Spin state energies were calculated for an antiferromagnetic linear chain composed of a doublet (S = 1/2) radical and a biradical with a triplet (S = 1) ground state by numerical diagonalization of a finite-size Heisenberg-Dirac spin Hamiltonian. A ferrimagnetic-like ground state with a spin value of S = N/2 (N stands for the number of repeating units) appears if the intermolecular antiferromagnetic exchange interactions are uniform between all the S = 1/2 sites. This finding is consistent with a simple picture of differing and neighboring spin angular moments S’s ordered in sublattices in an antiparallel manner. On the other hand, quasi-degenerate low-lying states appear as the spatial symmetry of the intermolecular antiferromagnetic interactions is lowered. The quasi-degeneracy destabilizes the ferrimagnetic-like ground stare, ?his instability is inherent in multicentered antiferromagnetic interactions between open-shell organic molecular systems, suggesting a prerequisite for long-range magnetic order in purely organic molecule-based ferrimagnetics, Such prerequisite has never been reported until now. The results of the calculations are invoked to explain the susceptibility and the spin-spin relaxation time measured for the First model system for purely organic ferrimagnetics, a nitronyl nitroxide-based molecular crystal composed of an S = 1/2 and S = 1 molecules.