The main goal of this doctoral work was to develop theoretical advances of the semiclassical theory applied to molecular spectroscopy. In particular, the attention was centered at the coherent states based Time Averaging Semiclassical Initial Value Representation (TA-SCIVR) approximation to the vibrational spectral density. This approach is a solid way to access accurate vibrational spectra of molecular systems at a quantum approximate level. Nevertheless, it is affected by some criticalities as numerical issues and the so-called curse of dimensionality problem. Both represent an important stumbling block for the exploitation of the methodology towards molecules of increasing dimensions and complexity, preventing its application to general problems in the vibrational spectroscopy field. In my doctoral work we tried to face both issues, taming the numerical issues of the spectral density by introducing analytic and numerical approximations, and later developing with the group the Divide and Conquer Semiclassical dynamics (DC-SCIVR), a method which exploits the standard semiclassical formalism, but it works in reduced dimensional subspaces, with the aim of overcoming the curse of dimensionality. The advances first have been tested on simple molecules and then they have been employed to study spectroscopic relevant molecules. Main results show that it is possible to recover vibrational spectra even of those molecules affected by significant numerical issues, as well as high-dimensional ones, retaining the same accuracy of TA-SCIVR. In this thesis I first present some basics of the Semiclassical theory, with focus on vibrational spectroscopy, and then are shown the advances proposed, with applications on some relevant molecular systems in vibrational spectroscopy as supramolecular systems made by clusters of water and protonated glycine dimer, or high-dimensional molecules as benzene and C60
