M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 73
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There has been considerable progress in this respect, however, mainly due to the utilization ofthe wealth of information from data banks, and in particular, from theCambridge Crystallographic Data Centre.4729 CrystalsIt has also proved fruitful to use energy calculations with computergraphic analysis. Plausible crystal-building scenarios have beendescribed which, while not being necessarily unique solutions, seemto point in the right direction in conquering this important frontier ofstructural science. An example is the construction of organometalliccrystals, illustrated here with Ru3 (CO)12 in Figure 9-53. It is a simultaneous process in reality, but is broken down into three steps inthe model. First, a row of molecules is constructed in a head-to-tailarrangement.
The second step involves adding rows to form a layerutilizing interlocking interactions. Finally, whole layers are added toform a crystal [97]. By now, these studies have acquired rather historical importance because there is an increasing number of computational efforts to predict molecular packing from the composition ofsubstances. These efforts concentrate on selected classes of related(a)(b)(c)Figure 9-53.
Building a crystal of Ru3 (CO)12 according to Braga and Grepioni[98]; (a) Row of molecules; (b) Forming a layer; (c) Extending in three dimensions.Copyright (1991) American Chemical Society.9.6. Molecular Crystals473compounds rather than aim at finding a general approach. Maddox’stwo-decade-old lamentation seems to maintain its general validity.A concerted use of geometry and energy considerations, as demonstrated by the crystal-building of Ru3 (CO)12 , seems very promising.Extending such studies point in the direction of a “Kitaigorodskiandream,” as they “provide the starting point for the formulation ofa generalized force field for intermolecular interactions in organiccrystals” [99].There seems to be a remarkable consistency between BuckminsterFuller’s evaluation of chemistry (“chemists consider volumes asmaterial domains and not merely as abstractions,” see Chapter 1—Introduction) and Kitaigorodskii’s geometrical model of crystal structures.
In one of his last statements Kitaigorodskii (Figure 9-54) said(when asked about his most important achievements in science): “I’veshown that the molecule is a body.† One can take it, one can hitwith it; it has mass, volume, form, hardness. I followed the ideas ofDemocritos...” [100].Figure 9-54. A. I. Kitaigorodskii (1914–1985) among his students in the late 1960sin Moscow. István Orosz’s rendition of “Complementary Kitaigorodsky” [101].†Another version is also attributed to Kitaigorodskii, “The molecule also has a body;when it’s hit, it feels hurt all over.” This implied the possibility of structural changesin the molecule upon entering the crystal structure, a symbolic departure fromKitaigorodskii’s earlier views about the constancy of molecular geometry regardless whether in the gas phase or in the crystal.4749 Crystals9.6.4.
HypersymmetryThere are some crystal structures in which further symmetries arepresent in addition to those prescribed by their three-dimensionalspace groups. The phenomenon is called hypersymmetry [102]. Thus,it refers to symmetry features not included in the system of the230 three-dimensional space groups. For example, phenol molecules,connected by hydrogen bonds, form spirals with threefold screw axesas indicated in Figure 9-55. This screw axis does not extend, however,to the whole crystal, and it does not occur in the three-dimensionalspace group characterizing the phenol crystal.A typical characteristic of hypersymmetry operations is that theyexercise their influence in well-defined discrete domains.
Thesedomains do not overlap—they do not even touch each other. The usualhypersymmetry elements lead to point-group properties. This meansthat no infinite molecular chains could be selected, for example, towhich these hypersymmetry operations would apply. They affect,instead, pairs of molecules or very small groups of molecules. Thus,they can really be considered as local point-group operations.
Thesehypersymmetry elements, accordingly, divide the whole crystallinesystem into numerous small groups of molecules, or transform thecrystal space into a layered structure.Figure 9-55. The molecules in the phenol crystal are connected by hydrogen bondsand are forming spirals with a threefold screw axis. This symmetry element is notpart of the three-dimensional space group of the phenol crystal. After Zorky andKoptsik [103].9.6. Molecular Crystals475A prerequisite for hypersymmetry is that there should be chemically identical (having the same structural formula), but symmetricallyindependent, molecules in the crystal structure—symmetrically independent, that is, in the sense of the three-dimensional space group towhich the crystal belongs.
The question then arises as to whether thesesymmetrically independent but chemically identical molecules willhave the same structure or not. Only if they do have the same structure, conformation as well as bond configuration, can we talk aboutthe validity of the hypersymmetry operations. Here, preferably, quantitative criteria should be introduced, which is the more difficult since,for example, with increasing accuracy, structures that could be considered identical before, may no longer be considered so later when moreaccurate data become available.On the other hand, since even a slightly different environment willhave some influence on the molecular structure, the hypersymmetryoperations will not be absolute. In this, the hypersymmetry operationsare somewhat different from the usual symmetry operations.
The ultimate goal is to find such a generalized formulation of the space-groupsystem that would allow the simultaneous consideration of the usualsymmetry as well as the hypersymmetry. When such a generalizedformulation of space groups encompassing usual and hypersymmetryoperations becomes available, the task of discovering crystals withhypersymmetry will be greatly facilitated.A special case of hypersymmetry is when the otherwise symmetrically independent molecules in the crystal are related by hypersymmetry operations making them enantiomorphous pairs.Hypersymmetry is a rather widely observed, and sometimesignored, phenomenon which is not restricted to any special classof compounds.
It may be supposed, however, that certain types ofmolecules are more apt to have this kind of additional symmetry intheir crystal structures than others.There are hypersymmetry phenomena in some crystal structuresthat are characterized by extra symmetry operations applicable to infinite chains of molecules. This kind of hypersymmetry has proved tobe more easily detectable and has been reported often in the literature [104].Hypersymmetry may be interpreted on the basis of the symmetryof the potential energy functions describing the conditions of theformation of the molecular crystal.
The molecules around a certain4769 Crystalsstarting molecule will be related by the symmetry of the potential energy function itself or the symmetry of certain combinations of the potential energy functions. The occurrence of somescrew axes of rotation by hypersymmetry elements has been successfully interpreted this way.
In some instances energy calculationsas well as geometrical reasoning have shown the physical importance of hypersymmetry. This may appear, e.g., as stronger chemicalbonding among molecules. Hypersymmetry may often be describedas involving layered structure of a molecular crystal. This, again, mayhave advantages for geometrical and energy considerations. Thus,the phenomenon of hypersymmetry is another good example of howsymmetry properties and other properties are related to each other.9.6.5.
Crystal Field EffectsElucidating the effects of intermolecular interactions may greatlyfacilitate our understanding of the structure and energetics of crystals.The geometrical changes of molecular structures cover a wide range inenergy. Molecular shape, symmetry, and conformation change moreeasily upon the molecule becoming part of a crystal than do bondangles and especially bond lengths.Kitaigorodskii suggested four approaches to investigating theeffects of the crystalline field on molecular structure [105]: (1)comparison of gaseous (i.e., free) and crystalline molecules; (2)comparison of symmetrically (i.e., crystallographically) independentmolecules in the crystal; (3) analysis of the structure of moleculeswhose symmetry in the crystal is lower than their free molecularsymmetry; and (4) comparison of the molecular structure in differentpolymorphic modifications.It is also possible that the molecule has higher symmetry in thecrystal than as a free unit in the gas.
Thus, e.g., biphenyl has a highermolecular symmetry—a coplanar structure—in the crystal than in thevapor, where the two benzene rings are rotated by about 45◦ relativeto each other as shown below (9-1).9-19.6. Molecular Crystals4779.6.5.1. Structure Differences in Free and Crystalline MoleculesThe points 1 and 3 above both refer to the comparison of the structures of free and crystalline molecules as does the last example inthe previous section.
Such comparisons provide, perhaps, the moststraightforward information, since the structure of the free molecule isdetermined exclusively by intramolecular interactions. Any differencethat is reliably detected will carry information as to the effects of thecrystal field on the molecular structure.
However, before discussingmore subtle structural differences in molecular crystals as comparedwith free molecules, it is appropriate to point out some more strikingdifferences between ionic crystals and the corresponding vapor-phasemolecules.Although molecules cannot be identified as the building blocks ofionic crystals, the free molecules of some compounds may be considered as if they were taken out of the crystal.
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