Download Competing mechanisms of catalytic H2 formation and dissociation

MNRAS 435, 1486–1492 (2013)
doi:10.1093/mnras/stt1389
Advance Access publication 2013 September 3
Competing mechanisms of catalytic H2 formation and dissociation
on ultrasmall silicate nanocluster dust grains
Boutheı̈na Kerkeni1,2‹ and Stefan T. Bromley3,4‹
1 LPMC,
Département de Physique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis, Tunisia
Supérieur des Arts Multimédia de la Manouba, Université de la Manouba, 2010 la Manouba, Tunisia
3 Departament de Quı́mica Fı́sica i Institut de Quı́mica Teorica i Computational (IQTCUB), Universitat de Barcelona, E-08028 Barcelona, Spain
4 Institució Catalana de Recerca i Estudis Avançats (ICREA), E-08010 Barcelona, Spain
2 Institut
Accepted 2013 July 24. Received 2013 July 23; in original form 2013 February 13
ABSTRACT
Silicate dust grains are thought to be essential in catalysing the formation of H2 . Ultrasmall
silicates (diameter ≤1.5 nm) are fundamental intermediates in silicate dust formation in stellar
outflows, and are ubiquitous in the interstellar medium. To investigate the catalytic formation
and dissociation of H2 on such nanosilicates, we have performed ab initio quantum chemical
calculations of hydrogen interacting with a stable 21 atom nanosilicate cluster having the
stoichiometry of forsterite, (MgO)6 (SiO2 )3 . Due to its small size and high percentage of
surface atoms, our particle inherently does not exhibit the bulk forsterite crystal structure and
possesses a range of chemisorption and physisorption sites, presumably similar to those that
larger amorphous silicates would offer. We find a number of exothermic H2 formation routes
and pathways for H2 catalytic dissociation on the nanosilicate. In particular, we discover some
H2 formation routes that are energetically more favourable than that reported for the forsterite
(010) surface. Further, we find a linear correlation between the dissociative chemisorption of
two H atoms and the dissociation transition state, suggestive of a general Brønsted–Evans–
Polanyi relation for H2 dissociation on bare silicates independent of dust grain size and/or
crystallinity.
Key words: astrochemistry – molecular processes – ISM: molecules.
1 I N T RO D U C T I O N
The Universe is rich in molecules and dust particles, which form
the solid component of matter diffused among the stars. The most
abundant molecule, H2 , attracts considerable attention in this context since the amount of energy deposited in its external and internal
degrees of freedom governs both the infrared emission in interstellar clouds (Burton et al. 1992; Le Bourlot et al. 1995) and its gas
phase reactivity. For example, many reactions like O(3 P) + H2 and
C+ +H2 become efficient when H2 is vibrationally excited (Flower
& Launay 1977; Jaquet et al. 1992). The abundance of molecular
hydrogen in the interstellar medium (ISM) is therefore clearly important in the evolution of molecular complexity that occurs in this
region, in addition to its essential role in star formation in diffuse
clouds (Weinberger 2005).
Due to the low gas density and to the very low temperatures
in the ISM, H2 cannot form in the gas phase efficiently enough
via two-body radiative association or three-body collision processes (Gould & Salpeter 1963; Duley & Williams 1984; Williams
2003). It is hence generally accepted that H atom recombination
E-mail: [email protected] (BK); [email protected] (STB)
takes place on the surface of dust grains (Gould & Salpeter 1963;
Duley & Williams 1984; Williams 2003) that act as a catalyst for
the step-wise release of the 4.5 eV (5222 K) excess energy in a
time comparable to the vibration period of the highly vibrationally
excited state in which it is formed. The fundamentals of astrochemistry in the gas phase are relatively well established, in contrast
to the special relevance attributed to processes involving interstellar dust grains. While dust particles make up only one mass per
cent of the total matter in the ISM, they play a crucial role in
its chemical evolution (Williams & Herbst 2002) by catalysing
molecule formation and scattering dissociating radiation. Carbonrich stars mainly produce carbonaceous dust particles at the end
of their lives, while oxygen-rich stars (M-type) generate silicate
dust particles. In oxygen-rich stars, the surplus of O atoms can
start forming metal oxides in the cooler regions further away from
the dying star. The observed stardust silicates are predominantly
magnesium-rich pyroxenes (Mgn Fe(n − 1) SiO3 ), with a significant
crystalline fraction (∼10 per cent; Molster et al. 2001). While the
ISM is refuelled with crystalline silicate grains from stellar outflows,
these must subsequently be efficiently amorphized since in the ISM
only amorphous silicates are observed of mainly Mg-rich olivinic
composition (Mgn Fe(2 − n) SiO4 ) (Kemper, Vriend & Tielens 2004;
Molster & Kemper 2005). It has been estimated that up to 10 per
C 2013 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society
Catalytic H2 formation on dust nanosilicates
cent of the mass of interstellar silicates may be in ≤1.5 nm sized
particles (Draine & Li 2001).
Previous theoretical investigations of H2 formation on dust grains
have mainly focused on carbonaceous grains, probably because
of the simplicity of the model surface that can be used (Meijer,
Farebrother & Clary 2002; Sha, Jackson & Lemoine 2002; Morisset
et al. 2004a,b, 2005; Kerkeni & Clary 2007; Rutigliano & Cacciatore 2008) allowing for extensive quantum dynamics studies. H2
formation on the crystalline forsterite silicate surface (010) was
studied with an embedded cluster approach (Sherwood et al. 2003),
showing that H and O can chemisorb barrierlessly with adsorption energies ≥12 000 K (Goumans, Catlow & Brown 2009). Calculations on a small pyroxene silicate nanoparticle with respect
to its reactivity towards H2 and H2 O and oxygen depletion have
also been reported (Goumans & Bromley 2011). Experimentally,
the formation of H2 has been studied on the surface of water ice
(Hornekær et al. 2003; Perets et al. 2005; Vidali et al. 2006, 2007),
graphite (Baouche et al. 2006; Creighan, Perry & Price 2006;
Hornekær et al. 2006; Islam, Latimer & Price 2007), amorphous
carbon (Katz et al. 1999) and amorphous silicates (Vidali et al.
2006, 2007; Perets et al. 2007).
Nanoscale structure and properties of oxides such as silicates
often differ dramatically from those of the parent bulk material
(Bromley et al. 2009; Catlow et al. 2010). We have thus selected
a silicate nanocluster near the lower size limit expected for ultrasmall dust grains in an attempt to theoretically assess the influence
of such extreme reduced scale on H2 formation/dissociation. The
intrinsically non-crystalline structure of our stable nanosilicate also
provides us with a natural way to mimic the effects of amorphicity (most larger silicate dust grains being amorphous) with a small
system. We consider a stable nanosilicate with a forsterite composition, (MgO)6 (SiO2 )3 (see details below), and perform a detailed
analysis of gas phase atomic hydrogens adsorption, diffusion, recombination and molecular desorption energies. The choice of a
forsterite composition also allows us to provide a detailed comparison with analogous calculations conducted by Goumans et al.
(2009) on a forsterite (010) crystalline surface. The results from
the latter study may be taken as representative of the properties
for a crystalline silicate dust grain particle at the upper size limit.
Taking all reaction pathways into account, we find evidence for a
general Brønsted–Evans–Polanyi (BEP; Brønsted 1928; Evans &
Polanyi 1938) relation for catalysed H2 formation on bare silicates
irrespective of dust grain size and/or crystallinity.
The paper is organized as follows. In Section 2, we describe the
derivation of the nanosilicate dust grain structure and the quantum
chemistry methodology that was followed. The results of the calculations of hydrogen interacting with the nanosilicate cluster are
introduced in Section 3. Subsequent analysis and results are presented in Sections 3.1 and 3.2, followed by a discussion in Section
3.3 and a summary in Section 4.
1487
Figure 1. Optimized structure of the (MgO)6 (SiO2 )3 nanocluster from three
perpendicular viewpoints. Key: blue = Mg, yellow = Si, red = oxygen.
The colour key and the upper viewpoint are used consistently for all clusters
in Figs 2–4 in order to facilitate comparisons.
of (MgO)6 (SiO2 )3 cluster isomers using Monte Carlo basin hopping
(Wales & Doye 1997) global searches employing suitable interionic
potentials (Roberts & Johnston 2001; Flikkema & Bromley 2003).
The structures and energies of the lower energy isomers resulting
from our searches were then refined employing ab initio quantum
chemical calculations (see details below). The final optimized structure of the nanosilicate cluster employed is depicted in Fig. 1.
2.2 Quantum chemistry modelling
We use density functional theory as implemented in the Gaussian 09
code (Frish et al. 2004) to perform the structural optimizations, and
to compute harmonic frequencies and transition states. In all calculations, we employed the MPWB1K functional (Zhao & Truhlar
2004), which was designed to reproduce non-bonded interactions,
that are important for physisorption energies, reaction barriers and
thus, ultimately, for reaction rates (Zhao & Truhlar 2004, 2005).
For Mg and Si atoms we used a 6-31G(d) basis set, and for O
and H atoms we used a 6-31+G(d,p) set of basis functions. In all
optimizations, all atom positions in the cluster together with the reactants/products were fully relaxed with no symmetry constraints.
The structures resulting from the optimizations were checked to
have all positive frequencies and thus be true local energy minima.
Transition states were obtained using the Berny algorithm (Schlegel
1982) and were all verified to have a single imaginary vibrational
frequency.
2 METHODOLOGY
2.1 Nanosilicate model
3 R E S U LT S
The nanosilicate dust grain cluster considered possesses 21 atoms,
a forsterite-like composition [i.e. (MgO)6 (SiO2 )3 ] and has a diameter of ∼0.9 nm. Although not crystalline, the nanocluster has
the most energetically stable structure that we were able to find
through a global optimization search using a methodology detailed
in previous works (Goumans & Bromley 2011, 2012). Briefly described, we first extensively search the potential energy landscape
Our results reveal numerous adsorbate structures for a single H atom
and for two chemisorbed H atoms on the ultrasmall (MgO)6 (SiO2 )3
nanocluster. Subsequently, we also considered various pathways to
H2 recombination followed by desorption into the gas phase. The
calculated full energetic profiles can then be used to assess the
viability of both H2 formation and dissociation on the nanosilicate
dust grain.
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B. Kerkeni and S. T. Bromley
3.1 Adsorption of H atoms
Unlike bulk crystalline forsterite, where the SiO4 tetrahedra are
equally separated by Mg cations, in the nanocluster the SiO4 tetrahedra are directly joined by bridging oxygen (Si–O–Si) linkages
(see Fig. 1). This nanoscale structural feature combined with the
cluster’s relatively less ordered structure allows our nanocluster
model to offer a variety of sites for impinging gas phase hydrogen
atoms for both physisorption (Hphys ) and chemisorption (Hchem ).
3.1.1 Physisorption of H atoms
When a single H atom physisorbs on the cluster, it energetically
preferentially occupies either the centre of a ring circumscribed by
the atoms MgOSiOMgO, atop an Mg cation, or above an Mg–O
bond. Four examples of such possibilities are depicted in Figs 2(a)–
(d) in order of increasing H-cluster binding energies (Ebind =
− [E(total) − [E(Hgas ) + E(cluster)]]). We note that this definition applies equally well to Hphys and Hchem states.
The first example, Fig. 2(a), corresponds to the case where an H
atom is physisorbed atop an Mg cation at a distance of 2.48 Å with
a binding energy of 788 K. Two of these configurations (i.e. Figs 2b
and d) correspond to an H atom above a centre of an MgOSiOMgO
ring with binding energies of 1036 and 2894 K, respectively. The
nearest H–O and H–Mg distances for these configurations are also
shown in Fig. 2. In most Hphys cases, the H-cluster interatomic
distances are between 2.0 and 2.85 Å. In the case of Fig. 2(d), however, where the H atom is most strongly bound, we also find a rather
small H–O distance of 1.63 Å, consistent with a relatively strong
non-bonded electrostatic interaction. In Fig. 2(c), one can also see
an example where an H atom is physisorbed over an Mg–O bond
with distances of 2.05 Å from the Mg cation and 1.89 Å from the
O anion. This configuration has a fairly strong physisorption binding
energy of 1327 K. Similar calculations of an H atom interacting with
a (010) forsterite surface (Goumans et al. 2009) found that H preferentially physisorbs at a distance of ∼1.8 Å from the surface and
is situated above the surface, between a surface Mg cation (2.08 Å)
Table 1. Calculated energy barriers for atomic diffusion, E0 , and atomic
desorption, E1 of Hphys on the nanosilicate cluster. Note that E1 is equivalent to Ebind (Hphys ), and the values corresponding to the configurations
in Fig. 2 are indicated. Columns 2 and 3 show comparative data from
experiment and calculations on the bulk (010) forsterite surface.
Energy (K)
Katz et al.
(1999)
Goumans et al.
(2009)
This
work
E0
287
813, 1240
373
1240
71, 74, 87, 228
293(a→d), 492(a→c)
1030(c→a), 2398(d→a)
724, 788(2a), 868, 881
1036(2b), 1327(2c)
2894(2d)
E1
and an oxygen anion (1.93 Å) with a physisorption binding energy of 1240 K, which is very similar to that found in our example
shown in Fig. 2(c). The smallest physisorption binding energies we
found were 724 and 881 K for an H atom sitting above the centre
of an MgOSiOMgO ring and above an Mg cation, respectively (not
shown).
To investigate whether Hphys atoms could diffuse over the surface of the nanocluster under the physical conditions of the ISM,
we computed a range of activation barriers for transitions between
the physisorbed states shown in Fig. 2 and three others (not shown).
The activation barriers range between 71 and 2398 K, depending
on the specific diffusion step. In all cases, the activation barriers
are easily overcome by the physisorption energy of the initial Hphys
state. This indicates that gas phase physisorbed H atoms could diffuse freely on such ultrasmall silicate nanoclusters.
The best fit by Katz et al. (1999) to experimental temperature
programmed desorption (TPD) curves for H2 formation on polycrystalline olivine involved three parameters resulting from solving
the rate equations: the barrier for atomic diffusion (E0 ), and the
barriers for atomic and molecular desorption (E1 and E2 , respectively). A comparison between our values, those of Katz et al. (1999)
and those from an embedded cluster calculation on the crystalline
forsterite (010) surface is reported in Table 1. Our smallest value
(E1 = 724 K), which corresponds to an H atom physisorbed over
the centre of an MgOSiOMgO ring, is approximately twice of the
value E1 = 373 K reported by Katz et al. (1999). The experimental
value is a third of that reported by Goumans et al. (2009) from
calculations on the (010) surface of forsterite. The relatively small
experimental value compared to both theoretical estimates could be
an indication of the measured system having a less electrostatically
attracting surface towards H atom adsorption. This in turn could
be due to hydroxylation of the surface of the ionic silicate sample,
as suggested by Arsic et al. (2004). Silicate dust grains with precursor icy mantles are also likely to be hydroxylated (Vidali et al.
2006; Goumans & Bromley 2011) in molecular clouds and will
be considered in future studies with respect to their H2 formation
and dissociation properties. The present work mainly pertains to
processes on bare silicate dust grains in diffuse clouds.
3.1.2 Chemisorption of H atoms
Figure 2. Different sites for a single physisorbed H atom on the nanosilicate cluster, ordered by increasing Ebind (Hphys ) (a–d). Selected interatomic
distances (in Å) are shown. Hydrogen atoms are indicated by light grey balls
(also in Figs 3 and 4).
Our calculations reveal that single H atoms can chemisorb only on
top of oxygen anions on the nanosilicate cluster. Furthermore, these
reactions induce subsequent structural relaxations with respect to
the positions of the oxygen centres that the H atom binds to and the
immediate neighbouring atoms of this O anion within the cluster
Catalytic H2 formation on dust nanosilicates
1489
the cluster along the reaction path, we did not find any potential
barrier to chemisorption.
An Hphys -to-Hchem activation energy barrier height of 855 K was
found for the most strongly physisorbed H atom (Fig. 2d) to become chemisorbed in the state shown in Fig. 3(c). Taking this as a
typical barrier, and noting the generally relatively deep physisorption binding energy wells (724–2894 K), we can expect physisorbed
H atoms to either thermalize and subsequently move to chemisorption sites via tunnelling, or immediately get trapped into a
chemisorption well. Considering as a starting point two such
chemisorbed H atoms, in the following we investigate H2 formation.
3.2 Formation of H2
−
Figure 3. Different sites for a single chemisorbed H atom (H+
chem + e ) on
the nanosilicate cluster ordered by increasing Ebind (a–f). The Mg cation that
gains negative charge is indicated by a grey line linking it to the protonated
O anion.
(see structures in Fig. 3 relative to that in Fig. 1). The final relaxed
structures of the cluster with a chemisorbed H atom at various
locations in Fig. 3 are organized from (a) to (f) in ascending order
of H-cluster binding energy.
By analysing the Mulliken partitioned atomic charges (Mulliken
1955) before and after H chemisorption for all of the cases in
Fig. 3, we find a reduction in the positive charge of the nearby
Mg cations (decrease of between +0.33e and +0.43e), while the
bonding H atom gains positive charge (increase of between +0.39e
and +0.43e). We can chemically interpret this as donation of negative charge (from H to O) via the protonation of the O anion with
subsequent donation of the negative charge from the O anion to a
single nearby Mg cation site. In terms of a bulk surface, this process
can be described as giving rise to a surface charge, as observed
in calculations of H chemisorption on the (010) forsterite surface
(Goumans et al. 2009). Hereafter, we refer to such single H atom
−
chemisorption as H+
chem + e .
The simultaneous formation of an O–H bond (0.95–0.96 Å) and
charge localization at only one adjacent Mg cation gives rise to a
strong H-cluster interaction leading to a range of large chemisorption energies (see Table 2). Our nanocluster model gives a range
of chemisorption binding energies which lay above and below that
calculated for the bulk crystalline forsterite surface (Goumans et al.
2009). Our range of calculated values are due to the diversity of
available adsorption sites on our inherently non-crystalline nanosilicate. As it is known that interstellar silicate dust grains typically
have a low crystallinity (Li, Zhao & Li 2007), our data should better reflect the energies of H adsorption on such grains. After testing
numerous pathways for an incoming gas phase H atom to approach
To investigate whether H2 formation would be catalysed or not
at the low-temperature conditions of the ISM, the barriers for the
recombination of two chemisorbed H atoms on the nanosilicate
Mg6 Si3 O12 were calculated for various configurations. Our quantum chemical calculations reveal that our nanosilicate cluster can
adsorb a second gas phase H atom without a barrier, which could
catalyse H2 formation. Furthermore, we notice that the second
H atom approaching the cluster always binds strongly to only one
Mg adjacent cation. In Fig. 4, we show a set of such configurations.
The binding energies of the second H atom each taken relative to
a corresponding cluster with a single chemisorbed H atom (see
Table 3 for correspondence and associated Ebind values) are all considerably larger than that of the first chemisorbed H atom. We find
that the Mg cation to which the second H atom chemisorbs is always that which already gained charge from the first protonation
event. This Mg centre binds the second incoming H atom, forming a
hydride-like Mg–H bond (∼1.7 Å) without any barrier. We refer to
−
this pair of separate chemisorbed H atoms as H+
chem +Hchem , where
the first Hchem is that of the O–H and the second of the Mg–H,
respectively. Upon sampling different cluster approach possibilities
for the second H atom, in all cases we found that the H atom ends
up chemisorbed to this Mg centre. In no cases did we find the direct formation of H2 . The distance between the two chemisorbed
H atoms varies between 1.49 and 4.44 Å (see Fig. 4). In order to see
if these two separated chemisorbed H atoms could recombine and
desorb in the cold ISM to form gas phase H2 (H2,g ), we conducted
a search for possible relevant transition states.
Table 2. O–Mg interatomic distances and binding energies for a
−
single chemisorbed H atom (H+
chem + e ) at sites on the nanosilicate cluster corresponding to those in Fig. 3. The O–Mg distances
in parentheses are those before H chemisorption.
Configuration
dOMg (Å)
(a)
(b)
(c)
(d)
(e)
(f)
3.37 (2.07)
3.70 (1.97)
3.67 (1.95)
2.34 (1.88)
3.62 (1.92)
2.20 (1.90)
Ebind (K)
9115
9723
11 445
19 731
21 630
22 640
Figure 4. Different configurations for two chemisorbed H atoms
−
(H+
chem +Hchem ) on the nanosilicate cluster. Clusters are ordered with respect to increasing Ebind of the second H atom (i.e. H−
chem ) relative to a
cluster with one chemisorbed H atom (see Table 3 for correspondence).
1490
B. Kerkeni and S. T. Bromley
−
Table 3. Summary of energetic data for H2 formation starting from the H+
chem +Hchem configurations in column 1 (following
labelling in Fig. 4). Column 2 lists the binding energy of the second H atom for each configuration in column 1 with respect to
−
the initial H+
chem + e configurations listed in column 3 (following labelling in Fig. 3). Column 4 lists the total binding energy
−
of both chemisorbed H atoms (as used in Figs 5 and 6). Reaction barriers: TS(H+
chem +Hchem → H2,phys ) and recombination
−
energies: (H+
+H
→
H
)
are
in
columns
5
and
6,
respectively.
Desorption
energy
for H2,g release is given in column
2,phys
chem
chem
−
7. The H+
+H
configuration
labelling
in
column
1
also
corresponds
to
the
reaction
profile
labelling in Fig. 5.
chem
chem
−
H+
chem +Hchem
configuration
(Fig. 4)
Ebind of
H−
chem (K)
−
Corresponding H+
chem +e
configuration
(Fig. 3)
−
Ebind (H+
chem +Hchem )
(far left lines
of Fig. 5)
(a)
(b)
(c)
(d)
(e)
(f)
36 241
37 132
37 639
37 856
37 943
40 281
(b)
(c)
(e)
(f)
(d)
(a)
45 964
48 577
57 674
60 496
57 674
49 396
We found that the nanosilicate cluster allows for several reaction paths of two separated chemisorbed H atoms to recombine
and desorb into the gas phase. Each reaction path corresponds to
a given initial configuration of chemisorbed H atoms, as shown in
Fig. 4 [where (a) to (f) are arranged in increasing binding energy
−
of the second H atom]. The H+
chem +Hchem chemisorbed configurations depicted in (a), (b) and (f) in Fig. 4 correspond to precursors of exothermic H2 formation, while the others are precursor
states to endothermic H2 formation (corresponding barrier energies
are given in Table 3). One can see that the adsorption of a single
H atom is most energetically favoured with the configuration shown
in Fig. 3(f). This would thus be the most probable first chemisorption site on the cluster to be occupied by a gas phase H atom. This
site however corresponds to one that is not the most favourable for
binding the second gas phase H atom (Fig. 4d). The most energetically unfavourable site for the first H atom chemisorption (Fig. 3a)
is, conversely, the one that can bind the second gas phase H atom
most strongly (i.e. configuration 4f). Subsequently, the barrier to recombination from the latter configuration is 1515 K. However, the
barrier to H2 recombination from cluster 4(a) is the lowest found
(726 K). A summary of all considered H2 recombination barrier energies, reaction energies and desorption energies is given in Table 3.
3.3 Discussion
Fig. 5 shows the reaction energy profiles between (i) the binding
−
energies of both chemisorbed H atoms [i.e. Ebind (H+
chem +Hchem ),
which is equal to the sum of the respective Ebind values in Tables 2
and 3] and (ii) the energy of H2,g , where the latter is set to zero.
From left to right, the reaction profiles can be interpreted as paths
for H2,g formation. The most energetically favourable of these paths
corresponds to reaction path (a) (cyan line and row 1 of Table 3)
−
which starts from the least strongly bound H+
chem +Hchem configuration (Fig. 4a). This reaction path has a small barrier (726 K) and a
high exothermicity (−10 295 K) and would efficiently catalyse H2,g
formation. The total exothermicity of producing H2,g following reaction path (a) via the double chemisorption mechanism would be
−54 623 K (i.e. −9723 K − 36 241 K − 10 295 K + 1636 K). The
activation barrier for H+H recombination would easily be overcome by the high binding energy gained by the two chemisorbed H
atoms and would even lead to the formation of vibrationally excited
H2 molecules. An accurate rovibrational prediction of desorbed H2
molecules may be reached if quantum or molecular dynamics calculations were performed, which we are currently considering. The
Reaction
barrier (K)
Reaction
energy (K)
Desorption
energy (K)
726
2830
8539
10 646
7473
1515
−10 295
−7796
2549
3951
871
−7102
1636
1749
2097
1924
2180
1875
Figure 5. Reaction profiles relative to H2,g , indicating different possible
paths for H2,g formation on the nanosilicate cluster. Data from Goumans
et al. (2009) corresponding to the forsterite (010) surface are also shown.
Profile labelling follows that in Fig. 4 and column 1 of Table 3.
next two most exothermic reactions in Fig. 5 are given by the (b)
and (f) paths with reaction energies of −7796 and −7102 K and
fairly low reaction barriers of 2830 and 1515 K, respectively (see
also rows 2 and 6 in Table 3). The three remaining reaction paths (e,
c and d) are endothermic as mentioned earlier (see corresponding
rows in Table 3). All the endothermic pathways have the largest
−
Ebind (H+
chem +Hchem ) values and the largest recombination barriers.
In Fig. 5, we also plot the reaction energy profile corresponding to
the same process occurring on the forsterite (010) surface (Goumans
−
et al. 2009). With respect to both Ebind (H+
chem +Hchem ) and recombination barrier height, the bulk surface reaction pathway lies midway between the exothermic and endothermic pathways we find on
the nanocluster, and is itself exothermic with respect to H2,g formation. In Fig. 6, we plot the recombination barrier height versus
−
Ebind (H+
chem +Hchem ) for all our pathways and for that calculated for
the forsterite (010) surface, clearly showing a linear relation between the two. This shows that the ease of H2,g formation is largely
determined by how strongly both H atoms chemisorb with a silicate
dust grain surface. More generally, this suggests that there may be
a general BEP relation for H2 dissociation on bare silicate grains
independent of dust grain size or crystallinity.
Catalytic H2 formation on dust nanosilicates
−
Figure 6. Plot of TS(H+
chem +Hchem → H2,phys ) recombination barrier
+
−
height versus Ebind (Hchem +Hchem ). Labelling follows that in Fig. 4 and
column 1 of Table 3. The good linear fit is also indicated by the coefficient
of determination (R2 ).
Following the energy profiles from right to left in Fig. 5 also
shows that the reaction profiles (e, c and d) are exothermic towards
H2,g dissociation. Such processes may play a role in attenuating the
H2,g formation mechanism. Even though the reactions towards H2,g
dissociation (see Figs 5c–e) are exothermic, we find that each has
quite a large barrier (5990, 6695 and 6601 K, respectively). In the
cold regions of the ISM, it is assumed that H2,g formation follows
Langmuir kinetics (i.e. the immediate desorption of incoming atoms
or molecules on a surface already saturated with molecules) and thus
these barriers would tend to inhibit the dissociation process.
Interestingly, our results also provide evidence that ultrasmall
non-crystalline nanosilicate dust grains do not simply tend to be
more or less effective for H2,g formation, but, rather, provide a
greater range and variety of chemical pathways for both H2,g formation and dissociation. In order to achieve a further detailed understanding of H2,g formation on small silicate dust grains, it would
be interesting to also consider isotopically varied dust compositions
to be able to directly compare with TPD experiments and to study
the influence of H (or D) interaction with OH (or OD) coverage
on catalytic reaction paths. Work in this direction is currently in
progress.
1491
structure for its size, is inherently non-crystalline and thus offers
many more distinct sites for chemical processes compared to a
well-ordered bulk crystalline surface.
Our quantum chemical calculations of single H atom desorption
energies, hopping barriers, and activation energy barriers for desorption and recombination of molecular hydrogen on our nanosilicate
model indicate that the heterogeneous H2,g formation/dissociation
could be reversible. We do not find any barrier to chemisorption with
respect to gas phase H atoms, and therefore impinging H atoms are
likely to chemisorb.
Adsorption of atomic hydrogen is found to occur on the nanocluster as follows: (i) protonation of an oxygen atom and donation
of negative charge to a single nearby Mg cation and (ii) adsorption
of a second H atom on the Mg cation to form pairs of chemisorbed
−
H atoms (H+
chem +Hchem ). On the nanocluster, there exist many sites
to accommodate these two H atoms. We find three configurations
that lead to endothermic H2,g desorption, and three others that lead
to exothermic H2,g desorption. The energies for H2,g formation previously calculated for a crystalline forsterite surface (Goumans et al.
2009) are located in between our two sets of reaction paths with
respect to the H2,g limit.
The range of possible reaction paths on the nanosilicate cluster
model also allows for H2 dissociation to be a competing process.
This rich behaviour further demonstrates that our nanosilicate cluster model offers a greater variety of sites for H adsorption and
recombination than bulk crystalline surfaces. This is also consistent with experiments showing that the adsorption and mobility of
H atoms depend strongly on the nature and morphology of a surface (Vidali et al. 2006). Considering the set of H2 dissociation
pathways reported herein together with that reported for the (101)
forsterite surface (Goumans et al. 2009), we find that in all cases
−
Ebind (H+
chem +Hchem ) has a strong linear relation to the H2 dissociative
barrier height. This further suggests that there may be a general BEP
relation for catalysed H2 formation on bare silicates irrespective of
dust grain size and/or crystallinity.
AC K N OW L E D G E M E N T S
BK acknowledges the HPC-Europa2 project (project number
228398) with the support of the European Commission Capacities Area-Research Infrastructures Initiative, and is grateful to a
Short Term Scientific Mission within COST Action CM0805 ‘The
Chemical Cosmos: Understanding Chemistry in Astronomical Environments’ and to partial support of the European Community FP7ITN Marie-Curie Programme (LASSIE project, grant agreement no.
238258). STB acknowledges the support from the Spanish Government (Grants FIS2008-02238 and MAT2012-30924) and from
the Generalitat de Catalunya (Grants 2009SGR1041 and XRQTC).
Sergey Koslov is also thanked for useful discussions.
4 S U M M A RY
In summary, our work probes the reactivity of ultrasmall silicate dust
grain size with respect to H2,g formation and dissociation. Our work
thus provides a lower size limit benchmark for the astrochemical
relevance of such species with respect to that known for the upper
size limit of large grains with bulk crystalline facets (Goumans et al.
2009).
Specifically, we have considered a stable nanosilicate cluster with
composition (MgO)6 (SiO2 )3 and diameter 0.9 nm which is taken
to be a realistic model of an ultrasmall silicate dust grain. We have
calculated its ability to catalyse H2 formation and dissociation. Our
nanosilicate cluster, although having the most energetically stable
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This paper has been typeset from a TEX/LATEX file prepared by the author.