## 3 Results and Discussion
### Calculated Core-Level Binding Energies, XP Spectra, and Work Function Changes
#### 3.3.3 Coverage Dependence  
As a last aspect it should be addressed to what extent the above conclusions hold for less densely packed polar layers at the interface [42; 113]. To assess that, in a gedankenexperiment we constructed hypothetical low-coverage systems with upright-standing molecules (for details see the Methods  
Figure 5: (**a**) Simulated shifts of carbon 1s orbital energies, \(\Delta\)E\({}_{\text{C1s}}\), as a function of the escape depth of the electrons for the equally docked systems I, VII, and VIII and (**b**) corresponding XP spectra generated from the calculated energy levels. As the substituents significantly impact the extent of the SAMs above the top ring, but its volume density is rather low, the topmost carbon atom of the benzene ring was chosen as the origin of the \(x\)-axis. In this way, the axis is consistent with the \(x\)-axis of Figure 4 and the carbon rings are aligned at essentially the same positions. The large number of data points for each system is a consequence of the two inequivalent molecules per unit cell. Section and the Supplementary Materials). Based on the Helmholtz solution to the Poisson equation, one would expect a linear dependence of the dipole density and, thus, of \(\Delta\Phi\) and \(\Delta\mathrm{E_{Cls}}\) on coverage. The actual coverage-dependence of \(\Delta\Phi\) and \(\Delta\mathrm{E_{Cls}}\) is shown in Figure 6 for the same systems that had already been considered in Figure 3. Interestingly, one observes that \(\Delta\Phi\) changes much more strongly at low than at high coverages. This is a consequence of depolarization effects. These strongly reduce the interface dipoles at high coverages [140; 141; 142; 143; 144; 145; 146; 147; 148]. Therefore, work function changes at full coverages are strongly reduced compared to what one would expect based on the dipoles associated with the adsorption of a single molecule [149]. Another observation in Figure 6 is that the coverage-dependence of the core level binding energies (circles and solid line) is much weaker than that of \(\Delta\Phi\) (squares and dotted line). This is particularly obvious for system VI, for which there is almost no change of \(\Delta\mathrm{E_{Cls}}\) with coverage, while the work function still changes by 0.5 eV. Qualitatively, the behavior is, however, the same for all studied systems, as shown in Figure 7. There, one sees that the energy range covered by the \(\Delta\Phi\) values is significantly larger than that for \(\Delta\mathrm{E_{Cls}}\). As a result, the slope of the linear fit to the dependence of \(\Delta\Phi\) on \(\Delta\mathrm{E_{Cls}}\) (black lines in Figure 7) significantly decreases with decreasing coverage. The main consequence of this observation is that at low dipole densities (in contrast to the full-coverage case, see above) \(\Delta\mathrm{E_{Cls}}\) is no longer a direct measure for the interface dipole. This can be explained by the different degrees of locality with which \(\Delta\Phi\) and \(\Delta\mathrm{E_{Cls}}\) probe the electronic structure of the interface [148; 148; 150]. The value of \(\Delta\Phi\) is determined by the energy difference between the Fermi level and the vacuum level far above the surface, i.e., in the far field. Conversely, core level binding energies probe the electrostatic energy in the immediate vicinity of the atom whose core electron is excited [48]. The latter is comparably close to the interface dipole at the bond between the molecule and the substrate. Thus, the shift in the electrostatic energy due to the dipole is still relevant, even if it is strongly reduced due to the drop of the shift with the inverse of the third power of the distance between atom and dipole.