Infrared spectroscopy is very powerful tool to analyze the chemicals based on their molecular signatures. The registration of the fundamental vibrational modes that lie in the far IR is extensively explored, however the excitation of derivatives namely high harmonics molecular vibrations overtones is still a mystery. Although the absorption crosssection of molecular transition overtones is order of magnitude smaller compared to their fundamental vibrations, the research of overtones is of high importance if just would be possible to detect them. In this work, we show that the challenge in detection of molecular overtones may be overcome with localized surface plasmon resonance effect in gold nanorods antennas. We use N-Methylaniline as a probe molecule since we confirmed the excitation its molecular transitions overtones in near-infrared around 1.5 μm. We calculate absorption cross-section of gold nanorods with fixed diameter of 10 nm and different lengths varying from 80 to 160 nm surrounded by a homogeneous medium with the optical properties of N-Methylaniline, using the finite element method (FEM). To single out the contribution of the overtone modes, computations were repeated with N-Methylaniline replaced by the dispersionless media mimicking only the mean value of N-Methylaniline refractive index, n = 1.5712, and eliminating absorption. We show, that the differential absorption in the spectral range of the first overtone of the -NH vibration located at 1492 nm and the first overtone of the -CH vibration located at 1676 nm have both positive and negative values due to the shifting of the gold nanorod plasmon resonance band.