Energetic conditions that are required for favorable singlet exciton fission, an intermolecular electron correlation effect, are studied with relativistic quantum chemical methods as to investigate the effect of a varying fine-structure constant. Ethylene and derivatives thereof serve as simple model systems, whereas pentacene and perfluoropentacene, which display singlet exciton fission experimentally, are used as specific examples for possible applications. Effects are estimated to be small in this class of compounds, but substitution with heavier halogens might lead to oppositely shifting energy levels and thereby improved sensitivity in narrow resonance situations.