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A new scheme for calculating the x-ray absorption near edge structure (XANES) based on the finite-difference method is proposed. It allows completely free potential shape and, in particular, is not constrained to the muffin-tin approximation. In our approach, the calculation of the final states is performed in real space. The Schr\"odinger equation is solved in a discrete form on the node points of a three-dimensional grid. The unknowns are the values of the wave functions at the grid points. The validity of the method is shown on two different systems the metallic copper and the carbon monoxide molecule; then, the differences resulting from muffin-tin and non-muffin-tin calculations are shown on different typical molecules.
Yves Joly (Tue,) studied this question.