Large Distortion of Fused Aromatics on Dielectric Interlayers Quantified by Photoemission Orbital Tomography

Polycyclic aromatic compounds with fused benzene rings offer an extraordinary versatility as next-generation organic semiconducting materials for nanoelectronics and optoelectronics due to their tunable characteristics, including charge-carrier mobility and optical absorption. Nonplanarity can be an additional parameter to customize their electronic and optical properties without changing the aromatic core. In this work, we report a combined experimental and theoretical study in which we directly observe large, geometry-induced modifications in the frontier orbitals of a prototypical dye molecule when adsorbed on an atomically thin dielectric interlayer on a metallic substrate. Experimentally, we employ angle-resolved photoemission experiments, interpreted in the framework of the photoemission orbital tomography technique. We demonstrate its sensitivity to detect geometrical bends in adsorbed molecules and highlight the role of the photon energy used in experiment for detecting such geometrical distortions. Theoretically, we conduct density functional calculations to determine the geometric and electronic structure of the adsorbed molecule and simulate the photoemission angular distribution patterns. While we found an overall good agreement between experimental and theoretical data, our results also unveil limitations in current van der Waals corrected density functional approaches for such organic/dielectric interfaces. Hence, photoemission orbital tomography provides a vital experimental benchmark for such systems. By comparison with the state of the same molecule on a metallic substrate, we also offer an explanation why the adsorption on the dielectric induces such large bends in the molecule.


SI3. Dependence of the calculated PTCDA bend on the approach to treat the van der Waals interaction and on the work function of the MgO(001)/Ag(001) substrate
summarizes the values of the PTCDA bend obtained with different approaches for treating the van-der-Waals forces and different densities of extra oxygen at the oxide-metal interface, which strongly affects the work function of the MgO(001)/Ag(001) substrate. The magnitude of the bend clearly depends on the type of calculation employed with the argueably more objective vdW DFT methodology resulting in a ~0.1 Å lower bend than that of the PBE-TS calculations. The bend decreasing for lower substrate work functions is related to the increase in charge transfer to the LUMO and concomitant increase in electrostatic attraction. For the hypothetical bends of Figure 3 distortions beyond those predicted by the on surface calculations have been obtained by extrapolating the trajectories of the atomic positions within the molecule on the different work function substrates.

SI4. Considerations beyond the plane wave approximation of isolated molecules
To test if the discrepancy between experimental and simulated momentum maps might be explained by factors other than an altered shape of the molecular backbone, additional calculations have been carried out. Those comprised (i) a more accurate description of the final state with time-dependent density functional theory (TD-DFT), (ii) accounting for molecule-molecule interactions in the freestanding monolayer as well as (iii) including the substrate. The results are briefly discussed below.

i. Influence of the final-state approximation on the momentum maps
It has been suggested that the planarity of the molecule is a criterion for the validity of the plane-wave approximation [1]. Thus, it was first tested whether the approximation can properly capture the effect of the bend. This was achieved by simulating momentum maps for the isolated bent molecule with the time dependent DFT (TD-DFT) method, which essentially makes no assumptions of the final state (SI 5), and comparing these maps to the ones generated on the basis of the plane-wave approximation.
As can be seen in Fig. S3, the k-map of the HOMO obtained from TD-DFT is very similar to that obtained with the plane-wave final state approximation. Thus, it is concluded that final-state effects cannot account for the observed discrepancies between theory and experiment, which therefore have been attributed to the geometry of the molecule being more distorted than predicted by the DFT calculations.

ii. Influence of molecule-molecule interactions on the momentum maps
Secondly, the role of intermolecular interactions in the monolayer was evaluated by a DFT calculation of the free-standing monolayer with the atoms fixed to the positions found in calculations on the surface. The effect on the maps on the PTCDA LUMO and HOMO is shown in Fig. S4 and Fig. S5, respectively. Here the simulations have the polarization factor included and have not been symmetrized to simulate the raw experimental momentum maps shown. The two figures compare the maps of the free-standing layer in the second row to maps of the isolated molecule in the first row and the experimental maps in the fourth row for three different photon energies (columns). While there is little change in the resulting momentum map of the LUMO, changes are slightly more pronounced in the map of the HOMO. However, including the intermolecular interactions results in no apparent improvement of the fit with the experimental maps.

iii. Influence of the substrate on the momentum maps
Thirdly, the influence of the substrate on the electronic structure was evaluated by comparing calculations of the molecule on the surface to the calculations of the isolated molecule. The former are shown for the LUMO and the HOMO in the third row of Fig. S4 and Fig. S5, respectively. The comparison with the experimental maps in the fourth row of the figures shows that despite the use of damping in the final state to account for the surface sensitivity of POT [2], the contribution of the Ag substrate to the k-maps is significantly overestimated. Besides, the emission intensity of the HOMO is much more focused at the center of the emission feature compared to the free-standing molecular film, while the minor lobes of the LUMO adopt a more circular shape. This is surprising given that the frontier orbitals themselves are not involved in a chemical interaction with the substrate and even on metals, the influence of the substrate is small, as indicated by the close agreement between experimental maps and simulated maps of the molecule in the gas phase. However, accounting for the substrate does not lead to a clear improvement of the fit, and therefore a larger bend remains the most likely explanation for the differences between the theoretical and experimental maps. All simulations were carried out in the plane-wave approximation [3].

SI5. Methodology of the TD-DFT calculations
In time-dependent density functional theory calculations, the gas-phase molecule was subjected to a photon field and the flux of outgoing electron density was recorded over time [4] [5] with TD-DFT as implemented in the real-time real-space code OCTOPUS [6]. The electronic ground state was simulated in a spherical box (radius: 25 Å, grid spacing: 0.2 Å) and in the local density approximation [7] [8]. The system was then propagated for 10 fs, coupled to an electromagnetic field that would correspond to a laser with an intensity of 5•10 8 W/cm 2 at 40.8 eV photon energy. To eliminate nonadiabatic effects, the field was ramped up and down for 8 cycles each at the beginning and the end of the simulation. Throughout the simulation time, the outgoing photoelectron flux was recorded at half the simulation box radius, followed by a complex absorbing potential to avoid double-counting of reflected electrons [9].