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 = 0.22pm0.02 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.
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