Abstract

The formation of H2 on a pristine olivine surface [forsterite (010)] is investigated computationally. Calculations show that the forsterite surface catalyzes H2 formation by providing chemisorption sites for H atoms. The chemisorption route allows for stepwise release of the reaction exothermicity and stronger coupling to the surface, which increases the efficiency of energy dissipation. This suggests that H2 formed on a pristine olivine surface should be much less rovibrationally excited than H2 formed on a graphite surface. Gas-phase H atoms impinging on the surface will first physisorb relatively strongly (Ephys= 1240 K). The H atom can then migrate via desorption and re-adsorption, with a barrier equal to the adsorption energy. The barrier for a physisorbed H atom to become chemisorbed is equal to the physisorption energy, therefore there is almost no gas-phase barrier to chemisorption. An impinging gas-phase H atom can easily chemisorb (Echem= 12 200 K), creating a defect where a silicate O atom is protonated and a single electron resides on the surface above the adjacent magnesium ion. This defect directs any subsequent impinging H atoms to chemisorb strongly (39 800 K) on the surface electron site. The two adjacent chemisorbed atoms can subsequently recombine to form H2 via a barrier (5610 K) that is lower than the chemisorption energy of the second H atom. Alternatively, the adsorbed surface species can react with another incoming H atom to yield H2 and regenerate the surface electron site. This double chemisorption ‘relay mechanism’ catalyzes H2 formation on the olivine surface and is expected to attenuate the rovibrational excitation of H2 thus formed.

1 INTRODUCTION

Neither radiative association nor ionic processes can account for the observed abundances of H2 in both diffuse and dense clouds (Duley & Williams 1984). Accordingly, the heterogeneously catalyzed association of two H atoms on the surface of dust grains is thought to be the main mechanism for H2 formation in these regions (Gould & Salpeter 1963; Duley & Williams 1984; Williams 2003). Many studies of the dust-catalyzed formation of H2, both experimental and theoretical, are therefore being undertaken (see Williams et al. 2007 for a recent review). Experimentally, the formation of H2 has been studied on the surface of water ice (Hornekaer et al. 2003; Perets et al. 2005; Vidali et al. 2006), graphite (Baouche et al. 2006; Creighan, Perry & Price 2006; Hornekaer et al. 2006; Islam, Latimer & Price 2007), amorphous carbon (Katz et al. 1999) and amorphous silicates (Vidali et al. 2006; Perets et al. 2007; Vidali et al. 2007). Most theoretical studies to date have focused on H2 formation on model graphite surfaces (Farebrother et al. 2000; Ferro, Marinelli & Allouche 2002; Meijer, Farebrother & Clary 2002; Sha, Jackson & Lemoine 2002; Morisset et al. 2004a,b, 2005; Bonfanti et al. 2007; Kerkeni & Clary 2007; Rutigliano & Cacciatore 2008). The relative simplicity of the graphite model allows for extensive quantum dynamics studies which can be compared with experiment (Creighan et al. 2006; Islam et al. 2007). There have also been a few classical molecular dynamics studies of the formation of H2 on water ice surfaces (Takahashi, Masuda & Nagaoka 1999a,b; Al-Halabi & Van Dishoeck 2007). Here, the first computational results for H2 formation on a silicate surface are presented. The adsorption and mobility of H atoms, and their recombination to H2, on the (010) surface of the Mg-rich olivine forsterite (Mg2[SiO4]) are studied with an embedded cluster approach. Our results provide detailed models for the mechanisms of this key reaction.

2 COMPUTATIONAL METHODOLOGY

The full details of the computational methodology can be found in a study of H2O formation on the same surface (Goumans et al. 2008). Here, we give a short outline of the approach. We use the modular ChemShell code (Sherwood et al. 2003) to set up an embedded hemispherical cluster from the two-dimensional forsterite (010) surface, relaxed at the molecular mechanics (MM) level. This surface is the most stable both at the quantum mechanics (QM) (de Leeuw 2001) and at the MM level (de Leeuw et al. 2000) and is terminated by chains of alternating, zig-zagging Mg2+ ions and silicate (SiO2−4) groups (see Figs 1–3). The (010) surface is relatively flat, with the Mg2+ ions protruding slightly relative to the O atoms of the SiO2−4 groups (0.2 Å at the MM level and 0.1 Å at the QM level). Note that forsterite has an orthorhombic structure with space group Pbnm, where b > c > a and α=β=χ= 90°. The Pnma space group is equivalent to the Pbnm space group, however, in the Pnma space group a > b > c. In both the cases, the surface which is cut along the longest vector is the most stable. In Pbnm, this is the (010) surface, while in the Pnma space group this is the (100) surface.

Figure 1

Directions of hydrogen hopping of physisorbed H atoms across the forsterite (010) surface, across the a- and c-lattice vector. Top view of only the first surface layers of SiO2−4 and Mg2+. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

Figure 1

Directions of hydrogen hopping of physisorbed H atoms across the forsterite (010) surface, across the a- and c-lattice vector. Top view of only the first surface layers of SiO2−4 and Mg2+. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

Figure 2

Singly occupied molecular orbital (blue and red) for a chemisorbed H atom on the forsterite (010) surface, clearly displaying the surface electron. Only the QM atoms are shown. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

Figure 2

Singly occupied molecular orbital (blue and red) for a chemisorbed H atom on the forsterite (010) surface, clearly displaying the surface electron. Only the QM atoms are shown. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

Figure 3

Two chemisorbed H atoms (top) and physisorbed H2 (bottom) on the forsterite (010) surface, and the TS (middle). Only the QM atoms are shown. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

Figure 3

Two chemisorbed H atoms (top) and physisorbed H2 (bottom) on the forsterite (010) surface, and the TS (middle). Only the QM atoms are shown. Si: grey, Mg: yellow, O: red, H: white (grey-scale in print).

A moderately sized cluster (55 atoms for the bare surface) is treated with QM and then embedded in a larger cluster (109 active and 1520 inactive atoms) treated at the computationally cheaper MM level. For all the reactants, products and transition states (TS), the 55–57 QM atoms and surrounding 109 MM atoms are fully relaxed in the optimization. For the QM part, we use density functional theory in gamess-uk (Guest et al. 2005) with the MPWB1K functional, which has been designed to reproduce non-bonded interactions, that are important for physisorption, as well as accurate barrier heights which are important for reaction rates (Zhao & Truhlar 2005, 2004). We used harmonic (five-dimensional) basis sets, taken from the emsl Basis Set Library (Schuchardt et al. 2007). The basis sets used are as follows: the two surface Mg ions that are involved in the surface chemistry, 6-31G*; other QM Mg ions, LANL2DZ pseudopotential and basis; boundary Mg ions, LANL2DZ pseudopotential only (no basis); silicate O atoms, 6-31G*; Si, LANL2DZ pseudopotential and basis + polarization function; gas phase and adsorbed H and O atoms, 6-31+G**. gulp (Gale & Rohl 2003) is used for the MM calculations, using the full formal charge (i.e. Mg2+, Si4+, O2−) atomic potentials with a core-shell potential for O2− as described by de Leeuw et al. (2000). Even-electron systems are treated with a spin-restricted formalism (closed shell singlet) while odd-electron systems (doublets) are calculated with an unrestricted Kohn–Sham approach. TS are initially optimized with a modified (Goumans et al. 2008) climbing image-nudged elastic band (CI-NEB) algorithm (Henkelman, Uberuaga & Jónsson 2000). All active atoms (55–57 QM + 109 MM atoms) are fully optimized for the 8–12 images in the NEB. TS are further refined by optimizing the highest points on the reaction path with the HDLCopt (Billeter, Turner & Thiel 2000) or Baker (1986) algorithm in ChemShell, using a full Hessian only for two to six QM atoms, whilst fully optimizing all the other active QM + MM atoms with the limited memory formulation of the Broyden–Fletcher–Goldfarb–Shanno scheme (Liu & Nocedal 1989). Activation and reaction energies are given to three significant digits in temperature units (K), where 1 K = 0.008 3145 kJ mol−1.

3 RESULTS

First, the adsorption of H atoms on the olivine surface is discussed before we describe their mobility. Finally, we consider the formation of H2 via the reaction of the chemisorbed H atoms.

3.1 Adsorption of H atoms

3.1.1 Physisorption

On the pristine olivine [forsterite (010)] surface, H atoms can both physisorb and chemisorb. The calculated adsorption energies of H atoms are given in Table 1, along with the energies for all the processes studied. H preferentially physisorbs at a distance of about 1.8 Å from the surface, in between the surface Mg2+ ion (2.08 Å) and an oxygen atom (1.93 Å) from a silicate group. Upon physisorption of an H atom, the Mg2+ ion moves almost 0.1 Å out of the surface, while the other surface atoms hardly move. Even though there is no chemical bond, the ionic surface apparently binds the H atom strongly via electrostatic interactions. This is indicated by the large calculated physisorption energy (1240 K), which is twice as large as that predicted by the model of Katz et al. (1999) to fit the experimental temperature programmed desorption (TPD) data for H2 formation on polycrystalline olivine. This is not surprising, as experiments have shown that the adsorption and mobility of H depend strongly on the nature and morphology of the surface (Vidali et al. 2006). The experimental surface is likely to be hydroxylated or wetted, as is generally found for the surfaces of ionic materials (Arsic et al. 2004), considerably reducing the electrostatic interactions with adsorbates, even under ultra-high vacuum, as water binds very strongly to forsterite surfaces (de Leeuw et al. 2000; de Leeuw 2001; Stimpfl et al. 2006; Goumans et al. 2008). The experimental binding energy of H atoms on olivine (373 K) is therefore more likely to resemble that observed on water ice. Indeed, Al-Halabi & Van Dishoeck (2007) calculate the adsorption energy of H on crystalline water ice to be 400 K. Our computational model of pristine surfaces is hence most relevant to the dust grains in diffuse clouds, where no ices are observed, and to the experiments with freshly cleaved, ultra-dry olivine surfaces.

Table 1

Calculated energies for the adsorption of H and formation of H2 on a forsterite (010) surface in K.

Reactive event Energy 
Hg→ Hphys −1240 
Hg→ H+chem+ eS −12 200 
TS (Hphys→ H+chem+ eS1240 
TS (Hg→ H+chem+ eS
Hg+ H+chem+ eS→ H+chem+ Hchem −39 800 
TS (H +chem+ Hchem→ H2,phys5580 
H +chem+ Hchem→ H2,phys −3670 
H2,phys→ H2,g 1120 
Hg+ H+chem+ Hchem→ H2,g+ Hchem −14 800 
Reactive event Energy 
Hg→ Hphys −1240 
Hg→ H+chem+ eS −12 200 
TS (Hphys→ H+chem+ eS1240 
TS (Hg→ H+chem+ eS
Hg+ H+chem+ eS→ H+chem+ Hchem −39 800 
TS (H +chem+ Hchem→ H2,phys5580 
H +chem+ Hchem→ H2,phys −3670 
H2,phys→ H2,g 1120 
Hg+ H+chem+ Hchem→ H2,g+ Hchem −14 800 

Note. g = gas phase, chem = chemisorbed, phys = physisorbed, forumla surface electron, TS = transition state.

3.1.2 Chemisorption

On the pristine olivine surface studied here, H atoms can also chemisorb, with a very deep well of 12 200 K. The chemisorbed H atom preferentially binds to an oxygen site, protonating the O atom of a silicate group and donating an electron to the adjacent Mg2+ site, giving rise to a surface electron (Fig. 2). The chemisorption reduces the Mulliken charge of the Mg2+ from +0.9 to +0.4 while the adsorbed H atom acquires a charge of +0.4. The simultaneous formation of a strong OH bond (0.96 Å) and stabilization of the electron by the adjacent Mg2+ cation gives rise to a strong interaction leading to a large chemisorption energy and a very low barrier for its formation (see below). Similarly, a recent theoretical and experimental study found that H atoms can chemisorb on MgO surfaces, creating a surface electron and a protonated oxygen atom (Chiesa et al. 2006). However, on MgO, the H atom only chemisorbs on defects such as kinks and inverse corners, so that the surface electron is stabilized by binding to multiple surface cations. Although H chemisorbs even on the pristine forsterite (010) surface, we are also currently investigating the adsorption and mobility of H atoms on defective (stepped) forsterite surfaces and the surfaces with Fe2+ ions, which should more closely resemble interstellar silicate dust grains which have a low crystallinity (Li, Zhao & Li 2007).

3.2 Mobility of H atoms

3.2.1 Physisorbed H atoms

The mobility of H atoms on dust grains is of paramount importance for solid-state astrochemistry and has therefore been investigated widely, both experimentally and theoretically (Takahashi et al. 1999a; Hornekaer et al. 2003; Al-Halabi & Van Dishoeck 2007; Amiaud et al. 2007; Vidali et al. 2007). In astrochemical models, it is usually assumed that the barrier to hopping is about half of the desorption energy, although there is only limited experimental data to support this assumption and the exact ratio is thought to depend strongly on the type of surface (for a recent discussion, see Cuppen & Herbst 2007). Furthermore, experimentally determined values will implicitly take tunnelling into account for surface hopping, lowering the apparent activation barriers. We have investigated the hopping of a physisorbed H atom from one ‘O–Mg’ bridged position (illustrated in Fig. 1) either across the Mg2+ ion (moving along the c-lattice vector) or crossing to another Mg2+ ion (moving along the a-lattice vector). Our CI-NEB calculations indicate that for the first case, movement across a Mg2+ ion, the activation energy for hopping is the same as the desorption energy, i.e. a ratio of 1. In these calculations, the H atom in the climbing image moves away from the surface. For H atom hopping to another Mg2+, our calculations predict a lower hopping barrier (813 K) when compared to 1240 K for desorption, which gives a hopping barrier to desorption ratio of 0.66. This is in reasonably good agreement with the value of 0.78 for amorphous silicates (Katz et al. 1999), modelled to reproduce the experimental data. As mentioned previously, however, the experimental surfaces are likely to be wetted or hydroxylated.

Tunnelling is expected to increase the hopping rate most significantly across the Mg2+ ion (along the c-lattice vector), for which the hopping has the shortest distance of 2.66 Å. Hopping between different Mg2+ ions (along the a-lattice vector) has a significantly longer distance of 5 Å (Fig. 1). However, since the NEB reaction path indicates a relatively small, sharp barrier, especially for the hopping along the c-lattice vector, tunnelling could still be efficient over these large distances. To calculate accurate tunnelling frequencies, a full quantum dynamical or quantum statistical approach to the reaction path for H hopping must be considered. Nevertheless, it is expected that physisorbed H atoms are mobile on the surface via tunnelling from one adsorption site to the next in either direction, even at the very low temperatures of 10–20 K in molecular clouds, which could lead to efficient H2 formation via the Langmuir–Hinshelwood recombination of physisorbed H atoms.

3.2.2 Chemisorbed H atoms

To investigate whether, in the cold interstellar medium (ISM), H atoms could chemisorb on an olivine surface, we have calculated the activation barrier for the transition from the physisorbed to the chemisorbed state (Table 1). There is no activation energy for the chemisorption of a gas-phase H atom on the olivine surface, because the physisorption well is as deep as the activation energy from the physisorbed state (Table 1) which cancels out the chemisorption barrier for a gas-phase atom. Apparently, along the reaction path from gas phase to physisorption and then to chemisorption the electrostatic interaction of the H atom with the ionic surface is sufficiently strong to overcome the geometric and electronic rearrangements that accompany the adsorption process. Even if a physisorbed H atom has a sufficiently long lifetime on the surface to thermalize, the barrier to chemisorption can still be overcome via tunnelling. Therefore, it seems likely that the majority of the H atoms on a pristine olivine surface will chemisorb, creating surface electrons. Once an H atom is trapped in the deep chemisorption well, it is effectively immobilized on the surface.

3.3 Formation of H2

Assuming that the majority of H atoms become trapped on the olivine surface via chemisorption, we have investigated the formation of H2 starting from that structure. The surface electron, which is formed when chemisorption occurs (Fig. 2), strongly attracts subsequent incoming H atoms, presumably through an enhanced electrostatic attraction to the polarized surface. Optimizing the system where a second H atom is located above various sites on the surface on which an H atom is chemisorbed always results in the second H atom adsorbing on the Mg2+ ion adjacent to the chemisorbed H atom (the surface electron site), and never in the direct formation of H2. The chemisorption of a second H atom is even stronger (39 800 K) than that of the first (12 200 K). The adjacent chemisorbed H atoms can then recombine via a TS to yield physisorbed H2 (Fig. 3). This reaction has a sizeable barrier of 5580 K and only has a moderate exothermicity (−3670 K), which might prevent immediate desorption of H2Edes= 1120 K) into the gas phase. The activation barrier for H2 formation could easily be overcome from the excess energy of the second H atom chemisorption event. If H2 could be formed via this double chemisorption mechanism, the total reaction exothermicity (−54 600 K) will be released in a stepwise manner (−12 200 and −39 800 for the two chemisorption steps and −2550 K for the recombination and desorption). Furthermore, the excess energy could be more easily dissipated than for H2 formation from physisorbed H atoms, via coupling of the chemisorbed atoms to the surface phonon modes. These factors would strongly reduce the rovibrational excitation of H2 thus formed. To estimate the rovibrational excitation distribution, ideally ab initio molecular dynamics should be performed.

Should the chemisorption of the second H atom be quenched sufficiently rapidly to render the barrier to H2 formation insurmountable, there are still other efficient pathways to H2 formation on the pristine olivine surface. A third H atom could react with either of the two chemisorbed species to yield H2. This possibility has been investigated by adding a third H atom to the doubly chemisorbed system at various positions above the surface. In every case, the third H atom reacts with the second chemisorbed H atom (adsorbed at the surface electron site) to yield H2. No barrier could be found for this reaction, and it is sufficiently exothermic (−14 800 K; Table 1) immediately to desorb the H2 that has been formed. The third H atom, like the second, is attracted to the localized negative charge on the surface. If H2 is formed via this mechanism, the chemisorption of the first H atom yields a surface electron which is the effective catalytic site for subsequent H2 formation. The exothermicity of the H + H → H2 reaction is negated by the chemisorption step, and so it is likely that the H2 thus formed will not be strongly rovibrationally excited when it desorbs from the surface. Again, for a better understanding of this effect, a dynamical approach is needed. Nevertheless, it is expected that via either mechanism, H2 formation on a pristine olivine surface is efficient and takes place via a relay mechanism. H2 desorbing into the gas phase is significantly less rovibrationally excited than it is when formed on a carbonaceous surface due to chemisorption.

4 ASTROPHYSICAL CONSEQUENCES

Our computational study of a pristine forsterite (010) surface is of relevance for the surface chemistry of silicate grains, in particular, bare Mg-rich olivines, observed in diffuse interstellar clouds. This study is also of relevance to the initial stages of grain chemistry in dense molecular clouds. We are currently extending this model to include surface defects such as steps and kinks to simulate amorphicity and the substitution of Mg2+ for Fe2+, modelling more iron-rich olivine minerals. The forsterite surface is expected to have a large impact on astrochemistry because of its potential to chemisorb H atoms. There is no barrier to chemisorption with respect to gas-phase H atoms, and therefore impinging H atoms are likely to chemisorb. This has two important consequences. First, any subsequent H atom approaching the site of chemisorption is directed to the magnesium atom next to the chemisorption site, which carries an excess (surface) electron, where it becomes chemisorbed. Secondly, H2 molecules formed via the double chemisorption mechanism, either directly or via reaction with a third H atom, have a significant interaction with the surface which helps to dissipate a large part of the exothermicity of the otherwise barrierless, strongly exothermic radical–radical addition, H + H. Therefore, the H-chemisorption capacity of forsterite dictates astrochemical surface reactions by strongly directing incoming atoms as well as by modulating the reaction exothermicities. It is anticipated that any products formed on a pristine olivine surface are not as strongly rovibrationally excited as products on a carbonaceous surface, for which only weak, physisorbed interactions are possible.

The chemisorption H2-formation route also increases overall efficiency by immobilizing chemisorbed H atoms. Subsequent impinging H atoms are directed towards these chemisorbed atoms, strongly increasing reaction probabilities. In summary, our calculations indicate that pristine olivine surfaces should be good catalysts for H2 formation, with low product excitation and high reaction efficiencies.

The EPSRC is acknowledged for a post-doctoral fellowship for TPMG (EP/D500524) and for computer resources on NSCCS. We thank Paul Sherwood, Johannes Kästner and Jens Thomas for their help with ChemShell and the ccp1gui and Huub van Dam for implementing the MPWB1K functional in gamess-uk. This work forms part of the research currently being undertaken in the UCL Centre for Cosmic Chemistry and Physics.

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