A key factor in the search of high-spin ground state purely organic molecules concerns the effect of the inherent non-rigid structures on the magnetic and optical properties. This structural feature has not been properly addressed in previous theoretical works. Here, based on the experimentally characterized high-spin ground state of dendritic and star-branched polyradicals, we study four alternant hydrocarbon biradicals that intend to model these effects and, at the same time, provide a first step toward understanding more extended experimental structures. A series of density functional theory (DFT) and of wave function-based methods have been used to explore the richness of structural minima in the corresponding potential energy surfaces and to discuss its effect on the triplet-singlet gap of the proposed model systems. For a given model, the DFT-based B3LYP, M06-2X and MN-12SX methods provide a consistent description. Likewise, a multiconfigurational quasi-degenerate perturbation theory approach with the minimal π space as CASSCF reference is found to provide unbiased results. Despite the conformational richness found for these systems, they all can be described by a reduced set of values referred to only two structural parameters, being those the dihedral angles between the phenyl rings. For a given model, there is no significant change in the triplet-singlet gap depending on the chosen local minima.