palladium or ruthenium, the adsorbed atoms may interact with each other, however,
even at distances larger than the distance between two neighboring metal atoms.
Six dimensional calculations on the H 2 /Pd(111) system are currently being carried
out and will be published elsewhere, together with a scrutinized discussion of the
vibrational structure of the adsorbates.
4 Conclusions
The present studies of the diffusion motion of CO on Cu(100) have revealed
two facts:
1. Realistic 1D models of the diffusion motion in combination with the theory
developed by van Hove [4] allow us to rationalize the quasi-elastic broadening
of the
3 He spin echo experiments observed in [3]. To this end, we have to
assume that the total quasi-elastic broadening is given as the sum of the diffusion
broadening and the broadening due to non-adiabatic couplings, or couplings to
the phonon bath—the latter being related to the “friction” rate. Furthermore,
assuming reasonable values for the “friction” rate, we show that the broadening
observed in the experiments is an actual broadening difference.
2. When setting the “friction” rate to much smaller values, these models allow us
to correlate the observed variation of the quasi-elastic broadening as a function
of the momentum transfer with the tunneling splitting of low lying vibrational
levels. These splittings occur at low coverage degrees and are a genuine manifestation of a quantum effect.
Similar findings are found for the H/Pd(111) system, for which the present
results are so far predictions based on vague assumptions and simple models
regarding the intrinsic lifetimes of vibrational states. Full 6D treatments of the
diffusion dynamics of CO/Cu(100) as well as of H 2 /Pd(111), in which we shall also
consider in a more realistic way lifetimes of vibrational states of the adsorbates will
shed more light into the problem. In particular, such studies would enable us to
truly simulate the experimentally determined intermediate scattering function and
herewith give accurate values for the diffusion rate of adsorbates from first principle
calculations.
Acknowledgments This work was carried out within a research program from the Agence Nationale de la Recherce (project ANR 2010 BLAN 720 1). We thank ANR for the generous
financial support, as well as CNRS and Université de Strasbourg.
Note: Since the submission of this manuscript, the diffusion rate for the H/Pd(111) system has
been calculated from the DSF with in a realistic model and no adjustable parameters. These results
have been published recently [22].
Full Quantum Calculations of the Diffusion Rate of Adsorbates
191
even at distances larger than the distance between two neighboring metal atoms.
Six dimensional calculations on the H 2 /Pd(111) system are currently being carried
out and will be published elsewhere, together with a scrutinized discussion of the
vibrational structure of the adsorbates.
4 Conclusions
The present studies of the diffusion motion of CO on Cu(100) have revealed
two facts:
1. Realistic 1D models of the diffusion motion in combination with the theory
developed by van Hove [4] allow us to rationalize the quasi-elastic broadening
of the
3 He spin echo experiments observed in [3]. To this end, we have to
assume that the total quasi-elastic broadening is given as the sum of the diffusion
broadening and the broadening due to non-adiabatic couplings, or couplings to
the phonon bath—the latter being related to the “friction” rate. Furthermore,
assuming reasonable values for the “friction” rate, we show that the broadening
observed in the experiments is an actual broadening difference.
2. When setting the “friction” rate to much smaller values, these models allow us
to correlate the observed variation of the quasi-elastic broadening as a function
of the momentum transfer with the tunneling splitting of low lying vibrational
levels. These splittings occur at low coverage degrees and are a genuine manifestation of a quantum effect.
Similar findings are found for the H/Pd(111) system, for which the present
results are so far predictions based on vague assumptions and simple models
regarding the intrinsic lifetimes of vibrational states. Full 6D treatments of the
diffusion dynamics of CO/Cu(100) as well as of H 2 /Pd(111), in which we shall also
consider in a more realistic way lifetimes of vibrational states of the adsorbates will
shed more light into the problem. In particular, such studies would enable us to
truly simulate the experimentally determined intermediate scattering function and
herewith give accurate values for the diffusion rate of adsorbates from first principle
calculations.
Acknowledgments This work was carried out within a research program from the Agence Nationale de la Recherce (project ANR 2010 BLAN 720 1). We thank ANR for the generous
financial support, as well as CNRS and Université de Strasbourg.
Note: Since the submission of this manuscript, the diffusion rate for the H/Pd(111) system has
been calculated from the DSF with in a realistic model and no adjustable parameters. These results
have been published recently [22].
Full Quantum Calculations of the Diffusion Rate of Adsorbates
191