More familiar models distance-energy analyses

2 More familiar models distance-energy analyses 

Of extreme elegance and rigor, the Atoms in Molecules theory explains in clear quantitative terms a wide range of facts about chemical bonding within molecules, and hardly needs further praise here. In some instances, however, like the above mentioned biphenyl and NaCl cases, it remains for many practicing chemists a sour mouthful to swallow. 

To further analyze the assumption that a chemical bond is formed through, and is defined by, the occurrence of a short separation between two nuclear positions, we consider now the distribution of atom-atom distances in organic crystals, derived from a survey of the Cambridge Structural Database. To obtain distance distribution functions (DDF), an appropriate subset of the CSD is selected, and all atom-atom distances between atomic species i and j in all crystal structures in that sample are calculated, up to a certain limit / max- Let Ny R) be the number of atom-atom distances within the k-th distance bin defined by a separation a radial increment dR, and a volume dV = 4n/3[(/ k + d/ ) — (i k) ]- An inspection of the unnormalized distribution function reveals the exclusion radius ) J, or the separation below which 

Fn represents the condition of uniform distribution of the observed contacts over the available contact space. 

Some DDFs (CC, CH, HH, CN, OO, CF) show practically no peak and rise steadily from zero to unity. Others show a distinguishable peak with increasing isolation ratio, in the order NN, CO, CS, CCl significant peaks and larger isolation ratios are found for FF, SS, and especially the ClCl pair, whose DDF displays an almost completely developed, isolated peak. For the hydrogen bond contacts in acids, amides and alcohols, DDF peaks appear at very short distance between the H atom and the 

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