We present a novel computational method to accurately calculate Raman spectra from first principles. Together with an extension of the second-generation Car-Parrinello ab-initio molecular dynamics  (AIMD) method to propagate maximally localized Wannier functions along with the nuclei, a speed-up of one order of magnitude can be obtained. Due to expression of the total polarizability as a sum of Wannier polarizabilities, the method also enable us to find partial Raman activities corresponding to local vibrations of different fragments in the system.

We have used this method to investigate the Raman spectra of (Li₂S₄)_𝑛, 𝑛=1,4,8 clusters which are believed to be the last intermediates in the S₈→Li₂S transition in lithium-sulfur (Li-S) batteries, during the discharge cycle. However, it is not fully established whether or not any other products coexist with the Li₂S crystal in the discharged state. In this study, we have observed a clear evidence of Li₂S₄→Li₂S₂ transition by investigating the systematic changes in the simulated Raman spectra as the cluster size increases. In line with recent experiments, we found that the Raman-active sulfur-sulfur stretching mode at 440 cm^-1 can be considered as a signature of covalent bonding between two and more sulfur atoms per formula. We have also demonstrated that the transition is mainly due to the strong electrostatic interactions between polar Li₂S₄ monomers which result in energy lowering by arranging the local dipole moments in anti-parallel fashion. This arrangement result in the formation of crystal-like Li₂S₂ structures at the interfaces of Li₂S₄ monomers. 

Furthermore, through minimum-energy conformation search combined with AIMD simulations, we have shown that upon carbonization of polyacrylonitrile in early discharge stages of Li-S batteries and further exposure of the product to octasulfur, S₂ groups form a bridge between two consecutive nitrogen atom on the edge of carbon fiber. Moreover, our Raman simulations reveal a characteristic Raman activity for these -N-S-S-N- groups in 300 - 400 cm^-1 frequency range, in form of two distinct peaks which researchers could not experimentally assign before. Finally, we will discuss our recent studies on structure of complex cathode materials using our approach together with experimental measurements.