ON THE POSSIBLE PRESENCE OF WEAKLY BOUND FULLERENE–H₂ COMPLEXES IN THE INTERSTELLAR MEDIUM

Ninety years ago Heger discovered two absorption features superimposed on the interstellar extinction curve (Heger 1922). The number of such diffuse interstellar bands (DIBs) now exceeds 400 but they have not yet found a satisfactory, coherent explanation (Sarre 2006). It is generally believed that DIBs are due to electronic transitions in isolated neutral or charged molecular species. Initially, when just a few DIBs had been identified, it was argued that all DIBs arise from a single species or from closely related species (Douglas 1977). However, the current catalog of DIBs contains 414 entries between 3900 and 8100 Å (Hobbs et al. 2009), and few DIBs exhibit clear correlations (McCall et al. 2010; Sarre 2006), suggesting that there is a large variety of different carriers. Still, few bands have so far been assigned to specific molecules with some confidence.

Primary contenders for the carriers of DIBs are large, highly unsaturated hydrocarbons and bare carbon-containing molecules (Bettens & Herbst 1997; Fulara & Krelowski 2000; Fulara et al. 1993). They are favored by the large cosmic abundance of carbon and the strong chemical bonds that would render them resistant to ultraviolet radiation. All 57 molecules containing six or more atoms that have been identified in the interstellar medium or circumstellar shells contain carbon.³ The largest linear carbon molecule detected so far that may explain some DIBs is HC₄H⁺ (Krelowski et al. 2010) but this assignment has been questioned (Maier et al. 2011). Polycyclic aromatic hydrocarbons (PAHs) occur primarily in hydrogen-rich environments and are probably abundant in the interstellar medium but no PAHs have yet been matched with specific DIBs (Snow et al. 1998) although a mix of PAHs or defective carbon onions may possibly explain the prominent UV bump at 2175 Å (Iglesias-Groth 2004; Steglich et al. 2010; Tomita et al. 2004).

Fullerenes and their derivatives represent another class of carbon molecules that may contribute to the DIBs. Fullerenes form in hydrogen-depleted environments (Wang et al. 1995); in the presence of hydrogen they form at high (⩾3500 K) temperatures (Jäger et al. 2009). However, their occurrence may be much more wide spread (Kroto & Jura 1992). The first evidence for extraterrestrial fullerenes was found in the carbonaceous impact residue in a crater on a spacecraft (di Brozolo et al. 1994) although subsequent experimental evidence remained ambivalent (Petrie & Bohme 2000). Conclusive evidence for the existence of fullerenes has recently been identified in IR spectra recorded by the Spitzer Space Telescope in planetary nebulae where they represent ≈1% of the total carbon (Cami et al. 2010; Garcia-Hernandez et al. 2010), a protoplanetary nebula (Zhang & Kwok 2011), the interstellar medium (Sellgren et al. 2010), and around R Coronae Borealis (RCB) stars (Garcia-Hernandez et al. 2011; Jeffery 1995).

However, absorption spectra of bare, neutral C₆₀ and C₇₀ measured in the laboratory do not seem to explain any DIBs although the lack of low-temperature absorption spectra of gas-phase C₆₀ and C₇₀ does not allow for a definite conclusion (Herbig 2000; Sassara et al. 2001). Charged fullerenes were previously assigned to DIBs in the near-infrared (Foing & Ehrenfreund 1997).

A special group of fullerene derivatives that may be responsible for some DIBs are fulleranes, i.e., fullerenes with chemisorbed hydrogen bound at exohedral sites (Cataldo & Iglesias-Groth 2010; Webster 1997). They form upon exposure of C₆₀ to atomic hydrogen (Brühwiler et al. 1993), molecular hydrogen at elevated temperatures and pressures (Talyzin 2010), and by wet chemistry (Briggs & Miller 2010). However, they will not form in low-temperature collisions between fullerenes and molecular hydrogen because chemisorption is impeded by a high activation barrier (Chen et al. 2005).

Surprisingly, the possibility that fullerenes in the interstellar medium might be complexed with physisorbed hydrogen molecules has, to the best of our knowledge, not been discussed in the literature. These van der Waals bound systems would admittedly be prone to thermal desorption and photodissociation but the high cosmic abundance of hydrogen which constitutes 92% of all atoms in the universe (Oka 2006) will partly make up for this loss, at least in the colder regions of space.

During the course of mass spectrometric studies of fullerenes embedded in superfluid helium nanodroplets co-doped with molecular hydrogen we have observed copious amounts of [H_xC_m]⁺ where m = 60 or 70, and x (either even or odd) ranges from 1 to >120. Complexes with even-numbered x consist of x/2 H₂ molecules physisorbed to C⁺_m with a binding energy of about 50 meV; the H₂ binding energy in the neutral complex is probably similar. Stimulated by these results we assess the possible existence of weakly bound fullerene–H₂ complexes in interstellar clouds.

Neutral helium nanodroplets are produced by expanding helium from a stagnation pressure of 2 MPa through a 5 μm nozzle, cooled to about 8 K, into vacuum. The average number of atoms per droplet that form in the expansion is of the order 10⁶; the droplets are superfluid with a temperature of ≈0.37 K (Toennies & Vilesov 2004). The resulting supersonic beam is skimmed by a 0.8 mm conical skimmer, located 8 mm downstream from the nozzle. The skimmed beam traverses a 20 cm long pick-up region into which hydrogen or deuterium gas (Messer, purities 99.999% and 99.8%, respectively) are introduced at ≈1.5 × 10⁻⁷ Pa; a small amount of C₆₀ (purchased from MER Corporation, purity 99.9%) or C₇₀ (purchased from SES Research, 99%) is vaporized into the cell from a crucible. Neutral aggregates form in the superfluid helium droplets by successive, random pickup of H₂ and C₆₀ (Toennies & Vilesov 2004). Conditions are tuned to produce droplets that contain many hydrogen molecules but only one C₆₀.

After the pick-up region the doped helium droplets pass a region in which they are ionized by electron impact at energies of 30–70 eV; no significant effect of the electron energy on the mass spectra is observed. The ions are accelerated to 40 eV into the extraction region of a commercial time-of-flight mass spectrometer equipped with a reflectron (Tofwerk AG, model HTOF). Additional experimental details are described elsewhere (Schöbel et al. 2011).

Figure 1 displays sections of a representative mass spectrum of helium droplets doped with C₆₀ and D₂. The peak at 720 u corresponds to isotopically pure ¹²C₆₀. The expected abundance of heavier C₆₀ isotopologues, computed from the natural abundance of ¹³C (1.07%), is indicated by solid dots. The peak at 721 u corresponds to pure ¹³C ¹²C⁺₅₉, the one at 722 u consists of ¹³C₂ ¹²C⁺₅₈ plus a contribution from D ¹²C⁺₆₀; the peak at 724 u has contributions from ¹³C₄¹²C⁺₅₆, D ¹³C₂¹²C⁺₅₈, and D₂ ¹²C⁺₆₀.

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Above 724 u, the mass spectrum shows the presence of two ion series D_x C⁺₆₀ with x even or odd. Each ion gives rise to a multiplet of isotopologues with the isotopically pure D_x¹²C⁺₆₀ being most abundant; they are marked in Figure 1 by squares and triangles for x = even or odd, respectively. Each secondary (weaker) peak in a series corresponds to the case where one ¹²C is substituted by ¹³C. D_x C⁺₆₀ ions containing two ¹³C coincide in mass with D_{x + 1} ¹²C⁺₆₀. In other words, each mass peak that is marked by a square or triangle is mostly due to D_x ¹²C⁺₆₀ but does contain a non-negligible contribution from D_{x − 1} ¹³C₂ ¹²C⁺₅₈ plus a minor (typically <1%) contribution from D_x−2¹³C₄¹²C⁺₅₆. As described elsewhere (Denifl et al. 2009), the exact contributions can be quantified for each mass peak by a fitting routine because the relative abundance of C₆₀ isotopologues is known. Thus, the abundance of D_x C⁺₆₀ and, similarly, H_x C⁺₆₀ can be accurately extracted from our mass spectra.

What is the geometric structure of the observed D_x C⁺₆₀ ions? Mass spectra do not reveal the structure of ions but the way by which the ions are formed suggests that most if not all of the deuterium is in form of D₂, weakly bound (physisorbed) to C₆₀⁺. In our experiment, helium droplets containing ≈10⁶ atoms are doped via collisions with C₆₀ and D₂. The dopants will coalesce in the interior of the superfluid droplet and form a weakly bound (D₂)_yC₆₀ complex, with y being broadly distributed; chemisorption of D₂ is impeded by a high (>1 eV) activation barrier. Upon electron impact, He⁺ will form via direct ionization near the surface of the droplet (Echt et al. 2010; Toennies & Vilesov 2004). He⁺ migrates by charge hopping to the dopant followed by charge transfer which releases large amounts of energy (the ionization energies of He, D₂, and C₆₀ are 24.59, 15.47, and 7.60 eV, respectively.⁴ As a result, most or all of the weakly bound He atoms will quickly evaporate, some of the D₂ molecules are likely to evaporate as well, and the positive charge will eventually be localized on the fullerene.

If charge transfer proceeds directly from He⁺ to C⁺₆₀ then D₂ will act as spectator and remain in molecular form, physisorbed to C⁺₆₀. This interpretation is supported by experiment and theory, although indirectly (no work directly pertaining to D₂ (or H₂) + C⁺₆₀ has been published): solid C₆₀ does not react with molecular hydrogen unless pressure and temperature are high (Talyzin 2010). Calculations of H₂ adsorbed on carbon nanotubes show that an activation barrier of 2.7 eV has to be overcome to convert physisorbed molecular hydrogen to chemisorbed hydrogen (Chen et al. 2005). The calculated height of the barrier depends on the exact type of nanotube but it is always in the eV range. Therefore, we adopt the notation (D₂)_n C⁺₆₀ for ions that contain an even number (x = 2n) of D. The data in the inset of Figure 1 support this notation. The x-even series drops abruptly beyond x = 64 (mass 848 u), i.e., beyond (D₂)₃₂ C⁺₆₀. Why 32? Carbon atoms in C⁺₆₀ form 12 pentagons plus 20 hexagons. Thus, the observed anomaly suggests that a solvation shell closes when each face of C⁺₆₀ is occupied by one D₂. Calculations of H₂ physisorbed to graphene or carbon nanotubes show, indeed, that local energy minima exist over the centers of hexagons (Ferre-Vilaplana 2005; Rubes & Bludsky 2009); the binding over pentagon centers is probably almost as strong. D₂ that is added to (D₂)₃₂ C⁺₆₀ will be less strongly bound because the excess D₂ will either form a second shell, further away from C⁺₆₀, or squeeze between D₂ molecules in the first shell. The abrupt drop of the binding energy beyond n = 32 will cause a corresponding drop in the ion abundance.

Several mass spectra of helium droplets doped with C₆₀ and D₂ or H₂ have been recorded; all spectra show an abrupt drop in the abundance when >32 molecules are attached to C⁺₆₀. The spectra have been quantitatively analyzed by separating the contributions from different isotopologues (Denifl et al. 2009); results from such an analysis of experiments involving H₂ + C₆₀ are displayed in Figure 2(a). The abundance of the x-even series drops at n = 32 by more than a factor of two. Experiments were also performed with H₂ + C₇₀ which has 12 pentagonal and 25 hexagonal faces; results are shown in Figure 2(b). The abundance of the x-even series does, indeed, drop at (H₂)₃₇ C⁺₇₀ lending further support to our claim that hydrogen molecules are physisorbed to the fullerene ion.

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We now consider the x-odd ion series which is more abundant than the x-even one. The abundance of the x-odd series drops at n = 32 if the notation (H₂)_n H C⁺₆₀ is adopted; in experiments involving C₇₀ (37 faces) it drops at (H₂)₃₇ H C⁺₇₀, see Figure 2(b). The observation suggests that all but one hydrogen atom are weakly bound as H₂ to the fullerene ion.

A consideration of the ionization mechanism (Echt et al. 2010; Toennies & Vilesov 2004) supports this interpretation: if the He⁺ ion that is produced upon electron impact undergoes charge transfer to the hydrogen cluster rather than directly to C₆₀, H⁺₂ + H₂ will quickly react to form H⁺₃ + H because of the large (4.377 eV) proton affinity of H₂.⁴ However, the proton affinity of C₆₀ (8.577 eV) is even larger; proton transfer from H⁺₃ to C₆₀ will result in H₂ + H C⁺₆₀. On the other hand, the H atom produced in the initial proton transfer reaction from H⁺₂ to H₂ is likely to be expelled within a fraction of a picosecond, as demonstrated in an ab initio direct dynamics study of vertically ionized hydrogen clusters (Tachikawa 2000). The overall result would then be an ion composed of n physisorbed molecules plus one chemisorbed atom as implied by the notation (H₂)_n H C⁺₆₀. Note that n will be much smaller than the initial number of H₂ molecules in the neutral droplet because large amounts of energy are released upon charge and proton transfer; this also applies to the x-even series.

A theoretical study of the hydrogen + C⁺₆₀ system with density functional theory (DFT) with the PBE functional (Adamo & Barone 1999) and the 6–31(d,p) basis set provides further insight. Atomic hydrogen is bound by 3.1 eV relative to H + C⁺₆₀ above a carbon atom at a distance of 1.106 Å. The most stable structure of H₂ chemisorbed to C⁺₆₀ is when the H atoms are approximately above adjacent carbon atoms that separate two hexagons. The energy of the ion is approximately 1.45 eV below that of H₂ + C⁺₆₀; the chemisorbed system is bound although it is separated by a large energy barrier from the configuration where H₂ is merely physisorbed.

What is the possible relevance of the observed hydrogen–fullerene ions to DIBs? Could these ions, with H₂ weakly bound to C⁺₆₀ or perhaps C₆₀, exist in interstellar clouds? A significant fraction of C⁺₆₀ (or C₆₀) will be complexed with H₂ if the rate of formation exceeds the rate of destruction. For physisorption, capture of H₂ will proceed without barrier, hence the formation rate equals the rate at which C⁺₆₀ collides with H₂ (a caveat that applies at low temperatures will be discussed below). The main destruction channels will be photodissociation and thermally activated H₂ desorption. The former strongly depends on the photon flux, i.e., the type of cloud; the latter depends on the bond strength between H₂ and C⁺₆₀ and the ambient temperature.

For a first estimate we will ignore photodestruction and merely equate the rate of H₂ collision with the rate of thermally activated H₂ desorption. This will allow us to determine T_max, the upper temperature limit at which fullerene–H₂ complexes may occur for a given H₂ concentration. Snow and McCall have proposed a classification scheme for interstellar clouds, namely, diffuse atomic, diffuse molecular, translucent, and dense (Snow & McCall 2006). The temperatures of these clouds and the concentration n_H of hydrogen (in either atomic or molecular form) are listed in Table 1. The upper limit of n_H together with the upper limit of the fraction of hydrogen that is in molecular form is used to derive an upper limit of the concentration of molecular hydrogen, n_H2, see Table 1. From n_H2 and the Langevin collision rate coefficient for C⁺₆₀ with H₂, 1.5 × 10⁻⁹ cm³ s⁻¹ (Petrie et al. 1995), one obtains a collision rate of k_col > 8 × 10⁻⁶ s⁻¹ for dense clouds and <4 × 10⁻⁶ s⁻¹ for translucent clouds.

The thermal desorption rate can be estimated from the Arrhenius relation k_Arr(T) = ν₀ exp(−D/k_BT) where D is the activation energy for desorption; a typical value of the Arrhenius frequency factor is ν₀ = 10¹⁴ s⁻¹. Experimental information about the binding energy of H₂ physisorbed to C₆₀ or C⁺₆₀ does not exist, but values of 40–70 meV have been reported for H₂ physisorbed to single-walled carbon nanotubes (Brown et al. 2000; Williams et al. 2002). Calculated values are 40–70 meV for H₂ physisorbed to carbon nanotubes (Arellano et al. 2002) and 50 to 60 meV for graphite or graphene (Ferre-Vilaplana 2005; Rubes & Bludsky 2009). Our own DFT calculations presented above do not provide reliable binding energies for physisorbed H₂ but Denis et al. have computed a value of 52 meV for H₂ + C₆₀ (Denis 2008). DFT calculations of H₂-benzene complexes indicate that neutral and cationic complexes have comparable binding energies (H. Zettergren 2011, private communication). Thus, we adopt a value of D = 50 meV for the binding energy of H₂ to neutral or charged fullerenes.

By equating the rate of collision with the rate of thermal desorption we estimate T_max, the maximum ambient temperature at which charged or neutral fullerenes, if they exist in an interstellar cloud, would be likely to be complexed with one or more weakly bound H₂. The results are listed in Table 1. They represent upper limits because we have assumed upper limits for the H₂ concentration, except for dense clouds where n_H2 represents a lower limit. T_max depends logarithmically on n_H2, therefore its exact value has a rather weak effect on T_max; the same is true for the value chosen for the Arrhenius frequency ν₀. T_max is, however, proportional to the assumed value of the binding energy which has an estimated uncertainty of 20%.

With these uncertainties in mind we conclude that fullerenes in dense molecular clouds may very well be complexed with H₂. These clouds, however, are unlikely sources of DIBs. For translucent clouds the estimated temperature T_max is close to the lower temperature found in these clouds; C₆₀–H₂ complexes are not very likely but cannot be ruled out either.

In diffuse atomic and molecular clouds which are the major sources of DIBs, weakly bound C₆₀–H₂ are very unlikely to exist. The large photon flux found in diffuse clouds would, of course, be another reason for the rapid destruction of weakly bound C₆₀–H₂ complexes. Photon destruction may also play a role in translucent clouds but a quantitative estimate for its rate is beyond the scope of the present work.

An important caveat applies to our estimates. They are classical; they ignore the effects of the low density of vibrational states that C₆₀ complexes have at energies corresponding to ≈10 K. A low density of states will reduce both, the rate of formation and the rate of desorption: collisions will not lead to long-lived complexes unless the collision energy matches a specific excited state in the complex. On the other hand, when H₂ desorbs, the "vibrational temperature" of the products will be much less than the ambient temperature, i.e., the "emission temperature" that one should use in the Arrhenius relation will be much less than the value used in our estimate (Andersen et al. 2001). The existence of additional modes in H₂C⁺₆₀, rotational modes, loss of icosahedral symmetry, and their impact on the infrared activity and cooling rate will also be important. A refined estimate of T_max will require elaborate calculations which are beyond the scope of the present work.

Following electron ionization of helium nanodroplets that are doped with C₆₀ or C₇₀ and H₂ (or D₂), we observe copious amounts of hydrogen attached to fullerene ions. We conclude that most if not all of the hydrogen in these complexes is in molecular form, physisorbed to the fullerene ion with a binding energy of ≈50 meV. Abrupt drops in the ion abundance beyond (H₂)₃₂ C⁺₆₀, (H₂)₃₂ H C⁺₆₀, (H₂)₃₇ C⁺₇₀, and (H₂)₃₇ H C⁺₇₀ suggest that the first solvation shell around the fullerene ion consists of an ordered layer with one H₂ localized above each carbon ring. At ambient temperatures of 10–15 K, neutral or charged fullerenes would probably be complexed with molecular hydrogen because the collision frequency with H₂ would exceed the estimated rate of thermal H₂ desorption. Thus, if fullerenes exist in dense clouds they may very well be complexed with H₂. Complex formation in translucent clouds appears less likely but cannot be ruled out. The higher temperatures in diffuse clouds which are the major sources of DIBs make the presence of H₂–fullerene complexes unlikely. More accurate estimates of H₂–fullerene formation and desorption rates will require quantum mechanical calculations that are beyond the scope of the present work.

We thank H. Zettergren and K. Hansen for useful discussions and the unknown referee for numerous, insightful suggestions. C.L. and P.B. gratefully acknowledge a dissertation grant from the vice-rectorate for research of the University of Innsbruck. This work was supported in part by the Austrian Science Fund, Wien (FWF, projects P19073, L633, and I200 N29), and the European Commission, Brussels (ITS-LEIF).