^{1,2,a)}, Didier Lemoine

^{1,2,b)}, Zuleika Medina

^{3,c)}and Bret Jackson

^{4,d)}

### Abstract

We study the physisorption of atomic hydrogen on graphitic surfaces with four different quantum mechanical methods: perturbation and effective Hamiltonian theories, close coupling wavepacket, and reduced density matrix propagation methods. Corrugation is included in the modeling of the surface. Sticking is a fast process which is well described by all methods. Sticking probabilities are of the order of a few percent in the collision energy range 0–25 meV, but are enhanced for collision energies close to those of diffraction resonances. Sticking also increases with surface temperature. Desorption is a slow process which involves multiphonon processes. We show, however, how to correct the close coupling wavepacket method to account for such phenomena and obtain correct time constants for initial state decay. Desorption time constants are in the range of 20–50 ps for a surface temperature of 300 K.

B. L. thanks F. X. Gadéa for useful discussions on the effective Hamiltonian techniques. This work, supported by the European Communities under the contract of Association between EURATOM, CEA, and the French Research Federation for fusion studies, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Financial support was also received from the French Agence Nationale de la Recherche under Grant No. ANR-08-BLAN-0047-05. B. Jackson gratefully acknowledges support from the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U. S. Department of Energy (DOE) under Grant No. DE-FG02-87ER13744.

I. INTRODUCTION

II. METHODS

A. The Hamiltonian

B. Reduced density matrix propagation

C. Close coupling wavepacket (CCWP)

D. Perturbation theory (PT)

E. Effective Hamiltonian method (EH)

F. Calculation parameters

III. RESULTS

A. Sticking

B. Desorption

IV. CONCLUSION

### Key Topics

- Phonons
- 33.0
- Desorption
- 32.0
- Atom surface collisions
- 19.0
- Bound states
- 13.0
- Surface states
- 13.0

## Figures

Stuck state-resolved populations as a function of time at 10 K (upper frame) and 300 K (lower frame). The initial state corresponds to an hydrogen atom described by a Gaussian wavepacket centered at *z* = 50 a.u. and *E* = 7 meV average energy. The energy uncertainty is 0.9 meV. The labels of the populations are the quantum numbers of the states considered : *v* = 0, 1, or 2 describes the motion of the stuck H-atom perpendicular to the surface, and *g*/*e* refers to the ground or excited mode parallel to the surface. Lines: CCWP results, line-points: RDM results.

Stuck state-resolved populations as a function of time at 10 K (upper frame) and 300 K (lower frame). The initial state corresponds to an hydrogen atom described by a Gaussian wavepacket centered at *z* = 50 a.u. and *E* = 7 meV average energy. The energy uncertainty is 0.9 meV. The labels of the populations are the quantum numbers of the states considered : *v* = 0, 1, or 2 describes the motion of the stuck H-atom perpendicular to the surface, and *g*/*e* refers to the ground or excited mode parallel to the surface. Lines: CCWP results, line-points: RDM results.

Individual sticking probabilities at 10 and 300 K as a function of the collision energy obtained from CCWP. The initial state is a wavepacket centered at *z* = 50 a.u. with a 0.9 meV energy uncertainty. The quantum numbers of the populated states are defined in the caption of Fig. 1.

Individual sticking probabilities at 10 and 300 K as a function of the collision energy obtained from CCWP. The initial state is a wavepacket centered at *z* = 50 a.u. with a 0.9 meV energy uncertainty. The quantum numbers of the populated states are defined in the caption of Fig. 1.

Total sticking probabilities at 10 and 300 K as a function of collision energy. Different models are compared: connected filled circles: RDM; blue continuous lines: CCWP; empty circles: EH; red lines: PT. At 10 K, EH is not shown because it is almost indistinguishable from PT results. Also, at 10 K, RDM (connected filled circles) and CCWP results (plain line) for a flat surface (no diffraction) are also shown.

Total sticking probabilities at 10 and 300 K as a function of collision energy. Different models are compared: connected filled circles: RDM; blue continuous lines: CCWP; empty circles: EH; red lines: PT. At 10 K, EH is not shown because it is almost indistinguishable from PT results. Also, at 10 K, RDM (connected filled circles) and CCWP results (plain line) for a flat surface (no diffraction) are also shown.

Desorption at 300 K. Upper frame: population remaining in the initial state as a function of time. Each line color corresponds to a different initial stuck state. Lower frame: Total stuck population, defined as the sum over the populations of all the bound states of the system (*v* = 0 − 4,g + *v* = 0,e), as a function of time. Each line color corresponds to a different initial stuck state. Lines: corrected CCWP results, see text for the correction procedure. Line-points: RDM results.

Desorption at 300 K. Upper frame: population remaining in the initial state as a function of time. Each line color corresponds to a different initial stuck state. Lower frame: Total stuck population, defined as the sum over the populations of all the bound states of the system (*v* = 0 − 4,g + *v* = 0,e), as a function of time. Each line color corresponds to a different initial stuck state. Lines: corrected CCWP results, see text for the correction procedure. Line-points: RDM results.

Individual populations in different stuck states, for *v* = 0 − 1,g initial states. Surface temperature is 300 K. Lines: corrected CCWP results, line-points: RDM results.

Individual populations in different stuck states, for *v* = 0 − 1,g initial states. Surface temperature is 300 K. Lines: corrected CCWP results, line-points: RDM results.

Same as Fig. 5 for *v* = 0,e and *v* = 2,g initial states.

Same as Fig. 5 for *v* = 0,e and *v* = 2,g initial states.

## Tables

Resonant state energies and their lifetimes obtained from solution of Eq. (11). Energies of approximate separable states are also shown. These states are obtained by neglecting the coupling between the diffraction states and they can be labeled by quantum numbers which are approximate for the resonant states. The first one *v* describes vibration of the H atom with respect to the surface, the second one corresponds to the diffraction state *g* or *e*.

Resonant state energies and their lifetimes obtained from solution of Eq. (11). Energies of approximate separable states are also shown. These states are obtained by neglecting the coupling between the diffraction states and they can be labeled by quantum numbers which are approximate for the resonant states. The first one *v* describes vibration of the H atom with respect to the surface, the second one corresponds to the diffraction state *g* or *e*.

Time constants for exponential decay of the initial state (from modified CCWP results) and total trapped populations (from RDM results). Four different initial states are considered, labeled by the approximate quantum numbers *v* and *g*/*e* describing motion perpendicular and parallel to the surface, respectively. Surface temperature is 300 K.

Time constants for exponential decay of the initial state (from modified CCWP results) and total trapped populations (from RDM results). Four different initial states are considered, labeled by the approximate quantum numbers *v* and *g*/*e* describing motion perpendicular and parallel to the surface, respectively. Surface temperature is 300 K.

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