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The second and principal part of the review focuses on the DFT calculations that different groups have done. The detailed study of the screening in the static case settles the basis for the more complex treatment of finite velocity ions. The distinct character of bound and scattering states or the consequences of going from a 3D system to a 2D one are key features of the dynamic screening and of the stopping power of slow ions. A comparison between DFT and the quadratic response approach for positive and negative probe charges and the oscillatory behavior of the magnitudes related to stopping with the particle charge for heavier ions are also reviewed and updated.

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