Polar crystals exhibiting second-order harmonic generation (SHG) were designed by adjusting the intermolecular interactions of mononuclear Cu(ii) complexes in which one H2O, two pyridines (py), and two p-substituted benzoate (p-RBA) ligands (R = F, Cl, Br, I, CH3, and OCH3) were coordinated to a Cu(ii) ion, forming a penta-coordinated asymmetric [Cu(ii)(p-RBA)2(py)2(H2O)] mononuclear structure with a permanent dipole moment along the direction of the Cu-OH2 coordination axis. Each asymmetric [Cu(ii)(p-RBA)2(py)2(H2O)] complex formed a polar one-dimensional hydrogen-bonded chain, [Cu(ii)(p-RBA)2(py)2(H2O)]∞, between the non-coordinated carboxylate oxygen atom of the p-RBA ligand and the hydrogen atom of the H2O molecule. The formation of a polar crystal depended on the arrangement of polar hydrogen-bonded chains; the parallel arrangement of each polar chain resulted in a polar crystal. The chemical design of the R group in the p-RBA ligand enabled tuning of the magnitude of the interchain interactions and crystal polarity; polar crystals were obtained using p-RBA ligands with R = Cl, Br, I, and OCH3. In contrast, apolar crystals were grown from complexes containing p-RBA ligands with R = F and CH3. In all crystals, a polar two-dimensional (2D) layer constructed from the parallel polar [Cu(ii)(p-RBA)2(py)2(H2O)]∞ chain arrangement was formed based on weak van der Waals C-H⋯-O- interactions between the hydrogen atom of py and the carboxylate oxygen atom of the p-RBA ligand. Weak interlayer halogen (X)⋯π and multipoint C-H⋯π interactions played important roles in forming parallel arrangements of polar 2D layers and polar crystals, but there were no effective intermolecular interactions between the polar 2D layers in apolar [Cu(ii)(p-FBA)2(py)2(H2O)] and [Cu(ii)(p-CH3BA)2(py)2(H2O)] crystals. The magnitudes of the interlayer interactions in the polar crystals were larger than those in the apolar ones because of the effective intermolecular interactions. The SHG intensities of the four polar crystals were approximately 0.7 times larger than that of sucrose.