M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 74
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A nice example is sodiumchloride whose main vapor components are monomeric and dimericmolecules. They are indicated in the crystal structure in Figure 9-56,as is a tetrameric species. Mass spectrometric studies of cluster formation determined a great relative abundance of a species with 27 atomsin the cluster. The corresponding 3×3×3 cube may, again, be considered as a small crystal [106].Another series of simple molecules whose structure may easilybe traced back to the crystal structure is shown in Figure 9-57.It is evident, for example, that various MX2 and MX3 moleculesmay take different shapes and symmetries from the same kind ofFigure 9-56. Part of sodium chloride crystal structure with NaCl, (NaCl)2 , and(NaCl)4 units indicated.
The species of 3x3x3 ions itself has a high relative abundance in cluster formation.4789 CrystalsFigure 9-57. Different shapes of MX2 and MX3 molecules derived from the crystalstructure in which the central atom has an octahedral environment.crystal structure. The crystal structure is represented by the octahedral arrangement of six “ligands” around the “central atom.”There seems to be even less structural similarity for many othermetal halides as the crystalline systems are compared with themolecules in the vapor phase.
Aluminum trichloride, e.g., crystallizes in a hexagonal layer structure. Upon melting, and then,upon evaporation at relatively low temperatures, dimeric moleculesare formed. At higher temperatures they dissociate into monomers(Figure 9-58) [107]. The coordination number decreases from 6 to4 and then to 3 in this process. However, at closer scrutiny, eventhe dimeric aluminum trichloride molecules can be derived from thecrystal structure. Figure 9-59 shows another representation of crystalline aluminum trichloride which facilitates the identification ofthe dimeric units.
A further example is chromium dichloride illustrated in Figure 9-60. The small oligomers in its vapor have structures[108] that are closely related to the solid structure [109]. Correlation between the molecular composition of the vapor and their sourcecrystal has been established for some metal halides [110].Gas/solid differences of different nature may occur in substancesforming molecular crystals. In some cases, e.g., the vapor containsmore rotational isomers than the crystal. Thus, for example, the vaporof ethane–1,2–dithiol, HS–CH2 –CH2 –SH, consists of anti and gauche9.6.
Molecular Crystals479Figure 9-58. Structural changes upon evaporation of aluminium trichloride.Figure 9-59. The crystal structure of aluminium trichloride after Müller [111]. Thedimeric unit with four-member ring is discernible. Copyright 1993 John Wiley &Sons. Used by permission.forms with respect to rotation about the central bond while only theanti form was found in the crystal [113].The comparison of the structures of free and crystalline moleculeshas been based predominantly on the application of various experimental techniques, but theoretical calculations play an ever increasingrole. Thus, it is important to comment upon the inherent differencesin the physical meaning of the structural information originatingfrom such different sources [114].
The consequences of intramolecular vibrations on the geometry of free molecules have already been480(a)9 Crystals(b)Figure 9-60. Four-membered rings are present both in (a) The crystal; and (b) Thevapor-phase molecules of chromium dichloride [112].mentioned. The effects of molecular vibrations and librational motionin the crystal are not less important. To minimize their effects, itis desirable to examine the crystal molecular structure at the lowestpossible temperatures.
Also, the corrections for thermal motion are ofgreat importance. Especially when employing older data in comparisons and discussing subtle effects, these problems have to be considered. There is another source for differences in structural information,which are only apparent differences and originate from the differencein the physical meaning of the physical phenomena utilized in theexperimental techniques.
When all sources of apparent differenceshave been eliminated, and the molecular structure still differs in thegas and the crystal, the intermolecular interactions in the crystal mayindeed be responsible for these differences [115].The comparisons of gas/crystal structures may stimulate more accurate structure determinations by experiment as well as calculationsof ever increasing sophistication.
The gas/crystal structural changesdepend on the relative strengths of the intramolecular and intermolecular interactions. More pronounced changes are expected, forexample, in relatively weak coordination linkages under the influenceof the crystal field than in stronger bonds.
Thus, the N–B bond ofdonor-acceptor complexes is considerably longer in the gas than in thecrystal. The difference is about 5 pm for (CH3 )3 N–BCl3 (9-2) [116]9.6. Molecular Crystals4819-2and it may be supposed that the intermolecular forces somewhatcompress the molecule along the coordination bond in the crystal.An extreme case of an 84 pm difference was reported for HCN–BF3[117]. Another example is the silatrane structures where the relativelyweak N–Si dative bond is much longer in the gas than in the crystal.This difference is 28 pm for 1-fluorosilatrane [118], represented here(9-3) by the heavy-atom skeleton.9-3Gas/crystal comparisons are as of yet mainly confined to registering structural differences.
The interpretation of these results is ata qualitative initial stage. Further investigation of such differenceswill enhance our understanding of the intermolecular interactions incrystals.9.6.5.2. Conformational PolymorphismThe investigation of different rotational isomers of the samecompound in different crystal forms (polymorphs) is another efficienttool in elucidating intermolecular interactions.
The phenomenon iscalled conformational polymorphism. The energy differences between4829 Crystalsthe polymorphs of organic crystals are similar to the free energy differences of rotational isomers of many free molecules, viz., a few kilocalories per mole. When the molecules adopt different conformationsin the different polymorphs, the change in rotational isomerism isattributed to the influence of the crystal field since the difference inthe intermolecular forces is the single variable in the polymorphicsystems.Polymorphism is ubiquitous [119], and most compounds can existin more than one crystalline form.
Conformational polymorphism ofvarious organic compounds has been studied with a variety of techniques in addition to X-ray crystallography. Among the moleculesinvestigated were N-(p-chlorobenzylidine)-p-chloroaniline, [9-4,X = Cl (I)]XCHNX9-4which exists in at least two forms, and p-methyl-N(p-methylbenzylidene)aniline, [9-4, X = CH3 (II)], which existsin at least three forms. For I, a high-energy planar conformation wasshown to occur with a triclinic lattice. A lower-energy form withnormal exocyclic angles was found in the orthorhombic form.
It wasan intriguing question as to why molecule I would not always packwith its lowest-energy conformation.The X-ray diffraction work has been augmented by lattice energycalculations employing different potential functions. The results didnot depend on the choice of the potential function, and they showedthat the crystal packing and the (intra)molecular structure togetheradopt an optimal compromise. The minimized lattice energies wereanalyzed in terms of partial atomic contributions to the total energy.Even for the trimorphic molecule (II) the relative energy contributions of various groups were similar in all polymorphs. However, thiscould only be achieved in some lattices by adopting a conformation,different from the most favorable, with respect to the structure of theisolated molecule. The investigation of conformational polymorphismproved to be a promising tool for understanding the nature of thecrystal forces influencing molecular conformation, and even molecular structure, in a broader sense.9.7.
Beyond the Perfect System483Possible variations in bond angles and bond lengths have beenignored in the considerations described above. The energy requirements for changing bond angles and bond lengths are certainly higherthan those for conformational changes, and, accordingly, higher thanwhat may be available in polymorphic transitions.
However, somerelaxation of the bond configuration may take place, especially ifconsidering that the (intra)molecular structure is also adopted asa compromise between the bond configurations and the rotationalforms.Bond configuration relaxation during internal rotation is anotherphenomenon whose understanding might throw some light on thecorrelations among the various intramolecular and intermolecularinteractions. In this case, quantum chemical calculations may be thetechnique of choice.
An early study, for example, targeted a seriesof 1,2-dihaloethanes [120]. The bond angle C–C–X was observed tochange as much as 4◦ during internal rotation according to these calculations. If there is then a mixture of, say, anti and gauche forms, as isoften the case, and the relaxation of the bond configuration is ignored,this may lead to considerable errors in the determination of the gaucheangle of rotation.9.7. Beyond the Perfect SystemThe 230 space groups exhaustively characterize all the symmetriespossible for infinite lattice structures.
So “exhaustively” that sometime ago some crystallographers and other scientists started viewingthis perfect system as a little too perfect and a little too rigid. Theseviews pointed toward the further development of our ideas on structures and symmetries.There is an inherent deficiency in crystal symmetry in that crystalsare not really infinite. Alan Mackay argued that the crystal formationis not the insertion of components into a three-dimensional frameworkof symmetry elements; on the contrary, the symmetry elements arethe consequence [121].
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