Fully internally contracted multi-reference configuration interaction methods as efficient tools for the calculation of exchange couplings in organic biradicals

The accurate computation of magnetic exchange interactions in organic biradicals often requires computationally demanding multi-reference configuration interaction (MRCI) methods. However, the large configuration spaces associated with uncontracted approaches limit their application to relatively small systems and active spaces. Fully internally contracted schemes provide an efficient alternative by representing the excitation manifold in a compact form, thereby substantially reducing the computational cost. In this work, fully internally contracted difference-dedicated CI methods (FIC-DDCI2 and FIC-DDCI3) are applied to compute exchange coupling constants J for a series of organic biradicals, including nitroxide, nitronyl nitroxide, and iminyl nitroxide systems. Particular emphasis is placed on iteratively refined natural orbitals for improving the orbital representation and constructing truncated orbital spaces for uncontracted calculations. Overall, we show that FIC-DDCI methods combined with iterative natural-orbital refinement provide an efficient and accurate strategy for computing magnetic exchange couplings, provided that the reference space and excitation manifold are chosen appropriately. Natural-orbital iterations can effectively compensate for the missing reference relaxation inherent to fully internally contracted approaches and improve the molecular orbital description, while the contracted formulation retains a substantial computational advantage through its reduced CI space.