ABSTRACT:The ab initio periodic unrestricted Hartree-Fock method and several generalized gradient algorithm (GGA) and hybrid density functional theory (DFT) approaches have been used to investigate the ground-state electronic and magnetic properties of three low-dimensional magnetic copper insulators, namely, KCuF 3 , K 2 CuF 4 , and Sr 2 CuO 2 Cl 2 . A Gaussian atomic basis set optimized for the crystal environment has been used to construct the crystalline orbitals in the LCAO approximation as implemented in the CRYSTAL code. The interaction between magnetic moments on Cu 2ϩ ions (d 9 local configuration) strongly depends on the crystal structure and hence on the resulting electronic structure: Sr 2 CuO 2 Cl 2 is representative of 2-D antiferromagnetic systems, closely related to the high-T c parent cuprate superconductors; K 2 CuF 4 is a 2-D ferromagnetic system and KCuF 3 behaves as a quasi-1-D antiferromagnetic system. The most stable electronic state, the relevant magnetic coupling constants, and the magnetic form factors are calculated by means of the various Hamiltonians. The systems turn out to be large band-gap insulators in the UHF and hybrid DFT approximations, whereas they become metallic or narrow bandgap semiconductors in the local density approximation or GGA approximations. UHF gives a qualitatively correct description of this kind of magnetic insulators and, more important, good relative values for the relevant magnetic coupling constants. Hybrid functionals (like B3LYP) largely improve, with respect to the other Hamiltonians, the magnitude and nature of the band-gap, the spin densities on the Cu 2ϩ ions, and the most important magnetic coupling constants, providing a reasonable, semiquantitative description of this kind of strongly correlated materials. In addition, those functionals correctly account for the distortions due to the Jahn-Teller effect in KCuF 3 , in contrast to LDA and PW-GGA, where no stabilization appears when the distortion is included.