  Based on density functional calculations, we present a detailed theoretical
study of the electronic structure and the magnetic properties of the quasi-one
dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of
the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we
find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point
at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study
in detail the influence of structural peculiarities such as the reported Li
disorder and the non-planar chain geometry on the magnetic interactions
combining the results of LDA based tight-binding models with LDA+U derived
exchange parameters. Our investigation is complemented by an exact
diagonalization study of a multi-band Hubbard model for finite clusters
predicting a strong temperature dependence of the optical conductivity for
Li_2ZrCuO_4.
