A theoretical study on π-stacking and ferromagnetism of the perylene diimide radical anion dimer and tetramer

Ferromagnetism is rare in pure organic materials. Recently, the perylene diimide radical anion (PDI^-) salt prepared through solvothermal reduction by hydrazine hydrate has shown room-temperature ferromagnetism in our work [Jiang et al., Adv. Mater., 2022, 34, 2108103]. Based on this, herein we conduct a theoretical study based on density functional theory (DFT) to reveal the stacked geometries between two NH₄PDI monomers for low-spin (LS) and high-spin (HS) states and their magnetic exchange interactions (J_AB) using Yamaguchi's approximate spin projection. It is observed that the pancake-bonded dimer of NH₄PDI is the most stable pimer compared to others on both LS and HS potential energy surfaces. A transition of magnetic properties from strong antiferromagnetic (-1333.9 cm^-1) to moderate ferromagnetic (67.0 cm^-1) appears after increasing the interplanar distance between monomers and their relative rotation angle to access the HS state. According to energy decomposition analysis, the enhanced hydrogen bond formation and decrease of Pauli repulsion is able to counteract the decrease of attraction induced by electron correlation after accessing the HS state. Stacking patterns of exchange-coupled chain consisting of the NH₄PDI tetramer are obtained for the HS state after geometry optimization of the structure constructed by two most stable HS pimers. The exchange interactions (51.8 cm^-1, 381.2 cm^-1 and 53.2 cm^-1) between adjacent NH₄PDI monomers are ferromagnetic in the HS state, which is in accordance with the experimentally observed room-temperature ferromagnetism.