M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 71
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In general the use of a gene or avirus as a template would lead to the formationof a molecule not with identical structure but withcomplementary structure. . . If the structure thatserves as a template (the gene or virus molecule)consists of, say, two parts, which are themselvescomplementary in structure, then each of theseparts can serve as the mold for the production ofa replica of the other part, and the complex of twocomplementary parts thus can serve as the mold forthe production of duplicates itself.At the time Pauling was working on the structure of proteinsculminating eventually in his discovery of the alpha-helix.
Yet thisdeclaration sounds as if he were anticipating the mechanism of DNAreplication via the double helix. It came, however, only in 1953, andit was not Pauling, but Watson and Crick, who discovered it.Kitaigorodskii started his studies of molecular packing in the 1940sunder severe conditions at war time. His first paper [76] was very briefbut much to the point with the following title: “The Close-Packing of9.6. Molecular Crystals463Molecules in Crystals of Organic Compounds.” He introduced “theconcept of shape of the molecule, what in turn makes it possibleto raise .
. . the question concerning the packing of the moleculeswithin the crystal” [77]. In this paper, Kitaigorodskii proposed a threeaxial ellipsoid for the shapes of molecules, which was soon replacedby arbitrary shapes that facilitated making observations of generalvalidity.Because of the interlocking character, the packing in organic molecular crystals is usually characterized by large coordination numbers,i.e., by a relatively large number of adjacent or touching molecules.Experience shows that the most often occurring coordination numberin organic structures is 12, so it is the same as for the densest packingof equal spheres.
Coordinations 10 or 14 occur also but less often.Kitaigorodskii was a true pioneer in the field of molecular crystals. First of all, he assigned real sizes and volumes to the moleculesby accounting for the hydrogen atoms, however poorly their positionscould be determined at the time. The whole molecule was consideredin examining their packing, rather than the heavy-atom skeleton only.Figuratively speaking, and using Kitaigorodskii’s own expression, he“dressed the molecules in a fur-coat of van der Waals spheres” [78].This was in complete agreement with the molecular models introduced from the early 1930s by Stuart and Briegleb to represent thespace-filling nature of molecular structures [79].The geometrical model allowed Kitaigorodskii to make predictionsof the structure of organic crystals in numerous cases, knowing onlythe cell parameters and, obviously, the size of the molecule itself [80].In the age of fully automated, computerized diffractometers, this maynot seem to be so important, but it indeed is for our understanding thepacking principles in molecular crystals.The packing as established by the geometrical model is what isexpected to be the ideal arrangement.
Usually it does not differ muchfrom the real packing as determined by X-ray diffraction measurements. When there are differences between the ideal and experimentally determined packings, it is of interest to examine the reasonsof their occurrence. The geometrical model has some simplifyingfeatures. One of them is that it considers uniformly the intermolecularatom–atom distances. Another is that it considers interactions onlybetween adjacent atoms.4649 CrystalsThe development of experimental techniques and the appearanceof more sophisticated models have pushed the frontiers of molecularcrystal chemistry much beyond the original geometrical model.
Someof the limitations of this model will be mentioned later. However, itssimplicity and the facility of visualization ensure this model a lastingplace in the history of molecular crystallography. It has also exceptional didactic value.The so-called coefficient of molecular packing (k) has proved usefulin characterizing molecular packing. It is expressed in the followingway:k=molecular volumecrystal volume/moleculeThe molecular volume is calculated from the molecular geometryand the atomic radii. The quantity crystal volume/molecule is determined from the X-ray diffraction experiment.
For most crystals k isbetween 0.65 and 0.77. This is remarkably close to the coefficient ofthe dense packing of equal spheres (the density of closest packing ofequal spheres being 0.7405). If the form of the molecule does notallow the coefficient of molecular packing to be greater than 0.6,then the substance is predicted to transform into a glassy state withdecreasing temperature. It has also been observed that morphotropicchanges associated with loss of symmetry led to an increase in thepacking density. Comparison of analogous molecular crystals showsthat sometimes the decrease in crystal symmetry is accompanied byan increase in the density of packing.Another interesting comparison involves benzene, naphthalene, andanthracene.
When their coefficient of packing is greater than 0.68,they are in the solid state. There is a drop in this coefficient to 0.58when they go into liquid phase. Then, with increasing temperature,their k is decreasing gradually down to the point where they startto boil. The fused-ring aromatic hydrocarbons have served subsequently as targets of a systematic analysis of packing energies andother packing characteristics [81].Geometrical considerations have gained additional importancedue to their role in molecular recognition which implies “the(molecular) storage and (supramolecular) retrieval of molecular structural information” [82]. The formation of supramolecular structures necessitates commensurable and compatible geometries of the9.6.
Molecular Crystals465partners. The molecular structure of the inclusion complex para-tertbutylcalix[4]arene and anisole [83] is shown in Figure 9-47. Therepresentation is a combination of a line drawing of the calixaranemolecule and a space-filling model of anisole.Figure 9-47.
Two para-tert-butylcalix[4]arene molecules envelope an anisolemolecule after Andreetti et al. [84].The supramolecular formations and the molecular packing in thecrystals show close resemblance, and the nature of the interactionsinvolved is very much the same. There is great emphasis on weakinteractions in both. According to Lehn, “beyond molecular chemistry based on the covalent bond lies supramolecular chemistry basedon molecular interactions—the associations of two or more chemical entities and the intermolecular bond” [85].
Dunitz expressedeloquently the relevance of supramolecular structures to molecularcrystals and molecular packing [86]:... a crystal is, in a sense, the supramoleculepar excellence—a lump of matter, of macroscopic dimensions, millions of molecules long,held together in a periodic arrangement by justthe same kind of non-bonded interactions as thosethat are responsible for molecular recognition andcomplexation at all levels. Indeed, crystallizationitself is an impressive display of supramolecularself-assembly, involving specific molecular recognition at an amazing level of precision.4669 Crystals9.6.2.
Densest Molecular PackingKitaigorodskii examined the relationship between densest packingand crystal symmetry by means of the geometrical model [87]. Hedetermined that real structures will always be among those that havethe densest packing. First of all, he established the symmetry of thosetwo-dimensional layers that allow a coordination number of six inthe plane at an arbitrary tilt angle of the molecules with respect tothe axes of the layer unit cell. In the general case for molecules witharbitrary form, there are only two kinds of such layers.
One has inversion centers and is associated with a non-orthogonal lattice. The otherhas a rectangular net, from which the associated lattice is formed bytranslations, plus a second-order screw axis parallel to a translation.The next task was to select the space groups for which such layersare possible. This is an approach of great interest since the result willanswer the question as to why there is a high occurrence of a fewspace groups among the crystals while many of the 230 groups hardlyever occur.We present here some of the highlights of Kitaigorodskii’s considerations [88]. First, the problem of dense packing is examined forthe plane groups of symmetry. The distinction between dense-packed,densest-packed, and maximum density was introduced for the planelayer of molecules. The plane was called dense-packed when coordination of six was achieved for the molecules.
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