Close-packing principle

The close-packing principle implies that the energy minima are close to the minima of the multidimensional volume surface, provided that the distances between neighboring atoms of different molecules are not lower than the van der Waals distances. 

Besides the energy factors, defined by the close-packing principle, entropic factors are also involved in determining the mode of packing of molecules. A molecule in a crystal tends to maintain part of its symmetry elements, provided that this does not cause a serious loss of density. In a more symmetric position a molecule has a greater freedom of vibration, that is, the structure corresponds to a wider energy minimum.126... 

As a consequence of the close-packing principle, chemically different molecules with similar shape and volume should have identical crystal structures [27]. Substances forming mixed crystals must be isomorphous (i.e., not only must they have an identical space group and the same number of molecules, but also a similar molecular packing), otherwise there will be a discontinuity in their solubility curve [5]. For example, benzoic acid and isopropylbenzene, in spite of the similarity in... 

Ice is formed by a three-dimensional network of H-bonds and, for this reason, it is a very open structure. Liquid water has a packing coefficient higher than that of ice since its density is higher. Small energies are sufficient to break H-bonds and to create a closer structure. This shows the tendency to form the maximum number of interactions, as summarized by the close-packing principle. 

It was reported [53] that the LP influences the molecular and electronic distortions observed in [Cr(C6H6)(CO)3] and related carbine and carbene complexes. The mutual orientation of the first-neighboring CO groups in these species reflects more the balance between the molecular shape and the tendency of the molecules to lie as close as possible (close-packing principle), rather than an electronic requirement of the CO-CO intermolecular interactions. 

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. 

According to Kitaigorodskii s close-packing principle, molecules will pack in a manner that minimizes void space or, in other words, in a way to maximize van der Waals interactions [20]. Hence, effects of both molecular shape and size are important in crystal engineering. For example, since racemic crystals tend to pack into centrosymmetric space groups, this statistical preference was utilized to prepare cocrystal g in Appendix 2, which is a rare molecular compound called a quasiracemate. The formation of cocrystal g was made possible due to the isosteric nature of the isoptopenyl and dimethylamino substituents, indicating that shapes rather than dipoles can be in fact the dominant factor (cf. Ref. 31). 

Kitaigordoskii s principles of close packing are based on the ability of molecules to fill a space with an adequate number of energetically favorable intermolecular interactions. There are four stages in the close packing principle ... 

These two semi-quantitative principles, close packing and direction-specific interactions, would be quantified and combined in sufficiently reaUstic model intermolecular potentials for modelUng the organic soHd state. The development of model intermolecular potentials outhned in this review could be seen as starting from simple quantification of the close-packing principle, with continuing refinement by the addition of the contributions that determine the specific interactions. Thus, the earliest atom-atom potentials as reviewed by Pertsin and Kitaigorodsky [18] were mainly of the form... 

Another confirmation of the close packing principle can be found in the rather common occurrence [17] of the formation of clathrates, hydrates, and solvates whenever the shape of the crystallizing molecule is too complex to allow efficient self-recognition with total space occupation, highly mobile solvent molecules slip in between and are incorporated in the crystal structure as space fillers. Incidentally, no numerical indicator of the ability or even the tendency of a given molecule to form solvate crystals has ever been found, a confirmation of the difficulties encountered in the definition of numerical descriptors of molecular shape. 

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