the interaction of h atoms at graphite surfaces in

1 downloads 0 Views 202KB Size Report
3 Laboratoire de Physique des Interactions Ioniques et Moléculaires. .... H atoms the main trouble comes from the barriers that have to be overcome: (i) the.
Molecules in Space & Laboratory, Paris, 2007 J.L. Lemaire & F. Combes (eds)

THE INTERACTION OF H ATOMS AT GRAPHITE SURFACES IN RELATION WITH H2 FORMATION IN THE INTERSTELLAR MEDIUM V. Sidis 1 , F. Aguillon1 , M. Sizun1 , N. Rougeau1 , D. Teillet-Billy1 , L. Jeloaica 2 , S. Morisset 3 and D. Bachellerie1 Abstract. The adsorption of H atoms at the surface of dust grains and their subsequent desorptive recombination via Eley-Rideal (ER) or LangmuirHinshelwood (LH) reactions constitute the key steps for H2 formation and its anomalous large abundance in the interstellar medium. Over the past few years we have concerned ourselves at LCAM1 with model studies of interactions of H atoms at graphite-like surfaces (actually reasonably large PAH´s) assumed to represent the surface of carbonaceous dust grains. The studies are based on DFT electronic structure descriptions of the interacting species and dynamics calculations of the recombination reactions (quantal wavepacket and/or quasiclassical molecular dynamics techniques). The present contribution reviews results “premi`ered” by us on: (i) the characteristics of a single H atom adsorption onto a graphite surface; (ii) the dynamics of the ER reaction involving a chemisorbed H atom; (iii) the dynamics of the LH reaction involving two physisorbed H atoms; (iv) the characteristics of a second H atom adsorption near an already chemisorbed one on the same carbon ring of the surface; and (v) the dynamics of the ER reaction between two H atoms in presence of a third one chemisorbed at the para site of the same carbon ring.

1

Introduction

The interaction of H atoms at a graphite surface is a subject of great current interest: (i) it comes into play in the interactions at the walls of controlled fusion devices; (ii) it is of great concern for hydrogen storage; and (iii) it has great astrophysical importance in relation with the formation of H2 in the interstellar medium. The latter item is the specific subject of the present “digest” which retraces historically the main lines of the work done in this field at LCAM1 . From the astrophysical literature, the interstellar medium (ISM) appears to be composed of cold rarefied gas mainly in the form H and H2 , typically (> 75%) ∼ 1 Laboratoire des Collisions Atomiques et Mol´ eculaires. Unit´ e Mixte de Recherche: CNRS et Universit´ e Paris-Sud (UMR8625) Orsay, F-91405 France 2 Direction Chimie et Physico-Chimie Appliqu´ ees, Institut Fran¸cais du P´ etrole, 1 & 4 Av. de Bois-Pr´ eau, Rueil-Malmaison, F-92852 France 3 Laboratoire de Physique des Interactions Ioniques et Mol´ eculaires. Unit´ e Mixte de Recherche: CNRS et Universit´ e de Provence (UMR6633) Marseille, F-13397 France c Observatoire de Paris & Universit´ ° e de Cergy-Pontoise

2

Molecules in Space & Laboratory

90%, and to a lesser extent of He (< 25%) ∼ 10%. It is now well accepted that it also contains some dust ∼ 1%. Characteristic gas temperatures in the ISM are in the 10 K - 100 K range and atomic densities are below 103 per cm3 . In these conditions gas phase processes (3-body recombination or radiative association) have too low probabilities of occurrence and thus cannot account for the important abundances of H2 existing in the ISM. Since the mid sixties the astrophysical community has come to accept that the H atom recombination process producing H2 in the ISM is the result of a heterogeneous catalysis reaction on the surface of dust grains: H + H + grain → H2 + grain (Hollenbach & Salpeter 1971; Schlabach & Z¨ uttel 2001). The ISM dust grain sizes are in the range: 1 nm - 0.1 µm. They are considered to be composed of carbonaceous or silicate material. In dense molecular clouds of the ISM the grains are probably covered by ice mantles. The work gathered here considers grains having a carbonaceous composition; it also restricts to the case of graphite (0001)-like surfaces. We have considered both chemical and dynamical aspects of the interaction of H atoms at a graphite surface. In all quantum chemistry computations of the bonding properties of H atoms onto the grain we have used a cluster model in which the basal plane of the graphite surface is simply represented by a Coronene molecule (C24 H12 ). The C atoms in the C24 cluster form a planar hexagonal mesh with the same C-C bond length (1.415 ˚ A) as in graphite. The border H atoms serve only to passivate the dangling bonds of the C24 cluster. The adsorption of H atoms is studied at the inner carbon ring of the cluster to preclude border effects. All quantum chemistry calculations are carried out in the framework of the Density Functional Theory (Hohenberg & Kohn 1964). The spin unrestricted Kohn-Sham equations (Kohn & Sham 1965), including the PW91 (Perdew et al. 1992) generalized gradient correction of the exchange-correlation functional, are solved with the ADF code.4 Double- and triple-ζ + polarization (DZP and TZP resp.) bases of Slater-type orbitals provided with the ADF package have been used. 2

Single H atom adsorption onto a graphite surface

Jeloaica & Sidis (1999, Paper I) and Sidis et al. (2000, Paper II) were the first to investigate this problem by non-empirical, non-perturbative quantum mechanical calculations taking provision of electron correlation. This was achieved using DFT theory as indicated above. These calculations first showed that an H-atom does not chemisorb onto a planar graphite surface. The planar surface allows for a weak adsorption at rather large atom-surface distances (2.6 ˚ A - 2.8 ˚ A in I, 4.18 ˚ A in II). The adsorption characteristics atop the three sites investigated: C atom, middle of a C-C bond, center of a carbon ring, indicated that the bonding is of the physisorption type. Moreover the close values of the binding energies (0.067 eV - 0.074 eV in I, 0.008 eV in II) at these sites indicated that physisorbed H-atoms are likely to be quite mobile. The differences in the two calculations arise from the use of a DZP basis in I and TZP in II. TZP calculations are in principle more accurate. However, it is not commonly thought that van der Waals minima can be described correctly by GGA functionals. Yet, we believe that mutual cancellation between PW91 and DZP errors would be in favor of the latter basis set expansion. Recent MP2 calculations by Bonfanti et al. 4 ADF: Amsterdam Density Functional - Scientific Computing and Modeling (SCM) - Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands. h http://www.scm.com i

H2 formation at graphitic dust grains

3

(2007) provide some support to the latter prediction and confirm the high mobility of physisorbed H-atoms on a flat graphite surface. The calculations of I and II also first showed that H-atom chemisorption onto graphite may occur only atop a C atom provided the surface puckers: the C atom has to move out of the surface towards the impinging H atom by 0.35 ˚ A. This puckering of the surface corresponds to the formation of a CH bond with a sp3 hybridization of the implied C atom. It is associated with an activation barrier of ≈ 0.2 eV. This finding was then confirmed by periodic slab DFT calculations (Jacobson et al. 2002; Sha & Jackson 2002) and many subsequent calculations. The definitive confirmation has been brought by experiment (Zecho et al. 2002) which showed that H(D) atoms issued from thermal atom sources need to have energies near 0.2 eV (≈ 2320 K) in order to produce substantial H(D) chemisorption onto graphite. Earlier experiments with much colder atoms were concluded not to give rise to chemisorption. Such a high activation energy should hinder H chemisorption onto graphitic grains at temperatures characteristic of the ISM (10 K - 100 K). Exceptions however are Photon Dominated Regions (PDR) where the gas temperatures may reach 1000 K what could allow a significant fraction of H atoms to undergo chemisorption (Herbst et al. 2005). 3

Quantum dynamics of the Eley-Rideal mechanism of H2 formation

In the Eley-Rideal (ER) abstraction mechanism an H atom from the gas phase impinges on an adsorbed H atom to yield a desorbed H2 molecule. To our knowledge, Morisset et al. (2003b and 2004a Paper III) are the only authors who have investigated quantum mechanically the dynamics of the ER mechanism with three really active atoms, namely: the gas phase H atom, the initially chemisorbed (finally abstracted) H atom and the puckered C-atom. The investigation was restricted to the on top collinear case where the three atoms are constrained to move along a line perpendicular to the graphite basal plane. The calculations made use of the DFT PES determined by Jeloaica & Sidis (2001). In this latter PES a tiny barrier (12meV high) exists in the entrance reaction path (H-H distance ≈ 3.17 ˚ A)(Morisset et al. 2003a,b). Accordingly the ER reaction would barely occur below collision energies corresponding to ∼ 100 K. Similar PES calculations by Sha et al. (2001, 2002) also showed a small barrier in the entrance path of the reaction. While it is not expected that DFT calculations warrant such an accuracy at large inter-particle distances, this feature is still worth keeping in mind. Morisset et al. (III) investigated the ER reaction at collision energies between 0.4 meV and 0.46 eV. The reaction probability is 100% at all energies above 16 meV. It drops to 50% at 9.3 meV and then steadily decreases at lower energies. This is related to the above-mentioned barrier in the entrance channel. The state-to-state reaction probabilities have a much more complicated energy dependence, and exhibit many structures related to resonances. In the whole collision energy range studied, nearly 87% of the available energy (4.27 eV + collision energy) goes into the H2 vibration. The energy left in the vibration of the released C atom about the surface plane is 8-10 times lower, and the translational energy of the nascent H2 is still smaller (0.2 eV - 0.3 eV). At collision energies below 0.1 eV the vibrational distribution of the H2 molecule spans the range 6 < v < 11 with a maximum at v = 8-9. Another interesting result of this study is that quasi-classical trajectory (QCT) calculations consistently reproduce the quantal results at all energies above the entrance reaction barrier.

4

Molecules in Space & Laboratory

The exact 3D quantal results of III are admittedly limited by their restriction to the “collinear case”. Sha et al. (2002) actually studied the ER reaction without this restriction by resorting to a LEPS-type PES model adjusted to DFT data points for both collinear and quasi-collinear configurations. Yet they have actually dealt with approximate 2D-quantum dynamics calculations for the so-called “rigid puckered lattice case” and “relaxed case” which respectively correspond to the “sudden” and “adiabatic” approximations of Morisset et al. (2003a). Comparing these results indicates that non-collinear effects shift the H2 vibrational distribution to lower values by typically 2-3 quanta for collision energies lower than 0.1 eV. This may be taken as a rough estimate of non-collinear effects on the exact 3D results of III. The above studies show that the ER mechanism is problematic. For chemisorbed H atoms the main trouble comes from the barriers that have to be overcome: (i) the activation barrier for the prior chemisorption step and (ii) the entrance barrier for the ER reaction itself. Another trouble is the large internal energy in which the product molecule is left. This is true not only for the chemisorbed case but also for the physisorbed one (Sha et al. 2002). Recent experiments with presumably physisorbed H atoms on graphite (Islam et al. 2007) also indicate significant vibrational excitation (v ∼ 4) of the nascent H2 molecules though not as high as that found in the theory. This high internal energy is at variance with what is presently inferred from astrophysical observations (Giannini et al. 2004). 4

Quantum dynamics of the Langmuir-Hinshelwood mechanism of H2 formation

In the Langmuir-Hinshelwood (LH) associative desorption mechanism two adsorbed and mobile H atoms interact to recombine and desorb as an H2 molecule. As indicated in Sec. 2 physisorbed H atoms onto a graphite surface are quite mobile and thus should ideally lend themselves to the LH reaction. Morisset et al. (2004b, 2005) have studied this reaction quantum mechanically by the wavepacket propagation technique. In the calculations the substrate is assumed to be flat and rigid. The PES is represented by pairwise additive potentials among which the Hgraphite physisorption contribution is given the functional dependence proposed by Ghio et al. (1980) with their measured binding energy (43.3 meV) and the computed position of the potential well minimum (4.18 ˚ A) (II). The H atoms interact via a standard H2 Morse function. Except for these model approximations the calculations are exact in that they take full account of the four relevant degrees of freedom: the distance Z of the H2 center of mass from the surface plane and the three spherical coordinates of the H2 bond vector r(r, ϑ, ϕ) or, equivalently, the distances z1 and z2 of the two H atoms relative to the surface plane and the two cylindrical coordinates ρ (= r sinθ) and ϕ of the r bond vector. As the potential does not depend on ϕ, the wave function is expanded in partial waves eiνϕ and each ν is treated independently. ν is the projection of the angular momentum of the H-H motion along the Z axis. Classically, when ν = 0 the H-H motion takes place in the plane perpendicular to the surface (cartwheel-like); when ν increases more and more the plane containing the H-H motion becomes more and more oblique (helicopter-like). For small values of ν one may easily understand how the H+H collision and scattering near the rigid surface, i.e. without energy exchange with the surface, produces H2 : the H-H scattering causes one atom to be sent towards the vacuum and the other atom towards the surface; the latter atom thus rebounds and finally moves towards

H2 formation at graphitic dust grains

5

the vacuum too. This gives rise to a quite stretched H2 molecule that should thus contain substantial vibrational energy. In the simplest case, the translational energy of the nascent H2 molecule is large enough to lead to a direct desorption. Otherwise, the H2 molecule is trapped in a quasi stationary state where it oscillates in the physisorption well with a significant amount of vibrational and rotational energy. As these H2 motions are hindered by the surface there is a coupling between them and the H2 -surface translation, which allows for the escape of the molecule.

2.5

0

T (Kelvin) 250

500

Efficient length (Å)

2 1.5 1 0.5 0

0

25 Collision energy (meV)

50

Fig. 1. The LH “efficient length”. The full line refers to the quantum calculation and the dots to the quasiclassical trajectory (QCT) calculation.

The study of Morisset et al. (2004b, 2005) was undertaken in the energy range 4 meV - 50 meV for both para- and ortho-H2 . For relatively small ν values (< 6) the reaction probabilities are wildly bristling with complicate resonance structure; on the average they decrease from 80% to 50% as energy increases. The average reaction probabilities globally decrease with ν and fade away around ν ≈ 12 while quantum resonance spikes show up clearer and narrower. The relevant sum over ν of the reaction probabilities actually provide a so-called “efficient length”; the latter reflects the cross section when multiplied by another typical length (say 2 ˚ A) representative of the z-extent of the H atom vibrational motions in their physisorbed ground states. The “efficient length” steadily decreases from 2 ˚ A to 0.5 ˚ A in the investigated energy range (Fig.1). No significant ortho/para effect is found. It is remarkable that the quasiclassical QCT results quite nicely reproduce the quantal ones when looked at on the average. It is found that for each rotational quantum state j populated the vibrational distribution is peaked at its maximum allowed value (little translation). On the whole the rotational distribution covers the range below j = 20 and has a maximum at j ≈ 10-11; the vibrational distribution lies in the range 5 < v < 15 and peaks near v ≈ 11-13. The discussed LH process is seen to be quite efficient. However, the weakness of the

6

Molecules in Space & Laboratory

H-surface bond makes it unlikely to have simultaneously two H atoms physisorbed on the surface. In the diffuse regions of the ISM the dust grain is exposed to UV radiation from the surrounding stars; grain heating above 20 K readily leads to evaporation of the physisorbed H atoms (Pironello et al. 2000) before they may encounter. Another problem is the quite large vibrational energy of the nascent molecule which, as pointed out above (Sec. 3), has no counterpart in the astrophysical observations. 5

Surface impurities . . .

Rougeau et al. (2006) have investigated the adsorption properties of two H atoms on the same carbon ring of a graphite surface. They had in mind to consider the first chemisorbed H atom as constituting a surface defect for the subsequent adsorption of a second H atom. They have thus examined in some detail how the prior adsorption of one H atom influences the adsorption properties of a second one. Their study has dealt with both site and spin (↑↓ ”singlet coupling” or ↑↑ ”triplet coupling”) effects. There are three possible ways of chemisorbing two H atoms on the same carbon ring of a graphite surface: (i) ortho, nearest neighbor site; (ii) meta, next neighbor site; and (iii) para, opposite site. Among the six possible site and spin cases the para site for singlet spin coupling is really peculiar: contrary to all the other situations there is no barrier to chemisorption already when the C atom underneath is still lying in the surface plane; for this situation the binding energy is 0.58 eV. The C out of plane displacement (puckering) is not a prerequisite for the second H atom chemisorption. However, the puckering enhances the chemisorption energy by ∼ 1eV. Similar information has been obtained concurrently in an independent work by Hornekaer et al. (2006b). The absence of barrier and the increased chemisorption energy thereby make the para site a quite interesting candidate for H2 formation by the ER mechanism in the temperature conditions of the ISM. 6

Eley-Rideal formation of H2 involving one of two para-chemisorbed H atoms on a graphite surface.

Following the findings of Rougeau et al. (2006), Bachellerie et al. (2007) have investigated theoretically the ER reaction (noted ER2) in which a third H atom from the gas phase (HIII ) interacts with one of the two para-chemisorbed H atoms (say HII ). The study, undertaken for collision energies in the range 1 meV - 0.5 eV, was restricted to the “collinear case” where three atoms, namely: the H atom from the gas phase (HIII ), the initially para-chemisorbed H atom (HII ) and the C atom underneath (CII ) move along a line perpendicular to the surface. The puckered CI atom at the opposite site and the impurity HI attached on top of it remain fixed throughout the reaction.The results have been systematically compared with those of the ER reaction (noted ER1) for the singly chemisorbed H atom case (Paper III). The 3D PES for ER2 has been computed using DFT as delineated in Secs. 1-3. An important finding is that, contrary to ER1, the PES exhibits no barrier to the reaction. Accordingly, the ER2 QCT reaction probability is 100% at all investigated energies. Moreover, owing to the higher binding energy by 1.1 eV of the para-chemisorbed H atom as compared to a singly chemisorbed one, the exothermicity of ER2 is lower than that of ER1 by this amount. The energy sharing between degrees of freedom (Fig. 2) shows, as in ER1, that most of the available energy goes into H2 vibration; yet the average

H2 formation at graphitic dust grains

7

4

Energy (eV)

3

2

0,5

0,0 10

-3

10

-2

10

-1

Collision Energy (eV)

Fig. 2. Energy sharing in the reactions ER2 (full symbols: QCT) and ER1 (full lines: quantal, open symbols: QCT). Circles: internal (vibration) energy of the H2 molecule; squares: vibration energy of the released C atom about the surface plane; triangles: translation energy of the H2 molecule.

H2 vibrational energy is lower by ∼ 1.3 eV in ER2 than in ER1. This is due, on the one hand, to the reduced exothermicity of the reaction, and on the other hand, to the increase by 0.2 eV of the energy that goes into the CII vibration about the surface plane. The translation energy of the nascent H2 molecule is nearly the same in both ER2 and ER1. The H2 vibrational distribution for ER2 reflects what has just been stated: grossly the distribution found for ER1 is now shifted by 1.3 eV to lower energies and peaks near v ≈ 5 (instead of v ≈ 8-9 for ER1). 7

Conclusion and outlook

The above review gathers the successive steps taken forward at LCAM in the study of the interaction of H atoms at graphitic surfaces in relation with the important problem of H2 formation in the ISM. The results are unprecedented. Non empirical electronic structure calculations based on DFT have shed light on the physisorption and chemisorption characteristics of a single or neighboring H atoms onto graphite. Dynamical studies based on state-of-the-art techniques have been undertaken to explore basic ER and LH recombination mechanisms. The important questions of the energy sharing after the reaction has been addressed. In all cases investigated the internal energy content of the molecule (especially vibration) is found to be quite high. In the ER reaction, though a small fraction of the available energy (0.2 eV - 0.5 eV) is left in the surface this is a substantial contribution to grain heating. In the course of the review we have pointed out what makes this or that adsorption or recombination process problematic. Clearly, the field is open to the further exploration of the energy exchange with the surface phonons as well as to the study of H atom interactions at

8

Molecules in Space & Laboratory

less regular carbonaceous surfaces than graphite. The authors greatly acknowledge regular financial support from the French national programme “Physique Chimie du Milieu Interstellaire” (CNRS-INSU) since the beginning of this work

References Bachellerie, D., Sizun, M., Teillet-Billy, D., Rougeau, N. & Sidis, V. 2007, submitted Bonfanti, M., Martinazzo, R., Tantardini, G.F. & Ponti, A. 2007, J. Phys. Chem. C Letters 111, 5825 Ferro, Y., Marinelli, F. & Allouche, A. 2003, Chem. Phys. Lett. 368, 609 Ghio, E., Mattera, L., Salvo, C., Tommasini, F. & Valbusa, U. 1980, J. Chem. Phys. 73, 556 Giannini, T., McCoey, C., Caratti o Garatti, A., Nisini, B., Lorenzetti, D. & Flower, D.R. 2004, Astron. Astrophys. 419, 999 Herbst, E., Chang, Q. & Cuppen, H.M. 2005, J. Phys.: Conf. Ser. 6, 18 Hohenberg, P. & Kohn, W. 1964, Phys. Rev. B 136, 864 Hollenbach, D.H. & Salpeter, E.E. 1971, Astrophys. J. 163, 155 ˇ ˇ Xu, W., Otero, R., Rauls, E., Stengaard, I., Lægsgaard, Hornekær, L., Sljivancanin, Z., Hammer, E.B. & Besenbacher, F. 2006a, Phys. Rev. Lett. 96, 156104 ˇ ˇ Otero, R., Zecho, T., Steensgaard, I., Hornekær, L., Rauls, E., Xu, W., Sljivancanin, Z., Lægsgaard, E., Hammer, B. & Besenbacher, F. 2006b, Phys. Rev. Letters 97, 186102 Islam, F., Latimer, E.R. & Price, S.D. 2007, J. Chem. Phys. 127, 064701 Jacobson, N., Tegner, B., Schr¨ oder, E., Hyldgaard, P., & Lundqvist, B.I. 2002, Comput. Mater. Sci. 24, 273 Jeloaica, L. & Sidis, V. 1999, Chem. Phys. Lett. 300, 157 (Paper I) Jeloaica, L. & Sidis, V. 2001, DFT2001: 9th Int. Conf. on the Applications of the Density Functional Theory in Chemistry and Physics, SL de El Escorial, Madrid, 201 Kohn, W. & Sham, W. 1965, Phys. Rev. A 140, 1133 Morisset, S., Aguillon, F., Sizun, M. & Sidis, V. 2003a, Phys. Chem. Chem. Phys. 5, 506 Morisset, S., Aguillon, F., Sizun, M. & Sidis, V. 2003b, Chem. Phys. Lett. 378, 615 Morisset, S., Aguillon, F., Sizun, M. & Sidis, V. 2004a, J. Phys. Chem. A 108, 8571 (Paper III) Morisset, S., Aguillon, F., Sizun, M. & Sidis, V. 2004b, J. Chem. Phys. 121, 6493. Morisset, S., Aguillon, F., Sizun, M. & Sidis, V. 2005, J. Chem. Phys. 122, 194702 Perdew, J.P., Wang, Y. et al. 1992, Phys. Rev. B 46, 6671 Pirronello, V., Biham, O., Manic´ o, G., Roser, J.E. & Vidali, G. 2000 in Molecular Hydrogen in Space, ed. F. Combes, & G. Pineau des Forˆets, (Cambridge: Cambridge Contemporary Astrophysics Series, Cambridge University Press), 71 Rougeau, N., Teillet-Billy, D. & Sidis, V. 2006, Chem. Phys. Letters 431, 135 Schlabach, L. & Z¨ uttel, A. 2001, Nature (London) 414, 353 Sha, X.W. & Jackson, B. 2002, Surf. Sci. 496, 318 Sha, X.W., Jackson, B. & Lemoine, D. 2002, J. Chem. Phys. 116, 7158 Sidis, V., Jeloaica, L., Borisov, A.G. & Deutscher, S.A. 2000 in Molecular Hydrogen in Space, ed. F. Combes, & G. Pineau des Forˆets, (Cambridge: Cambridge Contemporary Astrophysics Series, Cambridge University Press), 89 (Paper II) Zecho, T., G¨ uttler, A., Sha, X., Jackson, B. & K¨ uppers, J. 2002, J. Chem. Phys. 117, 8486 Flower, D.R. 2004, Astron. Astrophys. 419, 999