where µ µ µ 0 denotes the dipole moment vector obtained from the field-free calculations. The components α αβ of the polarizability tensor are then given by α α,β=k = µ k ind,α /E. The dipole moments µ µ µ k and µ µ µ 0 can be calculated using different approaches, e.g., the Berry phase approach or ML-WFs. The induced dipole moment is unique since we take the difference between two dipole moments on the same polarization branch. The advantage compared to the DFPTbased approach (Section 2.3.2) is that IR and Raman spectra can be treated on equal footing, meaning that the dipole moment (IR) and the induced dipole moment/polarizability (Raman) can be computed with the same method. This also enables the computation of local contributions in Raman spectra by computing the induced dipole moments via MLWFs. A disadvantage of the induced dipole strategy is that the field strength E has to be selected with care such that i) the finite difference approach is valid and ii) that non-linear effects, which might be relevant for larger E-fields, can be neglected. However, employing field strengths that are too low can introduce noise into the spectrum, necessitating a trialand-error procedure to identify the optimal field strength for each material.