  Using the Landauer formulation of transport theory and tight binding models
of the electronic structure, we study electron transport through atomic wires
that form 1D constrictions between pairs of metallic nano-contacts. Our results
are interpreted in terms of electron standing waves formed in the atomic wires
due to interference of electron waves reflected at the ends of the atomic
constrictions. We explore the influence of the chemistry of the atomic
wire-metal contact interfaces on these standing waves and the associated
transport resonances by considering two types of atomic wires: gold wires
attached to gold contacts and carbon wires attached to gold contacts. We find
that the conductance of the gold wires is roughly $1 G_0 = 2 e^2/h$ for the
wire lengths studied, in agreement with experiments. By contrast, for the
carbon wires the conductance is found to oscillate strongly as the number of
atoms in the wire varies, the odd numbered chains being more conductive than
the even numbered ones, in agreement with previous theoretical work that was
based on a different model of the carbon wire and metal contacts.
