The Landauer-type formulation of current through a molecular junction with electronic-nuclear coupling introduced by Troisi et al [J. Chem. Phys.118, 6072 (2003)] is generalized to account for the dependence of the molecule-leads coupling terms on the nuclear coordinates. Although this electronic-nuclear coupling is external to the molecule there is no need to extend the molecular subspace when projection operators are employed for calculations of the current through the junction. A test case of a conductor with vibrating contacts to the leads is studied numerically. It is demonstrated that contact vibrations lead to inelastic contributions to the current and to characteristic features in the I-V curve and its derivatives, similar to the ones observed for internal (molecular) electronic-nuclear coupling.

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