First-order resonant Raman intensities of MoS₂ from first-principles

We investigate the laser-energy dependent Raman intensities of MoS₂ using two different approaches. In the first approach, we calculate the Raman intensities from finite differences of the dielectric susceptibility according to the phonon displacements. In the second, we formulate the Raman tensor in terms of time-dependent perturbation theory and calculate it using electron-photon and electron-phonon coupling matrix elements obtained from density functional theory. We demonstrate that the two approaches are formally and numerically equivalent in the adiabatic limit. The second approach allows to include the phonon dynamical effects and captures the Stokes and anti-Stokes shift with respect to the adiabatic case. This method, which is computationally more efficient, is also extended to include temperature effects with electronic lifetimes calculated from many-body perturbation theory.