5.4 Scattering of the CH 4 on Ni(111) Using SRP Density Functional
5.4.3. Site Averaged Probability
The site-averaged probabilities are plotted in Fig. 5-29. The probability to find the scattered molecules in ν3 and ν1 state are about 85% and 10%, respectively. The
experimental data reported the 40% and 15% value for ν3 and ν1 states. We also find about
2.5% probability for transition to the 2ν2 state from ν3 at higher incident energies, which is
comparable with the experimental value of 2%.
Figure 0-29. Site-averaged distribution of vibrational modes in scattered beam for incident beam excited to ν3 state, using the SRP functional.
110
Finally, in Fig. 5-30, we compare the site-averaged probability distribution using PBE and SRP functional. The probabilities correspond to PBE functional are shown with dashed lines and labeled as "PBE". The solid lines with no label correspond to SRP functional. As you can see, using the SRP functional correct the result at higher incident energies.
Figure 0-30. The site averaged probability using SRP (solid lines) and PBE (dashed lines) functional.
5.5 Summary
In summary, we have studied the vibrationally inelastic scattering of CH4 from a
Ni(111) surface to monitor the transitions between the vibrational states upon the collision with the surface. We find that interaction with the metal surface causes energy transfer between the vibrational states. We excite the incident beam into the antisymmetric stretch state, ν3, and compute the distribution of vibrational states in the scattered beam. The
probability distribution has been found for impact on four sites in the unit cell: The top, bridge, half-bridge and near-hollow sites. We averaged the results for the four sites to
111
approximate the site-averaged probability. The same set of calculations have been done using the PBE and SRP functionals. The SRP functional we use is a linear combination of the RPBE and PBE exchange functionals and a correlation function that describes the van der Waals forces, each with a proper weight. As a result of considering the vdW forces using the SRP functional, we find an adsorption well of about -0.2eV and the result for energy distribution changes for impact with higher incident energies.
112
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