Pair density short-range behavior

Around the same time, Becke [184] proposed a real-space normalized model for the correlation hole. He started from the observation that, for a given coupling strength A, the spin-polarized components of the spherically averaged pair densities have well-defined short-range behavior near the reference point [185] ... 

Its exponential behavior makes this term the dominant one when short atom-atom distances between the interacting molecules are produced. Consequently, this term prevents molecules from getting closer than some limiting distance this is the physical principle behind the hard-sphere model and Kitaigorodsky s close-packing principles [2]. Moreover, the shortest atom-atom distances that one can find in different intermolecular interactions for the same pair of atoms always fall in a restricted range, a fact that allows one to define atomic radii. They differ in ionic and neutral crystals due to the different electronic structure of ionic and neutral species, as easily shown when comparing the contours at 90% probability in electron density maps for isolated atoms and their ions. 

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