2

(Supporting Information). Fig. 1 B and C show the difference spectraafter H or D atom exposure for up to 180 min, respectively. In thedifference spectrum B, the C6H6 absorption bands at 3,000–3,100,1,480, and 1,036 cm−1 decreased, and new peaks for the C6H12products appeared at 2,800–3,000 and 1,453 cm−1. This indicatesthe formation of C6H12 by reactions R1–R6 with the consumptionof C6H6. After 180-min exposure, both the C6H6 consumptionand the C6H12 formation saturated at column densities of ∼9 ×1014 cm−2 at 20 K (Figs. S4 and S5), namely 15% of the C6H6molecules reacted with the H atoms. This value is higher than thecolumn density of monolayer coverage of crystalline C6H6, suggest-ing a large amount of reactive C6H6 on the surface. We speculatethat amorphous C6H6 had 3D island structures and a larger surfacearea than crystalline C6H6 (8, 21). Consumption of C6H6 was alsoobserved upon exposure to D atoms (Fig. 1C). Although the as-signment of the products is difficult from the IR spectra, tempera-ture-programmed desorption mass spectrometry showed that themain products were partially deuterated cyclohexane (C6H6D6)with further-deuterated cyclohexane (C6H5D7, C6H4D8. . .C6H1D11,C6D12) (Fig. S6). This shows that D atom addition to C6H6 oc-curred to form C6H6D6 by tunneling. Subsequent H–D sub-stitution reactions of C6H6D6 yielded C6H5D7. . .C6D12 alsoby tunneling (Figs. S7 and S8). Throughout the H atom expo-sure, C6H12 was the dominant product (Fig. 1 and Figs. S4 and S5).This indicates that reaction R1 is the rate-limiting step, because ithas the highest barrier of reactions R1–R6. Here, we concentrateon the KIE of H and D atoms on C6H6 consumption.Fig. 2 plots the variation in the column density of amorphous

C6H6 (ΔC6H6) during exposure to H or D atoms at temperaturesof 10–50 K. Absolute rate constants of the surface reactionscould not be determined owing to the surface heterogeneity andto the difficulty of measuring the surface number density ofatoms. Hence, we used the reaction probabilities of C6H6 perincident H or D atom (PH or PD) during the initial 3-min ex-posure to evaluate the KIE (Fig. 3A), where the subscripts H andD represent H and D atoms, respectively. PH or PD were cal-culated as the ratio of C6H6 consumption to the fluence of eitherH or D atoms. For reference, the fluences of H and D atomsafter 3-min exposure were estimated to be 8.1 × 1016 and 6.5 ×1016 cm−2, respectively, assuming a flux of H atoms of 4.5 × 1014

cm−2·s−1 and of D atoms of 3.6 × 1014 cm−2·s−1 (Figs. S2 and S3).We also plotted the amounts of C6H6 consumed after H or D

atom exposure for 180 min (ΔC6H6_H or ΔC6H6_D) (Fig. 3B). At30–50 K, PH was two to five times larger than PD. Values ofΔC6H6_H were also two to four times larger than those ofΔC6H6_D at 30–50 K. PH and ΔC6H6_H were greatest at 20 K.Remarkably, both PH/PD and ΔC6H6_H/ΔC6H6_D lay between1.0–1.5 at 15–25 K despite the intrinsic H/D KIE associated withtunneling (J100) (11). These small differences between additionby H or D tunneling clearly show that isotopically insensitivesurface processes strongly contributed to the outcome of thesesurface reactions. Note that heating the sample to 50 K slightlyaltered the surface structure but did not greatly affect PH or PD(Fig. S4).At the lowest studied temperatures (10–12 K), PH and ΔC6H6_H

decreased, whereas both PH/PD and ΔC6H6_H/ΔC6H6_D increased(Figs. 2 and 3). At 10–12 K, H2 or D2 ejected as undissociatedmolecules from the atomic source can efficiently physisorb ontothe amorphous C6H6 surface (2). Therefore, we tested the effect ofadsorbed molecules on the hydrogenation/deuteration reactionsvia additional H2 or D2 codeposition at (1–2) × 10−3 Pa (Fig. 4).At 15 K, the variations of C6H6 were similar both with and withoutthe additional H2 or D2 codeposition. However, C6H6 con-sumption decreased at 10 K when additional H2 was deposited onthe amorphous C6H6 surface. In the D/D2 codeposition exper-iment, the decrease in C6H6 consumption was observed at 12 K.These results show that the atomic addition reactions are inhibitedby competing long-term adsorption of molecules on the surface at10–12 K, and reaction R1 at 10–12 K is controlled by the ad-sorption of atoms that overcame the inhibiting effect of the ad-sorbed molecules.

Fig. 1. Typical infrared reflection–absorption spectra at 3,200–800 cm−1.(A, upper spectrum) Amorphous solid benzene (C6H6) at 20 K before atomicexposure. (A, lower spectrum) Amorphous solid cyclohexane (C6H12) de-posited at 20 K. (B and C) Difference spectra for amorphous solid C6H6 at20 K after 180-min exposure to H or D atoms, respectively.

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DiscussionBefore discussing the KIE of the hydrogenation/deuteration ofamorphous C6H6, we briefly describe the reaction mechanism.There are two major mechanisms for surface reactions: the Eley–Rideal (ER) mechanism, which is a direct reaction between aparticle from the gas phase and an adsorbate on the surface, andthe Langmuir–Hinshelwood (LH) mechanism, which is the re-action of two species after adsorption and diffusion (i.e., ther-malization) on the surface (2). The ER mechanism should providea yield that is largely independent of the surface temperature,whereas the yield of a LH reaction should reflect the adsorptiontime of atoms on the surface. Fig. 3B shows that the values ofΔC6H6_H and ΔC6H6_D strongly depend on surface temperature.They increased at low temperatures (15–25 K), until competitiveadsorption of H2 or D2 occurred at 10–12 K (Fig. 4). This suggeststhat reaction R1 occurred mainly via the LH pathway. A largebarrier exists for reaction R1, and we previously showed thatC6H6−C6H6 intermolecular interactions only act as inhibitorsthrough steric hindrance (8). Hence, reaction R1 mainly proceedson the surface, not in the bulk. The LH mechanism at low tem-peratures (10–50 K) also indicates that the atomic H and D ad-ditions require tunneling (11). Our previous study also found thatthe reactivity of C6H6 with H atoms is inhomogeneous across itsamorphous surface (8). Both reactive and nonreactive C6H6 mole-cules are distributed on the surface; C6H6 becomes less reactiveas its number of neighboring C6H6 molecules increases, and dan-gling C6H6 molecules that lack near neighbors are the mostreactive (8). In addition, the surface becomes covered with cy-clohexane products following the atomic addition reactions(Fig. 1). Therefore, the tunneling addition reaction requires atomsto encounter and stay with reactive C6H6 before thermal de-sorption; that is, atomic diffusion is essential.Neglecting the surface diffusion of C6H6, a rate equation for

the consumption of C6H6 by reaction with H atoms (rH) via theLH mechanism can be expressed as

rH =d½C6H6�

d  t=−κH   kdiff H   ½H�½C6H6�, [1]

where [C6H6], [H], and kdiff_H represent the surface number den-sity of reactive C6H6 molecules and H atoms and the diffusion rate

of H atoms, respectively. [H] should be determined by the balancebetween the atomic flux, the atom’s adsorption probability, and theloss of the atom by desorption and recombination following sur-face diffusion. Adsorption and desorption of H and D atoms inter-acting with the surface through van der Waals forces only havesemiclassical KIEs owing to the lower zero-point energy of a Datom than an H atom. Smoluchowski (22–24) theoretically showedthat the tunneling diffusion of physisorbed H atoms is stronglysuppressed on an amorphous surface because of the nonperiodicadsorption potential sites with different energy depths (25). Wepreviously observed a small KIE during the surface diffusion ofH and D atoms on amorphous solid water (25). Vidali, Pirronello,and coworkers also reported the thermally activated diffusion of Hand D atoms on silicates and amorphous carbon (26–28). Even ona crystalline metal surface, surface defects and steps strongly sup-press the tunneling diffusion of H atoms (29). Hence, the surfacediffusion of H and D atoms on the amorphous C6H6 solid can belimited by thermal hopping with a small KIE (kdiff_H J kdiff_D). Inaddition, there should be a small difference between [H] and [D].The factor κ (0 K κ K 1) represents the probability of an atomreacting with a C6H6 molecule by tunneling instead of undergoinga competing process, such as escaping from the reaction site bydiffusive hopping or desorption (30):

κ=�

ktunnelktunnel +   kdiff +   kdes

�, [2]

where ktunnel and kdes represent the intrinsic tunneling and de-sorption rates of an atom, respectively. The KIE on the C6H6consumption (rH=rD) is written as

KIE=rHrD

=−κH   kdiff H   ½H�½C6H6�−κD   kdiff D   ½D�½C6H6�

=�

ktunnel H

ktunnel H + kdiff H + kdes H

�

�ktunnel D + kdiff D + kdes D

ktunnel D

�  kdiff H   ½H�  kdiff D   ½D�.

[3]

Fig. 2. Variations in the column density of C6H6 consumption (ΔC6H6) at surface temperatures of 10–50 K. ○, H atom exposure; △, D atom exposure.

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This rate equation is certainly an oversimplification for surfacereactions on amorphous surfaces. Nevertheless, it provides aconvenient qualitative explanation of the present results.Adsorption probabilities (ap) of atoms and molecules are

generally high on molecular solid surfaces at low temperatures(2, 31). Molecular dynamics calculations showed that ap = 0.8and 0.4 for H atoms with an incident energy of 100 K on anamorphous solid water surface at 10 and 70 K, respectively (32).Efficient adsorption can be also expected on the amorphousC6H6 surface, considering the stronger van der Waals interactionof H with C6H6 (2.5 kJ·mol−1) than with H2O (0.6 kJ·mol−1) andthe greater physisorption energy of H on graphite (3.9 kJ·mol−1)as a solid benzene analog than on water ice (3.3 kJ·mol−1) (33–37).These values of ap are much greater than the obtained reactionprobabilities PH and PD of <7 × 10−3 at 15–50 K (Fig. 3A),suggesting that adsorption is not the dominant rate-limitingprocess. The kinetics appear to be predominantly controlled bythe subsequent surface diffusion and tunneling reactions. Tun-neling through the barrier is almost temperature-independent(Fig. 3C and Fig. S9) (1, 11). In contrast, thermal diffusion anddesorption are strongly correlated with surface temperature in

the range 10–50 K. The inverse of the Arrhenius equation predictsa change of many orders of magnitude in the adsorption time of anatom physisorbed on amorphous C6H6: The variation is probablyaround 1/kdes = (10–10−10) s at 10–50 K (Fig. 3C and Fig. S9). Wefirst consider the case of kdes and kdiff being much larger thanktunnel (ktunnel � kdiff and kdes). This means that the average ad-sorption time of an atom on a C6H6 site (τads ∝ 1/kdes and 1/kdiff) isshort compared with the average time required for tunnelingthrough the barrier of reaction R1 (τtunnel = 1/ktunnel, thus τads �τtunnel) (Fig. 5). This condition is valid when the surface temper-ature is sufficiently high. In this case, the values of κH and κD areboth small (�1/3), and the ratio ðκH=  κDÞ can be approximated as

κH  κD

=�

ktunnel H

ktunnel H +   kdiff H +   kdes H

��ktunnel D + kdiff D + kdes D

ktunnel D

�

≈�ktunnel H

ktunnel D

��kdiff D + kdes D

kdiff H + kdes H

�.

[4]

Eq. 4 can be rewritten as a product of the KIEs owing to tun-neling and other surface processes:

KIE≈�ktunnel H

ktunnel D

��kdiff D + kdes D

kdiff H + kdes H

�  kdiff H   ½H�  kdiff D   ½D�. [5]

A D atom requires a longer time for tunneling than an H atomdoes (τtunnel_H � τtunnel_D and thus ktunnel_H � ktunnel_D). Hence,Eqs. 4 and 5 indicate that κH � κD and that large KIEs appear inthe observed rates owing to ðktunnel H=ktunnel DÞ (Fig. 5). In fact,Fig. 3 shows large KIEs at 30–50 K (PH/PD = 2–5). However,these values were much smaller than the calculated tunneling

Fig. 3. Surface temperature dependence of hydrogenation and deutera-tion of amorphous C6H6 solid samples at 10–50 K. (A) Reaction probabilitiesper incident H atom (PH, ○) and D atom (PD, △) during initial 3-min expo-sure. (B) C6H6 consumption after 180-min exposure to H atoms (ΔC6H6_H, ●)or D atoms (ΔC6H6_D, ▲). The H/D ratios of the reaction probabilities (PH/PD)and of the C6H6 consumption (ΔC6H6_H/ΔC6H6_D) are also plotted (□ and ▀ ,respectively). (C) Estimated desorption rate (kdes) and tunneling rate (ktunnel)of H atoms as a function of surface temperature. kdes is calculated with theArrhenius equation, kdes = ν exp(Edes ∕ kB T), where ν, kB, T, and Edes representthe frequency factor, Boltzmann constant, surface temperature, and de-sorption energy, respectively. ktunnel for the C6H6 + H → C6H7 reaction wascalculated with the Eckart model. d is the barrier width parameter. SeeSupporting Information and Fig. S9 for details.

Fig. 4. Variations in the column density of C6H6 consumption (ΔC6H6) withrespect to exposure time to (A) H atoms and (B) D atoms. Open symbolsindicate results without additional (A) H2 or (B) D2 codeposition at the sur-face temperature of 10 K (○), 11 K (□), 12 K (△), and 15 K (▽). These plotsare identical to those in Fig. 2. Filled symbols indicate results with additional(A) H2 or (B) D2 codeposition at (1–2) × 10−3 Pa by background deposition atsurface temperatures of 10 K (●), 11 K (▀ ), 12 K (▲), and 15 K (▼).

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KIE for reaction R1 ðktunnel H=ktunnel D J 100Þ at 10–50 K in thegas phase (11). This suggests that the observed KIEs at 30–50 Kare not the high-temperature limit of the KIE expressed in Eq. 5,but are affected by less isotopically sensitive surface diffusion asdescribed below. The high-temperature limit of the KIE wouldnot be observable in the present study, because κ becomes toosmall when (ktunnel � kdiff and kdes) (Eq. 2), making PH and PDzero at high temperatures.At low temperatures of 15–25 K, the KIEs became even

smaller (PH/PD = 1.0–1.5) (Fig. 2). Next, we consider the reversecase, kdiff and kdes � ktunnel. This situation would require asufficiently low temperature, because kdes and kdiff drasticallydecrease with surface cooling. An H or D atom can interact withC6H6 for a longer period than τtunnel (τtunnel � τads), which in-creases the values of κH and κD. Finally, they are close to unity:

κH =�

ktunnel H

ktunnel H + kdiff H + kdes H

�≈ 1, [6]

κD =�

ktunnel D

ktunnel D + kdiff D + kdes D

�≈ 1. [7]

Therefore, Eq. 3 can be approximated by only the surface diffu-sion and the number density of atoms,

KIE≈kdiff H   ½H�kdiff D   ½D�. [8]

Eq. 8 suggests that the surface diffusion of atoms before theyencounter reactive C6H6 predominantly controls the kinetics intunneling reaction R1 at low temperatures, and the KIE can bemuch smaller than that in Eq. 5 owing to the disappearance ofthe tunneling KIE, ktunnel H=ktunnel D (Fig. 5). The very smallKIE observed at 15–25 K can be explained by Eq. 8. The present

findings can also explain the unexpected KIEs observed in otherchemical reactions on surfaces. For example, the experimentallydeduced KIE value for the addition of H/D atoms by tunnelingto solid CO at 15 K (12.5) is 20 times smaller than that theoret-ically calculated at low temperature in the gas phase (250) (2, 38,39). This discrepancy should be partly attributable to the isoto-pically insensitive surface processes of the H and D atoms. Fig. 4shows that reaction R1 at 10–12 K is controlled by the adsorptionof atoms that overcame the inhibiting effect of the adsorbedmolecules. The KIEs observed at 10–12 K (Figs. 2 and 4) shouldbe attributable to a semiclassical KIE caused by D2’s having alarger adsorption energy than H2 on the amorphous C6H6, whichresulted in [D] being smaller than [H]. The adsorption and ac-cumulation of molecules over long periods also support largevalues of τads for atoms at low temperatures.In summary, the addition of H and D to amorphous solid C6H6

formed cyclohexane or deuterated cyclohexane by reactions R1–R6. The reactions proceeded via tunneling at low temperatures of10–50 K. Reaction R1 showed KIEs that depended on the surfacetemperature; their values (1–1.5 at 15–25 K) were considerablysmaller than the intrinsic KIE associated with tunneling (J100 at10–50 K). Our results show that the overall KIE at a given tem-perature is influenced by the effects of the reactants’ adsorption,diffusion, and tunneling. We found that the intrinsic KIE asso-ciated with tunneling can be almost completely masked by surfaceprocesses that are insensitive to the isotope of the reactant atoms.The detection of hydrogen tunneling often relies on the obser-vation of large KIEs. However, some reactions on condensedphases can be studied only around room temperature or within alimited range of temperatures, and they are often controlled bythe diffusion processes of the reactants, as in aerosol chemistry(40, 41), and enzyme catalysis (42, 43). The present findings in-dicate that tunneling should be considered in the study of chemicalreactions involving hydrogen and deuterium on condensed phases,even when an anomalously large reaction efficiency is observedalongside a small KIE. More complete understanding of the con-tribution of tunneling to heterogeneous reaction dynamics canimprove the prediction of chemical kinetics (e.g., temperaturedependence) and H/D isotope fractionation in astrochemistry,geochemistry, and biochemistry.The practical implications of this work are associated with the

reactions of interstellar aromatic and aliphatic hydrocarbons,two of the main components of interstellar and circumstellardust (7). C6H6 is a precursor of interstellar polycyclic aromatichydrocarbons (PAHs) and hydrogenated amorphous carbongrains (aromatic/aliphatic mixture) (44–46). Its structure is rep-resentative of the peripheral sites of a PAH. In comparison withC6H6, PAHs tend to have lower activation barriers to H or Daddition owing to the higher flexibility (11, 47, 48). In fact,quantum calculations have shown that H and D addition bytunneling on the peripheral sites of pyrene (C16H10) occurs atfaster rates than on C6H6 (11, 47). We suggest that interstellararomatic hydrocarbons including C6H6 can be hydrogenated ordeuterated by the tunneling of H or D atoms at low tempera-tures. The deuteration of interstellar aromatic hydrocarbons toform deuterated aliphatic structures is of particular interest (12–15, 19), because such materials could represent a major carrier ofdeuterium enrichment (D/H = 10−4 to 10−2) beyond levelsexpected from the elemental D/H ratio in space (1.5 × 10−5)observed in carbonaceous meteorites and interplanetary dustparticles (17, 20). They may carry signatures of the survival ofinterstellar materials within the solar system, because the deu-terium enrichment is most noticeable in cold, dense interstellarregions (e.g., molecular clouds), where deuterated species arethermodynamically more stable than their hydrogenated coun-terparts owing to the zero-point energy difference of several tensof kelvin (18). Because the gaseous atomic D/H ratio in mo-lecular clouds can also be strongly enhanced from elementalratios of 1.5 × 10−5 to 10−2 to 10−1 (18, 49), our results suggest thatthe deuterium enrichment of interstellar aromatic and aliphatic

Fig. 5. Representation of H and D atom additions to amorphous solid C6H6.Processes influencing the KIEs of the addition are summarized in the lowerpanel. τads is the average adsorption time of an atom on a C6H6 (τads ∝ 1/kdesand 1/kdiff). τtunnel is the average time required for tunneling through thebarrier of reaction R1 (τtunnel = 1/ktunnel). ktunnel, kdiff, and kdes represent therates of the tunneling reaction, diffusion, and desorption of atoms, re-spectively. κ (0 K κ K 1) is the probability of an atom reacting by tunnelingrather than undergoing a competing process (e.g., escaping from the re-action site by diffusive hopping or desorption) when it encounters a C6H6

molecule: κ = ktunnel/(ktunnel + kdes + kdiff). The subscripts H and D representH and D atoms, respectively. For details of reactive C6H6 on the surface ofamorphous solid C6H6, see the text and ref. 8.

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hydrocarbons may occur at low temperatures via the tunneling ofD atoms. Tunneling might represent a major deuteration mech-anism for interstellar aromatic hydrocarbons, in addition to en-ergetic deuteration processes (e.g., photolysis with solid D2O andhot D-atom irradiation) (50–52), because surface tunneling is fa-vored in the cold, dense interstellar environment (2, 7). Thepresent study indicates that the tunneling KIE would not stronglyinhibit the deuteration of interstellar aromatic hydrocarbons, andthus it possibly links reactions in the interstellar medium and ourobservation of bodies in the solar system.

MethodsExperiments were conducted in an ultrahigh vacuum chamber (base pressureof 10−8 Pa) equipped with an atomic source, an aluminum (Al) substratemounted on the cold head of a closed-cycle helium (He) refrigerator, aquadrupole mass spectrometer, and an FTIR spectrometer (Supporting In-formation and Fig. S1). Samples of amorphous solid C6H6 were formed onthe Al substrate at 10 K by the background vapor deposition of C6H6. Thecompositions of the samples were measured by in situ reflection–absorptionspectroscopy with the FTIR spectrometer. H or D atoms were produced by amicrowave-induced plasma in a Pyrex tube within the atomic source and

transferred to the solid C6H6 samples through an Al pipe cooled to 120 K byanother He refrigerator to reduce the kinetic temperature of the H or Datoms. The pressure in the main chamber was increased to 3–4 × 10−4 Paduring the atom exposure. The fluxes of H and D atoms were estimated tobe (4–5) × 1014 and (3–4) × 1014 atoms·cm−2·s−1, respectively. For reference,the typical flux of H atoms in molecular clouds at 10 K is 104 cm−2·s−1. Hence,the 120-min exposure in our experiments is roughly comparable to an ex-posure of about 107 y (3 × 1018 atoms·cm−2), which is the typical lifetime ofmolecular clouds (2). After the atom exposure, the sample was heated to300 K at 2 K·min−1 for temperature-programmed desorption mass spectrom-etry. For each experiment, a fresh amorphous solid C6H6 sample was prepared.In the additional H2 or D2 codeposition experiments, H2 or D2 molecules atroom temperature were introduced into the chamber by background vapordeposition at (1–2) × 10−3 Pa during the atom exposure. The fluxes of both H2

and D2 molecules were estimated to be (1–2) × 1016 cm−2·s−1.

ACKNOWLEDGMENTS. We thank Drs. Hiroshi Hidaka and Yasuhiro Oba(Institute of Low Temperature Science, Hokkaido University). We also thankDr. Yoichi Nakai of RIKEN for useful suggestions regarding the kinetic isotopeeffect. This work was supported by Japan Society for the Promotion of Sci-ence Grants-in-Aid for Scientific Research 26410001 and 24224012 and Min-istry of Education, Culture, Sports, Science and Technology Grant-in-Aid forScientific Research 25108002.

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