We present a new ab initio way to calculate X-ray Raman scattering spectra within the independent electron approximation. Our approach avoids any approximation about the shape of the used potential and leads to good agreement between experiment and theory. We show that the momentum transfer dependence in two typical cases, the F K-edge in LiF and the B and N K-edges in hexagonal BN, is well-reproduced. A more in-depth analysis of the electronic states and of the local atomic structure around the absorbing atoms is at hand.