Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on theĂ
ngström scale in bulk rutile (TiO 2 ) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.Electronic states shape the world around us as their characteristics give rise to nearly all macroscopical properties of materials. Be it optical properties such as colour and refractive index, chemical properties such as bonding and valency, mechanical properties such as adhesion, strength and ductility, electromagnetic properties such as conductance and magnetisation, or the properties of trap states: ultimately, all these properties can be traced back to the electronic states in the material under investigation. Therefore, it is not surprising that electronic states are of paramount importance across many fields, including physics, materials science, chemistry and the life sciences. It does come as a surprise, however, that while some of their aspects can be inferred indirectly from macroscopical material properties or some diffraction techniques, the direct observation of individual electronic states in real space so far has succeeded only under very special circumstances (e.g. on an insulating surface using a scanning tunnelling microscope (STM) with a specially functionalised tip [1]) due to both experimental and theoretical challenges. In this work, we endeavour to remedy this situation by using a combination of transmission electron microscopy (TEM), electron energy-loss spectrometry (EELS), and state-of-the-art simulations.TEM is a well-known technique for studying materials on the nanoscale while EELS adds element-specific information. Both are widely-used on a regular basis in many fields and are readily commercially available. Owing to these two techniques, tremendous progress has been made over the last decade in mapping atom positions with â 10 pm accuracy [2-4], determining charge densities [5][6][7], and performing atom-by-atom chemical mapping [8][9][10][11][12]. Furthermore, the fine-structures of the spectra allow the determination of the local chemical and structural environment as well as the hybridisation state of the scattering atoms [11][12][13][14][15][16][17][18] in the bulk, which can be substantially different from the surface states probed by STM. This suggests to use the EELS signal to probe the local environment in real-space and map, e.g., crystal fields, conduction states,...