Exciton models

Our experimental investigation of excitons in organic semiconductors are closely combined with theoretical modelling. Currently, microscopic models for the exciton structure are mainly developed in collaboration with Karin Schmidt from the Brédas Group.

Holstein models

one-dimensional molecular chains with arbitrary exciton-phonon configurations

example for a Frenkel exciton model: see Figure

Holstein model with one Frenkel exciton and linear coupling to one internal molecular vibration
basis set contains states where phonons can be excited at finite distances from the exciton
Hamiltonian is numerically diagonalized
left part of figure: position and spectral weight of eigenstates (corresponds to absorption spectrum)
right part of figure: internal structure of the phonon clouds around the exciton for two representative eigenstates (phonon occupation numbers and displacements)

properties of the dressed exciton (exciton + phonon cloud) can be analyzed

Numerical solution of a Holstein model for Frenkel excitons [Hoffmann et al., PRB 2002].

Holstein model with Frenkel and charge-transfer excitons

Model Hamiltonian includes:
- one electronic Frenkel exciton
- one symmetry-adapted charge-transfer exciton
- nearest neighbor Frenkel transfer
- mixing of Frenkel and charge-transfer excitons
- linear coupling of Frenkel and CT excitons to one molecular vibration
Figure: low temperature absorption spectra and general features of emission spectra can be interpreted by the exciton band structure
- left panel: experimental absorption spectrum and model spectrum from parameter fit
- right panel: experimenal emission spectrum and predicted emission peaks with fit parameters from absorption spectrum
- center part: characters of vibronic states from Holstein model at center and border of the Brillouin zone and compositon of electronic bands

Exciton structure of MePTCDI [Hoffmann et al., Nonl. O. 2002].

Finite chains

description of finite one-dimensional molecular chains on purely electronic level

applied Hamiltonian similar to model Hamiltonian above, includes idealized boundary conditions

one Frenkel exciton
two nearest neighbor charge-transfer excitons
(exept at the outermost molecules)
nearest neighbor Frenkel transfer
mixing of Frenkel and charge-transfer excitons

strongly coupled Frenkel and charge-transfer excitons responsible for appearance of an intrinsic quantum length

occurs as damping exponent of surface states [3]
origin of exciton quantum confinement [4]

Besides delocalized bulk states also states (A,B) arise, which are localized at the outermost molecules. The formation of such surface states as well as their effective size is determined by the coupling strength between Frenkel and charge-transfer excitons.

[3] V.M. Agranovich, K. Schmidt, K. Leo, Chem.Phys.Lett. 325 (2000) 308.
[4] K. Schmidt, Phys.Lett. A 293 (2002) 83.

Quantum chemistry

Application of standard semiempirical methods
Derivation of intermolecular interactions by projection methods