The effect of periodic structure on the effective exchange integral (J(ab)) was investigated using density functional theory calculations with plane-wave basis and approximate spin projection scheme (AP-DFT/plane-wave), for through-space (H-H) and through-bond (H-He-H) interaction systems. The calculation was validated by comparing single-molecule results for H-H and H-He-H with the full configuration interaction method. The estimated J(ab) suggests that periodic structures decrease J(ab); the effective bond order increases and low-spin states are stabilized owing to the band structure. The spin contamination error is higher for periodic assemblies.