The use of atom-surface band structures as a framework for considering quantum effects in surface diffusion
1Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK
2London Centre for Nanotechnology, University College London, London, WC1H 0AH, UK
3Shulich Faculty of Chemistry, Technion, Haifa 32000, Israel
4Science Institute, VR-III, University of Iceland, 107 Reykjavik, Iceland
5Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
6Department of Chemistry, University of Reading, Whiteknights, RG6 6AD, UK
We have used the helium spin echo (HeSE) technique to study the temperature dependence of H and D diffusion on the Cu(111), Pt(111) , Ru(0001) , and Ni(111) surfaces, finding both activated and tunnelling diffusion regimes. The quantum states occupied by the H/D atoms are central to any discussion of surface dynamics, so we have calculated the band structures of the H/D atoms moving in a 3D atom/surface potential derived from DFT calculations. These band structures are then used within a transition state theory formalism to calculate temperature dependent diffusion rate. Good agreement is found both with the adatom vibrational frequencies measured with EELS [3-6] and with the rate of diffusion in the 'activated' regime for all of the substrates indicating that the adatom-surface energy correlation time must be comparable with the time taken for the moving adatoms to complete a jump. However, the simulations significantly underestimate the diffusion rates in the tunnelling regime. We show that even in the tunnelling regime the band structures can be used as a basis for a discussion of the observed diffusion rates.
It is widely assumed that quantum effects are essentially limited to hydrogen diffusion. We present HeSE data that shows that during jumps on the Ni(111) surface, CO moves ballistically with an effective mass some 200 times larger than its actual mass. An empirical 2D CO-surface potential energy surface is constructed from the measured CO adsorption site energy differences and from the activation barrier to lateral diffusion. The calculated band structure of the CO centre of mass motion predicts an increase in effective mass for the diffusion CO that is comparable with the experimentally measured value. It is likely that the 3-fold increase in effective mass for methane diffusion on Pt(111) observed with ToF-quasi elastic helium scattering has a similar cause . The observation of such a large effective mass for a relatively massive molecule suggests that quantum effects can have a significant effect on the diffusion of relatively massive ad-species and will sometimes need to be included in attempts at first principles predictions of diffusion rates.
 A. P. Jardine et. al., Phys. Rev. Lett. 105, 136101 (2010)
 E. M. McIntosh et. al., J. Phys. Chem. Lett. 4, 1565 (2013)
 E. M. McCash et. al., Surf. Sci. 215, 363 (1989); C. L. A. Lamont et. al., Chem. Phys. Lett. 243, 429 (1995); G. Lee and W.E. Plummer Surf. Sci. 498, 229 (2002)
 S. C. Badescu et. al. Phys. Rev. Lett. 88, 136101 (2002)
 K. L. Kostove et.al., Surf.Sci. 560, 130 (2004)
 W. Ho et. al., J. Vac. Sci. and Technol 17, 134 (1980)
 A. P. Graham, J. Ellis, and J.P. Toennies, unpublished work