Four new inorganic-organic hybrid manganese frameworks, formulated as [Mn(Am-Hip)(2)] center dot 3H(2)O (1), [Mn-2(ip)(2)(H2O)] center dot CH3OH (2), [Mn-2(OH-ip)(2)(DMF)] center dot DMF (3), and (Me2NH2)[Mn-4(sdba)(4)(Hsdba)(H2O)] center dot 3H(2)O center dot 2DMF (4) (Am-H(2)ip = 5-aminoisophthalic acid, H(2)ip = isophthalic acid, OH-H(2)ip = 5-hydroxyisophthalic acid, and H(2)sdba = 4,4'-sulfonyldibenzoic acid), have been prepared by solvothermal reactions of Mn(II) ions with different polycarboxylate acids in the presence of LiNO3 or NH4NO3. Single-crystal X-ray diffraction studies reveal that the frameworks of 1-4 contain diverse Mn(II)-oxygen inorganic magnetic chain's sequences, -J(1)J(1)J(1)J(1)- for 1, -J(1)J(2)J(1)J(2)- for 2, -J(1)J(1)J(2)J(2)- for 3, and -J(1)J(2)J(3)J(3)- for 4. The sequence in 4 has never been seen for the magnetic chain compounds and is a new type of magnetic alternating sequence. Magnetic investigations indicate that these compounds all show weak antiferromagnetic couplings between the adjacent Mn(II) ions. Magnetostructural analyses based on the data of 1-4 and other related Mn(II) chain compounds imply that the magnitude of the magnetic coupling has some relationship with the Mn-O-Mn angle of the mu(2)-O bridge and the average Mn-O-C-O torsion angle of the carboxylate bridges. Compounds 2 and 4 crystallize in chiral and acentric space groups, and they both exhibit powder second harmonic generation (SHG) efficiencies approximately 0.6 and 0.9 times, respectively, that of the standard potassium dihydrogen phosphate (KDP) powder. In addition, the dielectric properties of 2 and 4 were also investigated.