A computational approach to the study of magnetism in molecular crystals is outlined, and applications are presented for three purely organic nitronyl nitroxide (NN) crystals: WILVIW (p-N-methylpyridiniumNN(+), TOLKEK (alpha-2-hydroNN), and KAXHAS (beta-p-nitrophenyINN). Data from ab initio electronic structure computations are used to parametrize an algebraic Heisenberg Hamiltonian. The magnetic susceptibility as a function of temperature X(T) is, in turn, obtained directly from the computed energy levels of the algebraic Heisenberg Hamiltonian. The parametrization of the two site interaction parameters JAB requires the identification of the (one-, two-, or three-dimensional) magnetic motifs (e.g., spin ladders, etc.) from a study of the magnetic structure of the crystal. The energy levels of the magnetic motif are then computed as a function of the extension of the constituent magnetic building blocks along the crystallographic axes until convergence on X(T) can be demonstrated. Rapid convergence has been demonstrated, showing that a simple model (the minimal magnetic model space) can be used as a realistic model of the magnetic motif for an infinite crystal lattice. Applications to the three organic NN crystals have demonstrated the efficacy of this theoretical approach for the simulation of the experimental magnetic susceptibility and heat capacity data.