We discuss theoretically the correlation between atomic configurations and coherent stationary electronic transport in molecular systems contacted with metallic electrodes in stationary conditions. The nonequilibrium Green’s function formalism is discussed as preliminary theoretical framework which allows, by means of a suitable mapping of electron-only Hamiltonians, the bridging between the atomic structure of the molecule+contacts system and the electron dynamics. Contrarily to the equilibrium case, the lack of a variational principle in nonequilibrium conditions, even when the stationary state is achieved, does not permit a correct formal approach to the correlation between the electron state in a biased molecular device and the molecule’s configuration. A conjecture is proposed to extend the free energy Mermin’s functional, and the related variational procedure, for a …