M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 24
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As the closest electron pairs exercise by farthe strongest repulsion, the axial positions are affected more than theequatorial ones. In agreement with this reasoning, the axial bonds areusually found to be longer than the equatorial ones. If there is a lonepair of electrons with a relatively large space requirement, it shouldbe found in the more advantageous equatorial position. Accordingly,the SF4 structure has C2v symmetry, as does the ClF3 molecule, whichis of the AX3 E2 type.
Finally, the XeF2 molecule is AX2 E3 with all3.7. Polyhedral Molecular Geometries149three lone pairs in the equatorial plane, hence its symmetry is D∞h .All these structures are depicted in Figure 3-38.By similar reasoning, the VSEPR model predicts that a double bondwill also occupy an equatorial position. Thus, the point group mayeasily be established for the molecules O=SF4 (C2v ), O=ClF3 (Cs ),XeO3 F2 (D3h ), and XeO2 F2 (C2v ).
We note the Cs symmetry for theOClF3 molecule (Figure 3-34) as a consequence of the bipyramidalgeometry with both the Cl=O double bond and the lone pair in theequatorial plane. The molecule OPF3 (Figure 3-34) is only seeminglyanalogous. There is no lone pair in the phosphorus valence shell inthis structure, and thus the molecule has a distorted tetrahedral bondconfiguration. The P=O double bond is along the three-fold axis, andthe point group is C3v , like that for ammonia.Lone pairs and/or double bonds replaced single bonds in the aboveexamples.
Similar considerations are applicable when only ligandelectronegativity changes take place. A typical example is demonstrated by a comparison of the structures of PF2 Cl3 and PF3 Cl2 . Thechlorine atoms are less electronegative ligands than the fluorines,and they will be in equatorial positions in both structures as seen inFigure 3-42. The point groups are C2v for PF3 Cl2 and D3h for PF2 Cl3[99]. Were the chlorines in the axial positions in PF3 Cl2 , this moleculewould also have the much higher symmetry D3h . This is an interestingexample also from the point of view that the highest symmetries donot necessarily occur in any given structure.
This is not, however, incontradiction with the “Principle of Maximum Symmetry” as statedby I. David Brown, “A compound will adopt the structure with thehighest symmetry that is consistent with the constraints acting on it”[100]. In the example above, the constraint is a chemical one, viz., theelectronegativity difference between the ligands chlorine and fluorinethat leads to a spatial constraint with respect to their bonding electrondomains.Figure 3-42.
The molecular structures of PF3 Cl2 and PF2 Cl3 are not analogous: thechlorine ligands occupy equatorial positions in both cases.1503 Molecular Shape and GeometryAll six electron pairs are equivalent in the AX6 molecule and sothe symmetry is unambiguously Oh . An example is SF6 . The IF5molecule, however, corresponds to AX5 E and its square pyramidalconfiguration has C4v symmetry.
There is no question here as tothe preferred position for the lone pair, as any of the six equivalentsites may be selected. When, however, a second lone pair is introduced, then the favored arrangement is that in which the two lonepairs find themselves at the maximum distance apart. Thus for XeF4 ,i.e., AX4 E2 , the bond configuration is square planar, point group D4h .These structures are depicted in Figure 3-38.The difficulties encountered in the discussion of the five-electronpair valence shells are intensified in the case of the seven-electronpair case. Here again the ligand arrangements are less favorable thanfor the nearest coordination neighbors, i.e., six and eight. It is notpossible to arrange seven equivalent points in a regular polyhedron,while the number of nonisomorphic polyhedra with seven vertices islarge, viz., 34 [101].
A few of them are shown in Figure 3-43. Nosingle one of them is distinguished, however, from the others on thebasis of relative stability. There may be quite rapid rearrangementsamong the various configurations. One of the early successes of theVSEPR model was that it correctly predicted a non-regular structurefor XeF6 by considering it as a seven-coordination case, AX6 E.Numerous examples, a wealth of structural data and detailedconsiderations on the potentials and limitations of the applicabilityof the VSEPR model are given in a monograph [102].Figure 3-43. A sample of configurations for seven electron pairs in the valenceshell.3.7. Polyhedral Molecular Geometries1513.7.5.3.
Historical RemarksThe simplicity of the VSEPR model is one of its primary strengths.In addition, the model provides a continuity in the development of thequalitative ideas about the nature of the chemical bond and its correlation with molecular structure. Abegg’s octet rule [103] and Lewis’theory of the shared electron pair [104] may be considered as directforerunners of the model. Lewis’ model of the cubical atom deservesspecial mention.
It was instrumental in shaping the concept of theshared electron pair. It also permitted a resolution of the apparentcontradiction between the two distinctly different bonding types, viz.,the shared electron pair and the ionic electron-transfer bond. In termsof Lewis’ theory, the two bonding types could be looked at as merelimiting cases.
Lewis’ cubical atoms are illustrated in Figure 3-44.They are also noteworthy as an example of a certainly useful thoughnot necessarily correct application of a polyhedral model.Sidgwick and Powell were first to correlate the number of electronpairs in the valence shell of a central atom and its bond configuration [106]. Then Gillespie and Nyholm introduced allowances for thedifference between the effects of bonding pairs and lone pairs, andapplied the model to large classes of inorganic compounds [107].There have been attempts to provide quantum-mechanical foundations for the VSEPR model. These attempts have developed along twolines.
One is concerned with assigning a rigorous theoretical basisto the model, primarily involving the Pauli exclusion principle. Theother line was the numerous quantum chemical calculations, whichhave already produced a large amount of structural data consistentwith the VSEPR model, demonstrating its ability to capture importanteffects determining the structure of molecules. It has also been shownthat while the total electron density distribution of a molecule doesnot provide any evidence for the localized electron pairs, the chargeconcentrations obtained by deriving the second derivative of thisdistribution parallel the features of these localized pairs [108]. Thismay be considered as supporting evidence, or even physical basis, forthe VSEPR model.
We would stress, however, that the VSEPR modelis a qualitative tool, and as such, it over-emphasizes some effects andignores many others. Its simplicity, wide applicability, and predictivepower have been repeatedly demonstrated, making it useful both inresearch and education.1523 Molecular Shape and GeometryFigure 3-44. G.
N. Lewis’ cubical atoms and some molecules built from such atoms(top) and his original sketches (bottom) [105].3.7.6. Consequences of Intramolecular MotionImagine the merry-go-round (Figure 3-45) revolving, and one of thewooden horses getting lifted and, upon its returning to the groundlevel, the next horse is getting lifted, and so on.
In addition to thereal revolution of the whole circle, the vertical motion is transmittedfrom horse to horse which can be considered pseudorotation. If wetake a snapshot of the merry-go-round in operation and the exposureis long enough, there will be a blurred image of all the horses upin the elevated position in addition to the ground circle.
With a veryshort exposure, however, we can get an image in which the momentis captured with a single horse being lifted. Another fitting analogy3.7. Polyhedral Molecular Geometries153may be the Dance by Henri Matisse (Figure 3-45). Let us imagine thefollowing coreography for this dance: one of the dancers jumps and isthus out of the plane of the other four. As soon as this dancer returnsinto the plane of the others, it is now the role of the next to jump, andso on.
The exchange of roles from one dancer to another throughoutthe five-member group is so quick that if we take a normal snapshot,we will have a blurred picture of the five dancers. However, if we canuse a very short exposure, it will be possible to capture a well-definedconfiguration of the dancers.The above descriptions well simulate the pseudorotation of thecyclopentane, (CH2 )5 , molecule (Figure 3-46), although on a differenttime scale.
This molecule has a special degree of freedom when theout-of-plane carbon atom exchanges roles with one of its two neigh-Figure 3-45. Merry-go-round in Bologna, Italy (photograph by the authors) andHenri Matisse’s Dance (The Hermitage, St. Petersburg, reproduced by permission).1543 Molecular Shape and GeometryFigure 3-46. Two models of the cyclopentane molecule from its pseudorotation.boring carbon atoms (and their hydrogen ligands). This is equivalentto a rotation of this motion by 2/5 about the axis perpendicular to theplane of the in-plane carbons [109]. All three examples emphasize theimportance of the relationship between the time-scale of motion andthe time-scale of measurement. This relationship must be taken intoaccount when making a conclusion about the symmetry of a structurein motion.In discussing molecular structure, an extreme approach is todisregard intramolecular motion and to consider the molecule to bemotionless.
A frozen, completely rigid molecule is a hypotheticalstate corresponding to the minimum position of the potential energyfunction for the molecule. Such a motionless structure has an important and well-defined physical meaning and is called the equilibriumstructure. It is this equilibrium structure that emerges from quantumchemical calculations. On the other hand, real molecules are nevermotionless, not even at the temperatures approaching 0 K. Furthermore, the various physical measurement techniques determine thestructures of real molecules.
As our discussion of the merry-go-roundand Matisse’s Dance illustrated, the relationship between the lifetime of the configuration under investigation and the time-scale ofthe investigating technique is of crucial importance.Large-amplitude, low-frequency intramolecular vibrations maylower the molecular symmetry of the average structure from the highersymmetry of the equilibrium structure. Some examples from metalhalide molecules are shown in Figure 3-47.If we determine the average interatomic distances of symmetrictriatomic molecules, for example, the emerging geometry will alwaysbe bent, regardless whether the equilibrium structure is linear or bentbecause of the consequences of bending vibrations (Figure 3-48).In order to distinguish between them, the potential energy func-3.7.
Polyhedral Molecular Geometries155Figure 3-47. Equilibrium versus average structures of simple metal halidemolecules with low-frequency, large-amplitude deformation vibrations.tion describing the bending motion must be scrutinized [110]. Thebending potential energy functions of ZnCl2 and SrBr2 are shownin Figure 3-48; the bending angle e = 0◦ corresponds to the linearconfiguration. The minimum of the potential energy appears at e = 0◦for both molecules. It is also seen though that the minimum is muchmore shallow for SrBr2 than for ZnCl2 . Figure 3-48 shows twomore bending potential energy functions, those of SiBr2 and, again,of SrBr2 , but at very diffent scales as compared with the previousexample.
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