Pouya Partovi-Azar a , Thomas D. E-mail: payamk zedat. Raman spectra have been obtained using a new technique to estimate polarizabilities using Wannier functions. This peak has been experimentally observed in the discharged state of LiβS batteries and has also been attributed to the formation of Li 2 S 2. We observe a clear tendency to form the Li 2 S 2 structure as the size of the cluster grows. Furthermore, by applying a periodic electric field using the Berry phase approach 52,53 one can obtain the polarizability tensor, 2 from the total dipole moment of the system M.
E j denotes Cartesian component j of the applied periodic electric field, and M i is the i th component of the total dipole moment. M i can be estimated unambiguously using Maximally Localized Wannier Functions MLWFs , which allow the total electronic density to be partitioned into individual fragments.
In a separate study see ref. The WP method, which has been used to simulate the Raman spectra in the present work, facilitates to routinely calculate finite-temperature spectra with only minimal extra computational cost. We have demonstrated that for typical test systems the simulated Raman spectra obtained using FD and WP methods are essentially the same in terms of relative intensity of the peaks and their lineshapes.
All Raman spectra in this work were obtained by performing 20 ps AIMD simulations in the canonical ensemble to achieve equilibration, followed by 10 ps AIMD in the micro-canonical ensemble to remove thermostat effects and to sample polarizabilities. A time-step of 1 fs was used in all the simulations and the polarizabilities were sampled for every 5 fs.
The averaged electron transfer using MPA is calculated to be 0. The calculated dipole moment for the isolated Li 2 S 4 molecule is 2. These results are also in line with the energy gain of the clusters as a function of the number of Li 2 S 4 monomers. The formation energy of Li 2 S 4 n as a function of the cluster size n can be written as 4 where E cluster tot , , and E Li tot are the total energy of Li 2 S 4 n clusters, a single S 8 molecule, and a Li atom, respectively.
