IR and Raman Spectroscopies beyond the Harmonic Approximation: The Second-Order Vibrational Perturbation Theory Formulation

Thanks to significant improvements in hardware and the development of efficient algorithms, computational spectroscopy can now be routinely used to a simulate spectra of medium-to-large molecular systems, offering valuable help in the analysis or prediction of experimental spectra. This is the case for infrared and Raman spectroscopies, commonly used for the identification and characterization of compounds. In practice, most simulations rely on the harmonic oscillator approximation, which can lead to a truncated description of the physical–chemical problem (for instance, missing overtones and combination bands). To overcome those limitations, important efforts have been dedicated to develop models able to include anharmonic effects and to implement them efficiently. However, they are sometimes scarcely known or their interest often overlooked. As implementations capable of simulating vibrational spectra at the anharmonic level become common, this article offers a brief overview of the theoretical background of infrared and Raman spectroscopies. This serves as an introduction to the discussion on the actual calculation of transition energies and intensities. For its cost-efficiency, which makes it applicable to molecules comprising several dozens of atoms, vibrational second-order perturbation theory has been chosen as the anharmonic model. Practical calculations are also discussed and illustrated with the case of naphthalene.