We present a microscopic study of the electronic and magnetic properties of the recently synthesized spin tetrahedron system Cu4Te5O12Cl4 based on density functional calculations and on ab initio-derived effective models. In view of these results, we discuss the origin of the observed differences in behavior between this system and the structurally similar Cu2Te2O5Cl2. Since the Br analog of the title compound has not been synthesized yet, we derive the crystal structure of Cu4Te5O12Br4 by geometry optimization in an ab initio molecular dynamics calculation and investigate the effect of substituting Cl by Br. The possible magnetic behavior of Cu4Te5O12Br4 in comparison with the recently studied Cu2Te2O5Br2 is also discussed.
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