Nature of Optical Excitations in Porphyrin Crystals: A Joint Experimental and Theoretical Study

Abstract

The nature of optical excitations and the spatial extent of excitons in organic semiconductors, both of which determine exciton diffusion and carrier mobilities, are key factors for the proper understanding and tuning of material performances. Using a combined experimental and theoretical approach, we investigate the excitonic properties of meso-tetraphenyl porphyrin-Zn(II) crystals. We find that several bands contribute to the optical absorption spectra, beyond the four main ones considered here as the analogue to the four frontier molecular orbitals of the Gouterman model commonly adopted for the isolated molecule. By using many-body perturbation theory in the GW and Bethe-Salpeter equation approach, we interpret the experimental large optical anisotropy as being due to the interplay between long- and short-range intermolecular interactions. In addition, both localized and delocalized excitons in the π-stacking direction are demonstrated to determine the optical response, in agreement with recent experimental observations reported for organic crystals with similar molecular packing.

Figure 1

(a) AFM (10 μm × 10 μm) height image of a 1 nm thick ZnTPP film grown on (010)_KAP. The [001]_KAP direction is reported in the panel. (b and c) Top and side views of the structure of a ZnTPP molecule in (b) the gas phase and (c) the triclinic crystal, respectively: H atoms in white, C in gray, N in light purple, and Zn in blue. (d) Structural model of the triclinic ZnTPP crystal with a perspective view along the [010]_ZnTPP axis. X- and Y-axes in panels c and d are reference axes lying in the molecular plane (see the text). (e) Normal incidence absorption spectra of the sample in panel a, as collected for light polarization E//[001]_ZnTPP and E⊥[001]_ZnTPP (red and black lines, respectively). A constant background has been subtracted for better comparison.

Figure 2

(a) GW band structure of ZnTPP crystal. Letters on the right indicate ranges of bands used in computing the optical spectra (see Figure 3d). Energy zero is set at the valence band maximum (VBM); CBM refers to the conduction band minimum. (b) |Ψ|² of selected states calculated at Γ.

Figure 3

Computed absorption spectra of (a) the ZnTPP crystal for the two indicated orientations of the electric field, (b) the isolated gas-phase ZnTPP molecule, and (c) the isolated ZnTPP molecule having the conformation it takes in the bulk crystal, for light polarized along the X- and Y-axes (see Figure 1c). A broadening of 0.05 eV is used throughout. (d) Optical spectrum of the ZnTPP crystal calculated for polarization with E//[001]_ZnTPP, as obtained by including an increasing number of states in the excitonic Hamiltonian (ranges a–e are indicated in Figure 2). Curves a–e include coupling; curve a(TDA) does not.

Figure 4

Square modulus of the excitonic wave function (green isosurface at 2% of the maximum value) obtained by fixing the hole position in a given molecule (large red circle). Top panels: Q, B, and B₁ excitons. Bottom panels: B* and B₁* excitons. The unit cell axes are reported: a_ZnTPP in green, b_ZnTPP in blue, and c_ZnTPP in red.