Detection of molecules is a key issue for many applications. Surface enhanced infrared absorption (SEIRA) uses arrays of resonant nanoantennas with good quality factors which can be used to locally enhance the illumination of molecules. The technique has proved to be an effective tool to detect small amount of material. However the use of nanoresonators only enables the detection of a few absorption lines, hampering the identification of the spectral fingerprint of a molecule. Here, we introduce a new paradigm and use low quality factor resonators with large radiative losses (over-coupled resonators). The bandwidth enables to detect all absorption lines between 5 and 10 μm. Counterintuitively, despite a lower quality factor, the system sensitivity is improved and we report a reflectivity variation as large as one percent per nanometer of molecular layer of PMMA. This paves the way to specific identification of molecules. We illustrate the potential of the technique with the detection of the explosive precursor dinitrotoluene (DNT). We compare the data with numerical simulations and introduce an analytic model of the results.