= Solution
An <organic semiconductor> has conjugated molecular units with strong intramolecular bonding and comparatively weak intermolecular electronic overlap. Optical excitation commonly promotes a $\pi$ electron from an occupied molecular orbital toward an unoccupied one. Weak dielectric screening and narrow bands favour bound <Frenkel excitons>, sometimes mixed with intermolecular charge-transfer states, rather than immediate production of free carriers. The optical excitation energy is below the unbound electron–hole threshold by the <exciton binding energy>, with relaxation conventions specified when comparing measured gaps.
The <electric-dipole interaction> selects bright states through their transition dipoles, producing polarization-dependent absorption in oriented samples. From a singlet ground state, strong electric-dipole absorption normally preserves spin and reaches singlet excitons; direct triplet excitation is weak without spin mixing. The <Franck-Condon principle> treats excitation as vertical on the nuclear-motion timescale. For one displaced harmonic vibration at low temperature, the <displaced-oscillator Franck-Condon progression> has relative strengths
$$
\boxed{I_\nu\propto e^{-S}\frac{S^\nu}{\nu!},\qquad
\hbar\omega_\nu=E_{00}+\nu\hbar\omega_v.}
$$
Here the <Huang-Rhys factor> $S$ measures the displacement and $E_{00}$ is the zero-vibration transition energy. Vibrational relaxation before emission produces a <Stokes shift>. Molecular packing and excitonic coupling shift or split bright features and change their intensities; disorder and vibrations broaden them. Consequently a universal parabolic-band absorption edge is inappropriate for a localized molecular excitation.<Organic Optoelectronics lecture notes by Vladimir Bulović>[Lectures4–7: molecular levels, Franck–Condon shifts, aggregates and Frenkel/charge-transfer excitons]{ref}
\Image[/past-exam-of-the-advanced-quantum-condensed-matter-physics-course-of-the-university-of-cambridge/2013/paper-1-aqc2013-vibronic-absorption.png]
{title=Illustrative low-temperature vibronic absorption progression from a displaced molecular vibration}
{source=paper-1-aqc2013-vibronic-absorption.py}
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