We propose a mixed analytical-ab-initio method for the accurate calculation of the conductance in monovalent atomic wires. The method relies on the most general formula for ballistic transport through a monovalent wire, whose parameters can be determined from first-principles calculations. Our central result is the demonstration of the highly non-universal behavior of the conductance, which depends on the fine details of the contacts to the leads. We are therefore able to reconcile a large number of the apparently contradictory results that have recently appeared in the literature. PACS numbers: 73.23.-b,73.63.Rt,73.40.Cg In the last two decades transport properties of atomic contacts have been the subject of intensive research (for overviews see Ruitenbeek  and Agraït, Yeyati and Ruitenbeek ). First experimental evidences of the formation of golden atomic chains have been reported by Yanson et al. and Ohnishi et al. . Experiments on chains of Au, Pt and Ir atoms  exhibit electrical conductance oscillations as a function of the wire length and similar oscillations as a function of bias voltage and electrode separation [5, 6]. Rodrigues et al.  investigated the energetically preferred orientation of the crystal planes of the wire by the application of highresolution transmission electron microscopy. Their results show a strong correlation between the atomic arrangement and the conductance. The above experiments were stimulated by early theoretical predictions of conductance quantization  and conductance oscillations [9, 10]. The latter issue generated a sequence of theoretical papers using a variety of technique
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