We employ five {pi}-conjugated model materials of different molecular shape --- oligomers and cyclic structures --- to investigate the extent of exciton self-trapping and torsional motion of the molecular framework following optical excitation. Our studies combine steady-state and transient fluorescence spectroscopy in the ensemble with measurements of polarization anisotropy on single molecules, supported by Monte Carlo simulations. The dimer exhibits a significant spectral red-shift within $sim$ 100 ps after photoexcitation which is attributed to torsional relaxation. This relaxation mechanism is inhibited in the structurally rigid macrocyclic analogue. However, both systems show a high degree of exciton localization but with very different consequences: while in the macrocycle the exciton localizes randomly on different parts of the ring, scrambling polarization memory, in the dimer, localization leads to a deterministic exciton position with luminescence characteristics of a dipole. Monte Carlo simulations allow us to quantify the structural difference between the emitting and absorbing units of the {pi}-conjugated system in terms of disorder parameters.
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