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FORMATION OF MOLECULAR HYDROGEN ON A GRAPHITE
SURFACE
S. Morisset1, F. Aguillon 2, M. Sizun 2, V.
Sidis 2 1 Laboratoire de Mécanique, Physique
et Géosciences, Université du Havre, FRANCE 2
Laboratoire des Collisions Atomiques et
Moléculaires, Université Paris-Sud, FRANCE
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INTERSTELLAR MEDIUM
- Composition - gas
(99) - dust
grains(1)
H
90
H2
He 10
Carbon
Silicate

• Physical conditions
• - dense clouds 103 - 107 H atoms / cm3
  
• - low temperature 10K
• Question
• How H2 is formed ?

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INTRODUCTION
- H2 fundamental constituant in cold
interstellar dust grains 10 K - Hypothesis of
H2 formation Two mechanisms are known

LANGMUIR-HINSHELWOOD
ELEY-RIDEAL
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The graphite surface is modelled by a coronene
C24H12 ( V. Sidis, L. Jeloaica, A.G.
Borisov and S.A. Deutscher in "Molecular
hydrogen in space, (Cambridge University
Press2000) pp.89-97.)
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WAVEPACKET METHOD

• DIRECT solution of the time dependent
  Schrödinger equation
• Evaluation of Hamiltonian action on the wave
  function

Fourier method
Gauss-Legendre method
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WAVEPACKET METHOD

• Propagation performed by Lanczos method
• Obtention of reaction probability by projection
  at each time step
• of the wave function on rovibrational states of
  H2 formed
• gt flux analysis method

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MAPPING

• Mapping in reactive valley

Potential minimum at each value of C-H distance
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MAPPING

• Mapping in reactive valley

We introduce a new coordinate x , which is a
function of x (the unmapped coordinate) x grid
non equidistant x grid equidistant !!! the
step dx in the interaction zone is smaller than
in the asymptotic zone

• Advantages
• - faster calculation (6x to 8x)
• - reduction of the number of
  gridpoints (500?100)

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ELEY-RIDEAL MECHANISM
Sudden approximation ? the carbon atom is
fixed
Carbon atom movement surface  relaxation 
gt 3 degrees of freedom
gt 2 degrees of freedom
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REACTION PROBABILITY
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LANGMUIR-HINSHELWOOD MECHANISM
- H atoms are physisorbed - they can freely
migrate on the surface - the study - full
dimensionality - ? (jz) is a constant of
motion - for each ? we perform a wavepacket
calculation with 3 degrees of freedom (R, r,
?) 0 lt ? lt 16
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PROBABILITY
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CROSS SECTION
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CONCLUSION
Methods
- Wavepacket calculation _at_ small collision
energy - Mapping technique ?  small  grid
Eley-Rideal mechanism
- surface relaxation favours the reaction
Langmuir-Hinshelwood mechanism

• - More efficient than ER

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PERSPECTIVES
Eley-Rideal Mechanism
- The relaxation of the substrate favours the
reaction ? Account of vibrational modes of ALL
carbon atoms of the surface - How H atom can
chemisorb on the graphite surface? Potential
wall 0.25eV ? Rôle of deffects - Isotopic
effects ? ? HD, DH, D2, HT, TH, T2 -
Chemisorption on other surfaces ? ? silica ?
Ice ?
Langmuir-Hinshelwood Mechanism
- H lifetime on the grain is VERY low _at_ Tgt30K ?
Alternative LH mechanism physisorbed H collides
chemisorbed H ? Rôle of the porosity of the
surface ? other surfaces silica ? Ice ? -
Isotopic effects ? ? HD, D2, TH, T2