Potential Energy Curves of Core-Excited States of the U M$_5$ Absorption Edge Manifold of UO$_2$$^{2+}$

X-Ray Absorption Near Edge Structure of the U M$_{5}$ X-ray absorption edge of UO$_2^{2+}$ is analyzed using the potential energy curves of an isolated UO$_2^{2+}$ obtained from rigorous, multiconfigurational all-electron \emph{ab initio}, wavefunctions for the ground and core-excited configurations. The spectroscopic parameters for the potential energy curves are reported.

Two novel theoretical methods have been used as measures of the covalent character of the U-O bond:

(1) The projection of the U(5f) and U(6d) orbitals of the isolated U$^{6+}$ cation on the orbitals of the ground and the core-excited states of UO$_2^{2+}$ and

(2) the size of the orbital charge distributions given by the $\langle z^2 \rangle$ expectation values.

This gives direct insight into the variation of the electronic structure of the bond as the U-O bond length is changed. The excellent agreement of the simulated with the experimental U M$_5$ XANES spectrum proves the validity of our theoretical model. The potential energy curves and the simulated XANES spectra for varying bond length together with the information from the two measures about the covalent character allow us to establish a link between X-ray spectroscopy and chemical bonding.