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The possible high-spin ground state of an alternant pi-conjugated hydrocarbon with unequal numbers of atoms on two sublattices, which has been predicted to be a good candidate for quasi-one-dimensional organic ferromagnets, is studied by Peierls-Hubbard model. Considering the non-nearest neighbor hopping interaction of pi-electrons and allowing for full lattice relaxation, a set of self-consistent iterative equations is established to study this system. The results of calculation show that the system can show a high-spin ground state owing to the topological structure and the electron-electron correlation. The second-nearest neighbor hopping interaction will destroy the stability of the high-spin ground state, and the third-nearest neighbor hopping interactions will make the high-spin ground state more stable.

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