  Periodic and cluster density-functional theory (DFT) calculations, including
DFT+U and hybrid functionals, are applied to study magnetostructural
correlations in spin-1/2 frustrated chain compounds CuX2: CuCl2, CuBr2, and a
fictitious chain structure of CuF2. The nearest-neighbor and second-neighbor
exchange integrals, J1 and J2, are evaluated as a function of the Cu-X-Cu
bridging angle, theta, in the physically relevant range 80-110deg. In the ionic
CuF2, J1 is ferromagnetic for theta smaller 100deg. For larger angles, the
antiferromagnetic superexchange contribution becomes dominant, in accord with
the Goodenough-Kanamori-Anderson rules. However, both CuCl2 and CuBr2 feature
ferromagnetic J1 in the whole angular range studied. This surprising behavior
is ascribed to the increased covalency in the Cl and Br compounds, which
amplifies the contribution from Hund's exchange on the ligand atoms and renders
J1 ferromagnetic. At the same time, the larger spatial extent of X orbitals
enhances the antiferromagnetic J2, which is realized via the long-range
Cu-X-X-Cu paths. Both, periodic and cluster approaches supply a consistent
description of the magnetic behavior which is in good agreement with the
experimental data for CuCl2 and CuBr2. Thus, owing to their simplicity, cluster
calculations have excellent potential to study magnetic correlations in more
involved spin lattices and facilitate application of quantum-chemical methods.
