^{1}and J. R. Manson

^{1,a)}

### Abstract

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam.Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.

This work was supported by the Department of Energy under Grant No. DE-FG02-98ER45704.

I. INTRODUCTION

II. ROTATIONAL INTENSITY SPECTRA

III. DEPENDENCE OF FINAL TRANSLATIONAL ENERGY ON ROTATIONAL ENERGY

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- Molecule scattering
- 26.0
- Rotation measurement
- 22.0
- Excitation energies
- 20.0
- Surface scattering
- 19.0
- Molecular excitation energies
- 18.0

## Figures

Final rotational energy resolved intensity at specular scattering angles for several incident energies and surface temperatures. (a) Data taken from Ref. 9: ; open circles are data for and , solid circles are data for and , open diamonds are data for and , and solid diamonds are data for and . (b) Data taken from Ref. 10. ; open squares are data for and , solid squares are data for and , and triangles are data for and . Curves are calculations.

Final rotational energy resolved intensity at specular scattering angles for several incident energies and surface temperatures. (a) Data taken from Ref. 9: ; open circles are data for and , solid circles are data for and , open diamonds are data for and , and solid diamonds are data for and . (b) Data taken from Ref. 10. ; open squares are data for and , solid squares are data for and , and triangles are data for and . Curves are calculations.

Normal incident energy dependence of the final rotational temperature for specular scattering at . Solid and long dash curves are theory for and 40°, respectively. Solid circles are data for , and open circles are data for . The dotted curve is a least squares fit to the experimental data. Data are taken from Ref. 9.

Normal incident energy dependence of the final rotational temperature for specular scattering at . Solid and long dash curves are theory for and 40°, respectively. Solid circles are data for , and open circles are data for . The dotted curve is a least squares fit to the experimental data. Data are taken from Ref. 9.

Final rotational energy resolved intensity for specular scattering geometry. (a) for and . The times symbols are data at , open circles are data for , and solid circles are data for . Data are from Ref. 11. (b) NO scattering from graphite for and . and 60° as marked. Data are from Ref. 12.

Final rotational energy resolved intensity for specular scattering geometry. (a) for and . The times symbols are data at , open circles are data for , and solid circles are data for . Data are from Ref. 11. (b) NO scattering from graphite for and . and 60° as marked. Data are from Ref. 12.

Final rotational energy resolved intensity at and incident energy for specular scattering of NO from a Pt(111) substrate covered with 0.5 ML of CO. Open circles are data for , solid circles are data for , open squares are data for , and solid squares are data for . Data are from Ref. 13.

Final rotational energy resolved intensity at and incident energy for specular scattering of NO from a Pt(111) substrate covered with 0.5 ML of CO. Open circles are data for , solid circles are data for , open squares are data for , and solid squares are data for . Data are from Ref. 13.

The final rotational energy distribution under specular geometry conditions for several incident energies and surface temperatures for . (a) ; , 350, 640, and as marked. (b) ; and . Symbols are experimental data from Ref. 14, and curves are theory.

The final rotational energy distribution under specular geometry conditions for several incident energies and surface temperatures for . (a) ; , 350, 640, and as marked. (b) ; and . Symbols are experimental data from Ref. 14, and curves are theory.

The rotational temperature as a function of incident energy for . Symbols are experimental data from Ref. 14, and the curve is theory. and .

The rotational temperature as a function of incident energy for . Symbols are experimental data from Ref. 14, and the curve is theory. and .

The final rotational temperature as a function of surface temperature for at and . Symbols are experimental data from Ref. 14, and curves are theory. .

The final rotational temperature as a function of surface temperature for at and . Symbols are experimental data from Ref. 14, and curves are theory. .

The final rotational energy distribution for and surface temperature of for . Symbols are experimental data from Ref. 14, the dash curve is theory with a cold initial rotational distribution of , the long dash curve is theory with initial rotational state with , solid curve is theory with initial rotational state at , and dot dashed curve is theory with initial rotational state at . .

The final rotational energy distribution for and surface temperature of for . Symbols are experimental data from Ref. 14, the dash curve is theory with a cold initial rotational distribution of , the long dash curve is theory with initial rotational state with , solid curve is theory with initial rotational state at , and dot dashed curve is theory with initial rotational state at . .

Final average translational energy as a function of final rotational energy for several incident energies and angles taken at the specular scattering angle for NO scattering from Ag(111). In each panel the experiment and theory for a given incident energy and angle are compared. Open circles are data at , solid circles are data at 45°, solid triangles are data at 30°, and solid squares are data at 15°. Calculations are the curves in each panel. and . Data are taken from Ref. 10.

Final average translational energy as a function of final rotational energy for several incident energies and angles taken at the specular scattering angle for NO scattering from Ag(111). In each panel the experiment and theory for a given incident energy and angle are compared. Open circles are data at , solid circles are data at 45°, solid triangles are data at 30°, and solid squares are data at 15°. Calculations are the curves in each panel. and . Data are taken from Ref. 10.

The normalized most probable translational energy and the sum of the most probable and the rotational energy as functions of the final rotational energy for two incident energies. (a) and (b) . Symbols are experimental data from Ref. 14, and lines are theory. and .

The normalized most probable translational energy and the sum of the most probable and the rotational energy as functions of the final rotational energy for two incident energies. (a) and (b) . Symbols are experimental data from Ref. 14, and lines are theory. and .

Same as Fig. 10 except with calculations for an effective surface mass of .

Same as Fig. 10 except with calculations for an effective surface mass of .

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