In this work, we apply a quantum discrete model to describe the electron transport through a molecular junction between electrodes and the accompanying phenomena: charging, polarization, inverse population of states, and injection radiation. The model represents the molecular bridge as a system of spatially distributed potential wells which capture affinity electrons from electrodes. We show that the current through the molecular bridge is accompanying by polarization in the applied field and by inversion of the states' population. The calculated I-V characteristics for nanocarbon sheets, carbon tubulenes, and hydrocarbon structures exhibit the stepped and nonmonotonous character, whose mechanism is discussed.