Fig. 1: Experimental setup to obtain the three-dimensional electron density of LiCoO₂.

The valence electron distribution of a free independent transition atom (e.g., Co) is spherical, and its five d-orbital energy levels are degenerate. In the case of transition-metal oxides, splitting of the d-orbital energy levels occurs under the crystal field of polyhedra, and the redistribution of valence electrons resulting from the bonding interactions gives rise to abundant physical properties for functional materials. Using a combination of quantitative convergent-beam electron diffraction (QCBED) and synchrotron powder X-ray diffraction (SPXRD), the deformed distributions of the valence electron and orbital population can be clearly detected. In terms of SPXRD, the structure information and high-order structure factors can be extracted via Rietveld refinement. For QCBED, the low-order structure factors can be obtained using the Bloch-wave method. Through multipole refinement and quantitative topological analysis of the electron distribution, the occupancies of the 3d-orbital can be measured.