Orbital states are quantum mechanical constructions that describe the probability to find an electron in an atom, molecule or solid. We know from atomic physics that an *s*-orbital is spherical or that a *p*-orbital is dumbbell-shaped, but how do the complicated distributions of the electrons that contribute to chemical bonds in solids look like? Knowledge of these orbital states or electron distributions is the basis for our understanding of chemical bonds and related physical properties, which is a crucial step towards tailoring materials with specific characteristics. Here X-ray spectroscopy has contributed tremendously, however, the interpretation of the spectra is not easy and is often based on some assumptions for the analysis of the data. Hence it would be very important to have an experimental method that gives a direct image of the local electron density.

*Image: (a) (b) Integrated intensities of the M*

_{1}transition 3s→3d in the Fig. above plotted on the respective projections of the^{3}A_{2}3d(x^{2-y2}/3z^{2}-r^{2}) orbital of Ni^{2+}. (c) The three dimensional plot of the^{3}A_{2}3d(x^{2}-y^{2}/3z^{2}-r^{2}) orbital (more specific: the hole density) with the projections as in (a) and (b), respectively.

**Credit:**© MPI CPfS