Systems and methods of identifying molecules of polymers such as, for example, a nucleic acid, are described. The method involves centering a bias voltage across a pair of nanoelectrodes separated by a channel that corresponds to one of any of the energy differences between any two internal energy levels of a molecule of interest, and modulating the bias voltage with a modulation waveform while the molecule of interest is in the channel. An electrical signal characteristic of the molecule of interest is derived from the tunneling current between the nanoelectrodes, and the characteristic electrical signal is compared with known values of the signal for chemically-known molecules in order to identify the molecule of interest. Multiple pairs of nano-electrodes may be employed to identify more reliably a single molecule or multiple molecules.