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Molecular Spectroscopy deals with absorption, emission, and scattering by moleculesand it is used to determine the structure of the molecules. Infrared spectroscopyplayed a vital role in the characterization of materials until Raman Spectroscopywas discovered. Raman and Krishnan jointly discovered scattering spectroscopywhich was named after Sir. C. V. Raman. Subsequently, he was awarded Nobel Prizefor his valuable discovery.After 1930, spectroscopic scenario changed in materials characterization. Combininggroup theory, infrared spectroscopy and Raman spectroscopy, the structureof molecules were established. The discovery of laser gave a big boost to spectroscopyand first renaissance was seen in Raman spectroscopy. Then, laser Ramanspectroscopy became popular and was widely used not only by physicists but alsoby material scientists, chemists, pharmacologists, geologists, etc. Around 1986,the emergence of Fourier transform spectroscopy gave rise to new instrumentationsuch as Fourier transform infrared spectroscopy and Fourier transform Ramanspectroscopy. Fourier transform Raman spectroscopy is free from fluorescence andhence it is possible to record spectra of grease and rhodamine 6G very precisely.In 1960s, theoretical spectroscopy which was developed by Wilson, Jr, et alwas widely studied to evaluate potential constants, vibrational frequencies, meanamplitudes, Coriolis coupling constants, centrifugal distortion constants, inertiadefects, shrinkage effects and thermodynamic properties of various molecules. Eventoday, this classical method has several problems in providing the solution for secularequations due to mathematical inability.