We validate that off-resonant electron transport across {it ultra-short} oligomer molecular junctions is characterised by a conductance which decays exponentially with length, and we discuss a method to determine the damping factor via the energy spectrum of a periodic structure as a function of complex wavevector. An exact mapping to the complex wavevector is demonstrated by first-principle-based calculations of: a) the conductance of molecular junctions of phenyl-ethynylene wires covalently bonded to graphitic ribbons as a function of the bridge length, and b) the complex-band structure of poly-phenyl-ethynylene.
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