Quantum tunneling observed without its characteristic large kinetic isotope effects

Significance

Quantum tunneling, an important phenomenon in many surface and interfacial chemical processes, is strongly dependent on the isotope of the tunneling atom. However, surface tunneling during the hydrogenation/deuteration of solid benzene at 15–25 K is accompanied by an almost semiclassical kinetic isotope effect (KIE) of 1–1.5, which is much lower than that intrinsic to tunneling (≳100), because isotopically insensitive surface diffusion of the adsorbed atoms controls the chemical kinetics. Our results suggest that tunneling has been unrecognized in studies of the chemistry of condensed phases, and small-KIE tunneling may account for the unexplained fast reactions of hydrogen and deuterium observed in surface/interface chemical systems such as aerosols, enzymes, and interstellar dust grains.

Abstract

Classical transition-state theory is fundamental to describing chemical kinetics; however, quantum tunneling is also important in explaining the unexpectedly large reaction efficiencies observed in many chemical systems. Tunneling is often indicated by anomalously large kinetic isotope effects (KIEs), because a particle’s ability to tunnel decreases significantly with its increasing mass. Here we experimentally demonstrate that cold hydrogen (H) and deuterium (D) atoms can add to solid benzene by tunneling; however, the observed H/D KIE was very small (1–1.5) despite the large intrinsic H/D KIE of tunneling (≳100). This strong reduction is due to the chemical kinetics being controlled not by tunneling but by the surface diffusion of the H/D atoms, a process not greatly affected by the isotope type. Because tunneling need not be accompanied by a large KIE in surface and interfacial chemical systems, it might be overlooked in other systems such as aerosols or enzymes. Our results suggest that surface tunneling reactions on interstellar dust may contribute to the deuteration of interstellar aromatic and aliphatic hydrocarbons, which could represent a major source of the deuterium enrichment observed in carbonaceous meteorites and interplanetary dust particles. These findings could improve our understanding of interstellar physicochemical processes, including those during the formation of the solar system.

Tunneling arises from the wave nature of matter, allowing particles to penetrate barriers that are impossible to overcome classically. Because the de Broglie wavelength is inversely proportional to particle momentum, tunneling becomes noticeable in small masses and at low temperatures. The de Broglie wavelengths 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 of activation barriers in chemical reactions (∼1 Å), which invalidates a purely classical description of their motion in chemistry (1, 2). Hydrogen, including its ionic forms (H⁺ and H⁻), is present in water and most organic compounds, and kinetic measurements have established that tunneling occurs in reactions involving hydrogen in gas (1), liquid (1, 3, 4), and solid phases (4). Tunneling has also been recognized as a significant factor in reactions on surfaces and at interfaces; for example, proton transfer reactions at the air/water interface (5) and enzyme catalysis (3, 6). Moreover, tunneling reactions (e.g., CO + H or D) on interstellar dust are crucial in explaining the abundances of organic molecules such as methanol and their deuterated isotopologues observed in cold and 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 drastically with its increasing mass. This means different isotopes of a given element show very different tunneling behaviors, and larger kinetic isotope effects (KIEs) than those expected from semiclassical theory have been regarded as a reliable indicator of tunneling (1). However, chemical reactions involving tunneling on condensed phases are usually accompanied by other surface processes such as adsorption, diffusion, and desorption. These are generally thermal processes, and thus much less sensitive to the reactant isotope than tunneling is (2). Therefore, the observed KIE can be much smaller than that intrinsically associated with tunneling in cases when the isotopically insensitive process determines the reaction rate. In other words, an observation of a small KIE under a given condition does not necessarily exclude tunneling, and tunneling may occur unrecognized in chemical reactions on condensed phases.

Using in situ IR reflection–absorption spectroscopy (Methods; See also Supporting Information and Figs. S1–S3), we previously showed 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 tunneling in the following hydrogenation/deuteration reactions of amorphous solid C₆H₆ over a wide temperature range (10–50 K):

$${\text{C}}_6{\text{H}}_6+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_7\left({\text{C}}_6{\text{H}}_6\text{D}\right)\hspace{1em}{E}_{\text{a}}=18\text{.}2\hspace{0.17em}\text{kJ}\cdot {\text{mol}}^{\mathrm{-}1},$$ [R1]

$${\text{C}}_6{\text{H}}_7+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_8\left({\text{C}}_6{\text{H}}_6{\text{D}}_2\right),$$ [R2]

$${\text{C}}_6{\text{H}}_8+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_9\left({\text{C}}_6{\text{H}}_6{\text{D}}_3\right)\hspace{1em}{E}_{\text{a}}=6\text{.}3\hspace{0.17em}\text{kJ}\cdot {\text{mol}}^{\mathrm{-}1},$$ [R3]

$${\text{C}}_6{\text{H}}_9+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_{10}\left({\text{C}}_6{\text{H}}_6{\text{D}}_4\right),$$ [R4]

$${\text{C}}_6{\text{H}}_{10}+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_{11}\left({\text{C}}_6{\text{H}}_6{\text{D}}_5\right)\hspace{1em}{E}_{\text{a}}=10\text{.}5\hspace{0.17em}\text{kJ}\cdot {\text{mol}}^{\mathrm{-}1},$$ [R5]

$${\text{C}}_6{\text{H}}_{11}+\text{H}\left(\text{D}\right)\to {\text{C}}_6{\text{H}}_{12}\left({\text{C}}_6{\text{H}}_6{\text{D}}_6\right),$$ [R6]

where E_a is the activation barrier for H-atom addition in the gas phase (9, 10). The radical recombination reactions R2, R4, and R6 are barrierless on the surface. We exposed amorphous C₆H₆ samples at 10–50 K to cold H or D atoms at 120 K. In situ IR spectroscopy revealed that cyclohexane or deuterated cyclohexane are efficiently formed by reactions R1–R6. Given the activation barriers and low temperatures, these reactions proceeded via tunneling (8, 11); however, we observed only small KIEs. The ratio of the hydrogenation and deuteration rates (H/D) was 1–1.5 at 15–25 K, whereas deuteration by tunneling typically occurs at a rate more than two orders of magnitude smaller than that of the comparable hydrogenation (11). This indicates that the isotopically insensitive surface processes of the atoms physisorbed on solid C₆H₆ masked the tunneling KIE, despite tunneling’s providing 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 temperature. We discuss the importance of our findings for astrochemistry and geochemistry in relation to the origin of deuterium enrichment observed in extraterrestrial materials such as interstellar aromatic/aliphatic hydrocarbons, carbonaceous meteorites, and interplanetary dust particles (12–17), the chemistry of which influences our understanding of interstellar physicochemical processes, including the formation of the solar system (18–20).

Results

Fig. 1A shows the IR spectra of amorphous C₆H₆ and C₆H₁₂ at 20 K. The column density (the amount of a substance per unit area integrated along a path perpendicular to the surface) was estimated to be 6 × 10¹⁵ cm⁻². For reference, the column density of monolayer coverage of crystalline C₆H₆ is (6–8) × 10¹⁴ cm⁻² (Supporting Information). Fig. 1 B and C show the difference spectra after H or D atom exposure for up to 180 min, respectively. In the difference spectrum B, the C₆H₆ absorption bands at 3,000–3,100, 1,480, and 1,036 cm⁻¹ decreased, and new peaks for the C₆H₁₂ products appeared at 2,800–3,000 and 1,453 cm⁻¹. This indicates the formation of C₆H₁₂ by reactions R1–R6 with the consumption of C₆H₆. After 180-min exposure, both the C₆H₆ consumption and the C₆H₁₂ formation saturated at column densities of ∼9 × 10¹⁴ cm⁻² at 20 K (Figs. S4 and S5), namely 15% of the C₆H₆ molecules reacted with the H atoms. This value is higher than the column density of monolayer coverage of crystalline C₆H₆, suggesting a large amount of reactive C₆H₆ on the surface. We speculate that amorphous C₆H₆ had 3D island structures and a larger surface area than crystalline C₆H₆ (8, 21). Consumption of C₆H₆ was also observed upon exposure to D atoms (Fig. 1C). Although the assignment of the products is difficult from the IR spectra, temperature-programmed desorption mass spectrometry showed that the main products were partially deuterated cyclohexane (C₆H₆D₆) with further-deuterated cyclohexane (C₆H₅D₇, C₆H₄D₈…C₆H₁D₁₁, C₆D₁₂) (Fig. S6). This shows that D atom addition to C₆H₆ occurred to form C₆H₆D₆ by tunneling. Subsequent H–D substitution reactions of C₆H₆D₆ yielded C₆H₅D₇…C₆D₁₂ also by tunneling (Figs. S7 and S8). Throughout the H atom exposure, C₆H₁₂ was the dominant product (Fig. 1 and Figs. S4 and S5). This indicates that reaction R1 is the rate-limiting step, because it has the highest barrier of reactions R1–R6. Here, we concentrate on the KIE of H and D atoms on C₆H₆ consumption.

Fig. 1.

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

Fig. 2 plots the variation in the column density of amorphous C₆H₆ (ΔC₆H₆) during exposure to H or D atoms at temperatures of 10–50 K. Absolute rate constants of the surface reactions could not be determined owing to the surface heterogeneity and to the difficulty of measuring the surface number density of atoms. Hence, we used the reaction probabilities of C₆H₆ per incident H or D atom (P_H or P_D) during the initial 3-min exposure to evaluate the KIE (Fig. 3A), where the subscripts H and D represent H and D atoms, respectively. P_H or P_D were calculated as the ratio of C₆H₆ consumption to the fluence of either H or D atoms. For reference, the fluences of H and D atoms after 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 (ΔC₆H_{6_H} or ΔC₆H_{6_D}) (Fig. 3B). At 30–50 K, P_H was two to five times larger than P_D. Values of ΔC₆H_{6_H} were also two to four times larger than those of ΔC₆H_{6_D} at 30–50 K. P_H and ΔC₆H_{6_H} were greatest at 20 K. Remarkably, both P_H/P_D and ΔC₆H_{6_H}/ΔC₆H_{6_D} lay between 1.0–1.5 at 15–25 K despite the intrinsic H/D KIE associated with tunneling (≳100) (11). These small differences between addition by H or D tunneling clearly show that isotopically insensitive surface processes strongly contributed to the outcome of these surface reactions. Note that heating the sample to 50 K slightly altered the surface structure but did not greatly affect P_H or P_D (Fig. S4).

Fig. 2.

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

Fig. 3.

Surface temperature dependence of hydrogenation and deuteration of amorphous C₆H₆ solid samples at 10–50 K. (A) Reaction probabilities per incident H atom (P_H, ○) and D atom (P_D, △) during initial 3-min exposure. (B) C₆H₆ consumption after 180-min exposure to H atoms (ΔC₆H_{6_H}, ●) or D atoms (ΔC₆H_{6_D}, ▲). The H/D ratios of the reaction probabilities (P_H/P_D) and of the C₆H₆ consumption (ΔC₆H_{6_H}/ΔC₆H_{6_D}) are also plotted (□ and ■, respectively). (C) Estimated desorption rate (k_des) and tunneling rate (k_tunnel) of H atoms as a function of surface temperature. k_des is calculated with the Arrhenius equation, k_des = ν exp(E_des ∕ k_B T), where ν, k_B, T, and E_des represent the frequency factor, Boltzmann constant, surface temperature, and desorption energy, respectively. k_tunnel for the C₆H₆ + H → C₆H₇ reaction was calculated with the Eckart model. d is the barrier width parameter. See Supporting Information and Fig. S9 for details.

At the lowest studied temperatures (10–12 K), P_H and ΔC₆H_{6_H} decreased, whereas both P_H/P_D and ΔC₆H_{6_H}/ΔC₆H_{6_D} increased (Figs. 2 and 3). At 10–12 K, H₂ or D₂ ejected as undissociated molecules from the atomic source can efficiently physisorb onto the amorphous C₆H₆ surface (2). Therefore, we tested the effect of adsorbed molecules on the hydrogenation/deuteration reactions via 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 without the additional H₂ or D₂ codeposition. However, C₆H₆ consumption decreased at 10 K when additional H₂ was deposited on the amorphous C₆H₆ surface. In the D/D₂ codeposition experiment, the decrease in C₆H₆ consumption was observed at 12 K. These results show that the atomic addition reactions are inhibited by competing long-term adsorption of molecules on the surface at 10–12 K, and reaction R1 at 10–12 K is controlled by the adsorption of atoms that overcame the inhibiting effect of the adsorbed molecules.

Fig. 4.

Variations in the column density of C₆H₆ consumption (ΔC₆H₆) with respect to exposure time to (A) H atoms and (B) D atoms. Open symbols indicate results without additional (A) H₂ or (B) D₂ codeposition at the surface temperature of 10 K (○), 11 K (□), 12 K (△), and 15 K (▽). These plots are 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 at surface temperatures of 10 K (●), 11 K (■), 12 K (▲), and 15 K (▼).

Discussion

Before discussing the KIE of the hydrogenation/deuteration of amorphous 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 a particle from the gas phase and an adsorbate on the surface, and the Langmuir–Hinshelwood (LH) mechanism, which is the reaction of two species after adsorption and diffusion (i.e., thermalization) on the surface (2). The ER mechanism should provide a yield that is largely independent of the surface temperature, whereas the yield of a LH reaction should reflect the adsorption time of atoms on the surface. Fig. 3B shows that the values of ΔC₆H_{6_H} and ΔC₆H_{6_D} strongly depend on surface temperature. They increased at low temperatures (15–25 K), until competitive adsorption of H₂ or D₂ occurred at 10–12 K (Fig. 4). This suggests that reaction R1 occurred mainly via the LH pathway. A large barrier exists for reaction R1, and we previously showed that C₆H₆−C₆H₆ intermolecular interactions only act as inhibitors through steric hindrance (8). Hence, reaction R1 mainly proceeds on the surface, not in the bulk. The LH mechanism at low temperatures (10–50 K) also indicates that the atomic H and D additions require tunneling (11). Our previous study also found that the reactivity of C₆H₆ with H atoms is inhomogeneous across its amorphous surface (8). Both reactive and nonreactive C₆H₆ molecules are distributed on the surface; C₆H₆ becomes less reactive as its number of neighboring C₆H₆ molecules increases, and dangling C₆H₆ molecules that lack near neighbors are the most reactive (8). In addition, the surface becomes covered with cyclohexane products following the atomic addition reactions (Fig. 1). Therefore, the tunneling addition reaction requires atoms to encounter and stay with reactive C₆H₆ before thermal desorption; 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 (r_H) via the LH mechanism can be expressed as

$$r_{\text{H}}=\frac{d\left[{\text{C}}_6{\text{H}}_6\right]}{d\hspace{0.17em}t}=-{\kappa }_{\text{H}}\hspace{0.17em}{k}_{\text{diff}\_\text{H}}\hspace{0.17em}\left[\text{H}\right]\left[{\text{C}}_6{\text{H}}_6\right],$$ [1]

where [C₆H₆], [H], and k_{diff_H} represent the surface number density of reactive C₆H₆ molecules and H atoms and the diffusion rate of H atoms, respectively. [H] should be determined by the balance between the atomic flux, the atom’s adsorption probability, and the loss of the atom by desorption and recombination following surface diffusion. Adsorption and desorption of H and D atoms interacting with the surface through van der Waals forces only have semiclassical KIEs owing to the lower zero-point energy of a D atom than an H atom. Smoluchowski (22–24) theoretically showed that the tunneling diffusion of physisorbed H atoms is strongly suppressed on an amorphous surface because of the nonperiodic adsorption potential sites with different energy depths (25). We previously observed a small KIE during the surface diffusion of H and D atoms on amorphous solid water (25). Vidali, Pirronello, and coworkers also reported the thermally activated diffusion of H and D atoms on silicates and amorphous carbon (26–28). Even on a crystalline metal surface, surface defects and steps strongly suppress the tunneling diffusion of H atoms (29). Hence, the surface diffusion of H and D atoms on the amorphous C₆H₆ solid can be limited by thermal hopping with a small KIE (k_{diff_H} ≳ k_{diff_D}). In addition, there should be a small difference between [H] and [D]. The factor κ (0 ≲ κ ≲ 1) represents the probability of an atom reacting with a C₆H₆ molecule by tunneling instead of undergoing a competing process, such as escaping from the reaction site by diffusive hopping or desorption (30):

$$\kappa =\left(\frac{k_{\text{tunnel}}}{k_{\text{tunnel}}+\hspace{0.17em}{k}_{\text{diff}}+\hspace{0.17em}{k}_{\text{des}}}\right),$$ [2]

where k_tunnel and k_des represent the intrinsic tunneling and desorption rates of an atom, respectively. The KIE on the C₆H₆ consumption ($r_{\text{H}}/r_{\text{D}}$) is written as

$$\begin{array}{c}\text{KIE}=\frac{r_{\text{H}}}{r_{\text{D}}}=\frac{-{\kappa }_{\text{H}}\hspace{0.17em}{k}_{\text{diff}\_\text{H}}\hspace{0.17em}\left[\text{H}\right]\left[{\text{C}}_6{\text{H}}_6\right]}{-{\kappa }_{\text{D}}\hspace{0.17em}{k}_{\text{diff}\_\text{D}}\hspace{0.17em}\left[\text{D}\right]\left[{\text{C}}_6{\text{H}}_6\right]}\\ =\left(\frac{k_{\text{tunnel}\_\text{H}}}{k_{\text{tunnel}\_\text{H}}+k_{\text{diff}\_\text{H}}+k_{\text{des}\_\text{H}}}\right)\\ \times \left(\frac{k_{\text{tunnel}\_\text{D}}+k_{\text{diff}\_\text{D}}+k_{\text{des}\_\text{D}}}{k_{\text{tunnel}\_\text{D}}}\right)\frac{\hspace{0.17em}{k}_{\text{diff}\_\text{H}}\hspace{0.17em}\left[\text{H}\right]}{\hspace{0.17em}{k}_{\text{diff}\_\text{D}}\hspace{0.17em}\left[\text{D}\right]}.\end{array}$$ [3]

This rate equation is certainly an oversimplification for surface reactions on amorphous surfaces. Nevertheless, it provides a convenient qualitative explanation of the present results.

Adsorption probabilities (a_p) of atoms and molecules are generally high on molecular solid surfaces at low temperatures (2, 31). Molecular dynamics calculations showed that a_p = 0.8 and 0.4 for H atoms with an incident energy of 100 K on an amorphous solid water surface at 10 and 70 K, respectively (32). Efficient adsorption can be also expected on the amorphous C₆H₆ surface, considering the stronger van der Waals interaction of H with C₆H₆ (2.5 kJ⋅mol⁻¹) than with H₂O (0.6 kJ⋅mol⁻¹) and the 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 a_p are much greater than the obtained reaction probabilities P_H and P_D of <7 × 10⁻³ at 15–50 K (Fig. 3A), suggesting that adsorption is not the dominant rate-limiting process. The kinetics appear to be predominantly controlled by the subsequent surface diffusion and tunneling reactions. Tunneling through the barrier is almost temperature-independent (Fig. 3C and Fig. S9) (1, 11). In contrast, thermal diffusion and desorption are strongly correlated with surface temperature in the range 10–50 K. The inverse of the Arrhenius equation predicts a change of many orders of magnitude in the adsorption time of an atom physisorbed on amorphous C₆H₆: The variation is probably around 1/k_des = (10–10⁻¹⁰) s at 10–50 K (Fig. 3C and Fig. S9). We first consider the case of k_des and k_diff being much larger than k_tunnel (k_tunnel ≪ k_diff and k_des). This means that the average adsorption time of an atom on a C₆H₆ site (τ_ads ∝ 1/k_des and 1/k_diff) is short compared with the average time required for tunneling through the barrier of reaction R1 (τ_tunnel = 1/k_tunnel, thus τ_ads ≪ τ_tunnel) (Fig. 5). This condition is valid when the surface temperature is sufficiently high. In this case, the values of κ_H and κ_D are both small (≪1/3), and the ratio $\left({\kappa }_{\text{H}}/\hspace{0.17em}{\kappa }_{\text{D}}\right)$ can be approximated as

$$\begin{array}{l}\frac{{\kappa }_{\text{H}}}{\hspace{0.17em}{\kappa }_{\text{D}}}=\left(\frac{k_{\text{tunnel}\_\text{H}}}{k_{\text{tunnel}\_\text{H}}+\hspace{0.17em}{k}_{\text{diff}\_\text{H}}+\hspace{0.17em}{k}_{\text{des}\_\text{H}}}\right)\left(\frac{k_{\text{tunnel}\_\text{D}}+k_{\text{diff}\_\text{D}}+k_{\text{des}\_\text{D}}}{k_{\text{tunnel}\_\text{D}}}\right)\\ \approx \left(\frac{k_{\text{tunnel}\_\text{H}}}{k_{\text{tunnel}\_\text{D}}}\right)\left(\frac{k_{\text{diff}\_\text{D}}+k_{\text{des}\_\text{D}}}{k_{\text{diff}\_\text{H}}+k_{\text{des}\_\text{H}}}\right).\end{array}$$ [4]

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

$$\text{KIE}\approx \left(\frac{k_{\text{tunnel}\_\text{H}}}{k_{\text{tunnel}\_\text{D}}}\right)\left(\frac{k_{\text{diff}\_\text{D}}+k_{\text{des}\_\text{D}}}{k_{\text{diff}\_\text{H}}+k_{\text{des}\_\text{H}}}\right)\frac{\hspace{0.17em}{k}_{\text{diff}\_\text{H}}\hspace{0.17em}\left[\text{H}\right]}{\hspace{0.17em}{k}_{\text{diff}\_\text{D}}\hspace{0.17em}\left[\text{D}\right]}.$$ [5]

A D atom requires a longer time for tunneling than an H atom does (τ_{tunnel_H} ≪ τ_{tunnel_D} and thus k_{tunnel_H} ≫ k_{tunnel_D}). Hence, Eqs. 4 and 5 indicate that κ_H ≫ κ_D and that large KIEs appear in the observed rates owing to $\left(k_{\text{tunnel}\_\text{H}}/k_{\text{tunnel}\_\text{D}}\right)$ (Fig. 5). In fact, Fig. 3 shows large KIEs at 30–50 K (P_H/P_D = 2–5). However, these values were much smaller than the calculated tunneling KIE for reaction R1 $\left(k_{\text{tunnel}\_\text{H}}/k_{\text{tunnel}\_\text{D}}\gtrsim 100\right)$ at 10–50 K in the gas phase (11). This suggests that the observed KIEs at 30–50 K are not the high-temperature limit of the KIE expressed in Eq. 5, but are affected by less isotopically sensitive surface diffusion as described below. The high-temperature limit of the KIE would not be observable in the present study, because κ becomes too small when (k_tunnel ≪ k_diff and k_des) (Eq. 2), making P_H and P_D zero at high temperatures.

Fig. 5.

Representation of H and D atom additions to amorphous solid C₆H₆. Processes influencing the KIEs of the addition are summarized in the lower panel. τ_ads is the average adsorption time of an atom on a C₆H₆ (τ_ads ∝ 1/k_des and 1/k_diff). τ_tunnel is the average time required for tunneling through the barrier of reaction R1 (τ_tunnel = 1/k_tunnel). k_tunnel, k_diff, and k_des represent the rates of the tunneling reaction, diffusion, and desorption of atoms, respectively. κ (0 ≲ κ ≲ 1) is the probability of an atom reacting by tunneling rather than undergoing a competing process (e.g., escaping from the reaction site by diffusive hopping or desorption) when it encounters a C₆H₆ molecule: κ = k_tunnel/(k_tunnel + k_des + k_diff). The subscripts H and D represent H and D atoms, respectively. For details of reactive C₆H₆ on the surface of amorphous solid C₆H₆, see the text and ref. 8.

At low temperatures of 15–25 K, the KIEs became even smaller (P_H/P_D = 1.0–1.5) (Fig. 2). Next, we consider the reverse case, k_diff and k_des ≪ k_tunnel. This situation would require a sufficiently low temperature, because k_des and k_diff drastically decrease with surface cooling. An H or D atom can interact with C₆H₆ for a longer period than τ_tunnel (τ_tunnel ≪ τ_ads), which increases the values of κ_H and κ_D. Finally, they are close to unity:

$${\kappa }_{\text{H}}=\left(\frac{k_{\text{tunnel}\_\text{H}}}{k_{\text{tunnel}\_\text{H}}+k_{\text{diff}\_\text{H}}+k_{\text{des}\_\text{H}}}\right)\approx 1,$$ [6]

$${\kappa }_{\text{D}}=\left(\frac{k_{\text{tunnel}\_\text{D}}}{k_{\text{tunnel}\_\text{D}}+k_{\text{diff}\_\text{D}}+k_{\text{des}\_\text{D}}}\right)\approx 1.$$ [7]

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

$$\text{KIE}\approx \frac{k_{\text{diff}\_\text{H}}\hspace{0.17em}\left[\text{H}\right]}{k_{\text{diff}\_\text{D}}\hspace{0.17em}\left[\text{D}\right]}.$$ [8]

Eq. 8 suggests that the surface diffusion of atoms before they encounter reactive C₆H₆ predominantly controls the kinetics in tunneling reaction R1 at low temperatures, and the KIE can be much smaller than that in Eq. 5 owing to the disappearance of the tunneling KIE, $k_{\text{tunnel}\_\text{H}}/k_{\text{tunnel}\_\text{D}}$ (Fig. 5). The very small KIE observed at 15–25 K can be explained by Eq. 8. The present findings can also explain the unexpected KIEs observed in other chemical reactions on surfaces. For example, the experimentally deduced KIE value for the addition of H/D atoms by tunneling to solid CO at 15 K (12.5) is 20 times smaller than that theoretically calculated at low temperature in the gas phase (250) (2, 38, 39). This discrepancy should be partly attributable to the isotopically insensitive surface processes of the H and D atoms. Fig. 4 shows that reaction R1 at 10–12 K is controlled by the adsorption of atoms that overcame the inhibiting effect of the adsorbed molecules. The KIEs observed at 10–12 K (Figs. 2 and 4) should be attributable to a semiclassical KIE caused by D₂’s having a larger adsorption energy than H₂ on the amorphous C₆H₆, which resulted in [D] being smaller than [H]. The adsorption and accumulation of molecules over long periods also support large values of τ_ads 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 of 10–50 K. Reaction R1 showed KIEs that depended on the surface temperature; their values (1–1.5 at 15–25 K) were considerably smaller than the intrinsic KIE associated with tunneling (≳100 at 10–50 K). Our results show that the overall KIE at a given temperature is influenced by the effects of the reactants’ adsorption, diffusion, and tunneling. We found that the intrinsic KIE associated with tunneling can be almost completely masked by surface processes that are insensitive to the isotope of the reactant atoms. The detection of hydrogen tunneling often relies on the observation of large KIEs. However, some reactions on condensed phases can be studied only around room temperature or within a limited range of temperatures, and they are often controlled by the diffusion processes of the reactants, as in aerosol chemistry (40, 41), and enzyme catalysis (42, 43). The present findings indicate that tunneling should be considered in the study of chemical reactions involving hydrogen and deuterium on condensed phases, even when an anomalously large reaction efficiency is observed alongside a small KIE. More complete understanding of the contribution of tunneling to heterogeneous reaction dynamics can improve the prediction of chemical kinetics (e.g., temperature dependence) 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 circumstellar dust (7). C₆H₆ is a precursor of interstellar polycyclic aromatic hydrocarbons (PAHs) and hydrogenated amorphous carbon grains (aromatic/aliphatic mixture) (44–46). Its structure is representative of the peripheral sites of a PAH. In comparison with C₆H₆, PAHs tend to have lower activation barriers to H or D addition owing to the higher flexibility (11, 47, 48). In fact, quantum calculations have shown that H and D addition by tunneling on the peripheral sites of pyrene (C₁₆H₁₀) occurs at faster rates than on C₆H₆ (11, 47). We suggest that interstellar aromatic hydrocarbons including C₆H₆ can be hydrogenated or deuterated by the tunneling of H or D atoms at low temperatures. The deuteration of interstellar aromatic hydrocarbons to form deuterated aliphatic structures is of particular interest (12–15, 19), because such materials could represent a major carrier of deuterium enrichment (D/H = 10⁻⁴ to 10⁻²) beyond levels expected from the elemental D/H ratio in space (1.5 × 10⁻⁵) observed in carbonaceous meteorites and interplanetary dust particles (17, 20). They may carry signatures of the survival of interstellar materials within the solar system, because the deuterium enrichment is most noticeable in cold, dense interstellar regions (e.g., molecular clouds), where deuterated species are thermodynamically more stable than their hydrogenated counterparts owing to the zero-point energy difference of several tens of kelvin (18). Because the gaseous atomic D/H ratio in molecular clouds can also be strongly enhanced from elemental ratios of 1.5 × 10⁻⁵ to 10⁻² tο 10⁻¹ (18, 49), our results suggest that the deuterium enrichment of interstellar aromatic and aliphatic hydrocarbons may occur at low temperatures via the tunneling of D atoms. Tunneling might represent a major deuteration mechanism for interstellar aromatic hydrocarbons, in addition to energetic deuteration processes (e.g., photolysis with solid D₂O and hot D-atom irradiation) (50–52), because surface tunneling is favored in the cold, dense interstellar environment (2, 7). The present study indicates that the tunneling KIE would not strongly inhibit the deuteration of interstellar aromatic hydrocarbons, and thus it possibly links reactions in the interstellar medium and our observation of bodies in the solar system.

Methods

Experiments were conducted in an ultrahigh vacuum chamber (base pressure of 10⁻⁸ Pa) equipped with an atomic source, an aluminum (Al) substrate mounted on the cold head of a closed-cycle helium (He) refrigerator, a quadrupole mass spectrometer, and an FTIR spectrometer (Supporting Information and Fig. S1). Samples of amorphous solid C₆H₆ were formed on the Al substrate at 10 K by the background vapor deposition of C₆H₆. The compositions of the samples were measured by in situ reflection–absorption spectroscopy with the FTIR spectrometer. H or D atoms were produced by a microwave-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 by another He refrigerator to reduce the kinetic temperature of the H or D atoms. The pressure in the main chamber was increased to 3–4 × 10⁻⁴ Pa during the atom exposure. The fluxes of H and D atoms were estimated to be (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 exposure of about 10⁷ y (3 × 10¹⁸ atoms⋅cm⁻²), which is the typical lifetime of molecular clouds (2). After the atom exposure, the sample was heated to 300 K at 2 K⋅min⁻¹ for temperature-programmed desorption mass spectrometry. For each experiment, a fresh amorphous solid C₆H₆ sample was prepared. In the additional H₂ or D₂ codeposition experiments, H₂ or D₂ molecules at room temperature were introduced into the chamber by background vapor deposition 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.