Charge−quadrupole interaction energy calculation

The energy is calculated for a given molecule at site r_j as a discrete sum including all other molecules (at sites r_i) in the considered geometry, according to

with the quadrupole tensor Q_i of molecule i and the relative dielectric permittivity (assuming ε_r = 2.8⁵⁶ for all F_nZnPcs). Hereby, q_j,k is the fractional excess charge at atom k of the molecule j and r_j + τ_k is its position. The quadrupole tensor and the fractional excess charges are obtained in gas phase for all molecules in their respective relaxed structures. The charge distributions and the resulting quadrupole moments might slightly differ in the film phase due to the surrounding polarisable medium. The film structure was generated according to the crystal structure of CuPc⁵⁷ (see Supplementary Figs. ¹–⁴). We assume a simplified orthorhombic lattice and take the intermolecular distances (approximately constant 3.8 Å and 13.5 Å) from literature^28,30. For face-on geometry, a film thickness of 20 nm implies that we take into account 53 layers along the surface normal. We restrict the summation in lateral directions to a large area of 400 nm × 400 nm, which is sufficient for convergence. For edge-on geometry, we have 15 layers in the direction of the surface normal for a 20 nm film, while the lateral dimension of the integration region is equally big. To investigate the relevant range for the interaction energy, we vary the summation in lateral direction between 10 and 200 nm (Supplementary Fig. ⁵). In addition, we reduced the thickness of the film in edge-on orientation from 20 to 3 nm and observe an increase of the interaction energy by 10% for ZnPc, in good agreement to the change of IE observed in experiment (Fig. 2d).