density of the material. A similar argument holds for the values for diamond, where $V_{\rm dia,theo} \sim 16 - 23$ V (theory) and $V_{\rm dia,exp}
\sim 15 - 21$ V (experiment).

The obvious discrepancy between the values of $V_{\rm subs}$ and $V_{\rm HL}$ cannot be resolved here. Possible origins of the discrepancies are (i) the underestimation of the substrate thickness by the manufacturer[@RB98; @AWWB03] and (ii) an increase of the internal potential for thin films similar to the increase of the internal potential in small Au clusters.[@IAO+03] Note that the latter effects would not have been observed for the thicker films with $d \ge 35$ nm in the investigations by Harscher and Lichte.[@HL98] We will discuss the implications of the discrepancy for the present work where appropriate.

Theory: density functional theory calculations
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We have calculated the interaction between Au atoms and the carbon substrate using first principles DFT calculations in the generalized gradient approximation (GGA).[@WP91] For all calculations we used the highly accurate Projector Augmented Wave method [@Bloe94] as implemented in the VASP electronic structure program.[@KJ99]

For the carbon substrate we used both a graphite surface as well as a model a-C surface consisting of 150 carbon atoms.[@DFTquote] The 