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Some theoretical studies using perturbation and tight-binding methods have tried to shed light on the magnetic behaviors of carbon-based nanostructures in the limit of wave vector q = 0 . In a recent work, we studied a half-filled model of helical carbon chains to gain new insights for q ≠ 0 . Although in carbon the energy bands are usually derived from partially filled atomic p-shells, here we explore the hole contribution to these magnetic responses. We calculate the longitudinal spin susceptibility of an almost-filled tight-binding model of a helical chain for q ≠ 0 . We find that when the Fermi level lies at the band edges, the system shows for positive chirality a divergent paramagnetic susceptibility. This result is in agreement with that previously reported for the macroscopic limit q = 0 . [ABSTRACT FROM AUTHOR]