^{1,a)}, M. Persson

^{2}, S. Wagner

^{3}, C. Frischkorn

^{3}and M. Wolf

^{3}

### Abstract

A three dimensional model based on molecular dynamics with electronic frictions is developed to describe the femtosecond laser induced associative desorption of from . Two molecular coordinates (internuclear separation and center of mass distance to surface) and a single phonon coordinate are included in the dynamics. Both the potential energy surface and the electronic friction tensor are calculated by density functional theory so that there are no adjustable parameters in the comparison of this model with the wide range of experiments available for this system. This “first principles” dynamic model gives results in semiquantitative agreement with all experimental results; nonlinear fluence dependence of the yield, isotope effect, two pulse correlation, and energy partitioning. The good agreement of theory with experiment supports a description of this surface femtochemistry in terms of thermalized hot electron induced chemistry with coupling to nuclear coordinates through electronic frictions. By comparing the dynamics with the analytical one dimensional frictional model used previously to fit the experiments for this system, we show that the success of the one dimensional model is based on the rapid intermixing of the and coordinates as the H–H climbs out of the adsorption well. However, projecting the three dimensional dynamics onto one dimension introduces a fluence (adsorbate temperature) dependent “entropic” barrier in addition to the potential barrier for the chemistry. This implies that some caution must be used in interpreting activation energies obtained in fitting experiments to the one dimensional model.

Two of the authors (A.C.L. and M.P.) wish to thank the Alexander von Humboldt Stiftung for support of their stays in Berlin where this work was initiated. The authors also wish to acknowledge the Danish Center for Scientific Computing, the Swedish Natural Research Council (VR) and the Deutsche Forschungsgemeinschaft (through SFb450) for support of this work.

I. INTRODUCTION

II. DYNAMIC MODEL

A. Potential energy surface

B. Friction coefficients

C. Langevin dynamics

III. RESULTS

IV. DISCUSSION

V. SUMMARY AND CONCLUSIONS

### Key Topics

- Desorption
- 83.0
- Frictions
- 32.0
- Hot carriers
- 28.0
- Mode locking
- 27.0
- Experiment design
- 25.0

## Figures

Schematic diagram of the 3D dynamic model used to describe hot electron induced associative desorption of from Ru(0001). All symbols are described in the text.

Schematic diagram of the 3D dynamic model used to describe hot electron induced associative desorption of from Ru(0001). All symbols are described in the text.

Diagram of the surface unit cell in the DFT calculations. The large circles are for Ru atoms and the smaller solid circles are H atoms in the configuration. The heavy (blue) circles are surface Ru atoms and the lighter (red) circles are second layer Ru atoms. The small open circle represents H atoms at a distance appropriate to the desorbed molecule. The solid arrows give the assumed desorption path projected onto the surface. The dashed arrows give the higher barrier desorption path.

Diagram of the surface unit cell in the DFT calculations. The large circles are for Ru atoms and the smaller solid circles are H atoms in the configuration. The heavy (blue) circles are surface Ru atoms and the lighter (red) circles are second layer Ru atoms. The small open circle represents H atoms at a distance appropriate to the desorbed molecule. The solid arrows give the assumed desorption path projected onto the surface. The dashed arrows give the higher barrier desorption path.

(a) DFT potential energy (in eV) projected along the minimum energy path for desorption (in angstrom). corresponds to the adsorbed state and corresponds to the asymptote. (b) Electronic friction coefficients along the minimum energy path for desorption .

(a) DFT potential energy (in eV) projected along the minimum energy path for desorption (in angstrom). corresponds to the adsorbed state and corresponds to the asymptote. (b) Electronic friction coefficients along the minimum energy path for desorption .

Contour plot of the two dimensional DFT potential energy surface for for desorption of a single from . Contours are at intervals. The arrow indicates the location of the barrier to associative desorption.

Contour plot of the two dimensional DFT potential energy surface for for desorption of a single from . Contours are at intervals. The arrow indicates the location of the barrier to associative desorption.

Electronic friction coefficients and as a function of electronic temperature for a point on the desorption path, .

Electronic friction coefficients and as a function of electronic temperature for a point on the desorption path, .

Desorption yield for and as a function of adsorbed laser fluence calculated by the 3D dynamic model. The lines are fits of the power law dependences used to describe the experimental data.

Desorption yield for and as a function of adsorbed laser fluence calculated by the 3D dynamic model. The lines are fits of the power law dependences used to describe the experimental data.

The two pulse correlation for associative desorption at a total adsorbed laser fluence of calculated by the dynamic model. The points are the desorption yield for different delays between the two nearly equal laser pulses. The line through the points is simply a visual aid.

The two pulse correlation for associative desorption at a total adsorbed laser fluence of calculated by the dynamic model. The points are the desorption yield for different delays between the two nearly equal laser pulses. The line through the points is simply a visual aid.

The translational temperature of desorbed and calculated by the dynamic model as a function adsorbed laser fluence .

The translational temperature of desorbed and calculated by the dynamic model as a function adsorbed laser fluence .

(a) Typical associative desorption trajectory for following an adsorbed laser fluence of overlayed on the 2D PES. (b) Typical trajectory that does not associatively desorb following an adsorbed laser fluence of overlayed on the 2D PES. (c) The total energy projected onto as a function of time for the two trajectories in (a) and (b) as labeled in the figure. Note the constant with at the time of desorption for the trajectory in (a).

(a) Typical associative desorption trajectory for following an adsorbed laser fluence of overlayed on the 2D PES. (b) Typical trajectory that does not associatively desorb following an adsorbed laser fluence of overlayed on the 2D PES. (c) The total energy projected onto as a function of time for the two trajectories in (a) and (b) as labeled in the figure. Note the constant with at the time of desorption for the trajectory in (a).

The electron temperature , phonon temperature and adsorbate temperature as a function of time following a laser pulse at of fluence . The bar graph is the induced rate of associative desorption as a function of .

The electron temperature , phonon temperature and adsorbate temperature as a function of time following a laser pulse at of fluence . The bar graph is the induced rate of associative desorption as a function of .

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