M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 22
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Pauling, The Nature of the Chemical Bond, 3rd ed. Cornell UniversityPress, Ithaca, New York, 1960.bAfter L. S. Bartell, “Molecular Geometry: Bonded Versus Nonbonded Interactions.” J. Chem. Educ. 1968, 45, 754–767; C. Glidewell, “Intramolecular Nonbonded Atomic Radii – Application to Heavier p Elements.” Inorg. Chim. Acta1976, 20, 113–118.1383 Molecular Shape and GeometryFigure 3-32. Geometrical consequences of nonbonded interactions after L. S.Bartell [85].
(a) The three outer carbon atoms of H2 C=C(CH3 )2 are in the cornersof an approximately equilateral triangle, leading to a relaxation of the bond anglebetween the ethyl groups; (b) Considerations of nonbonded interactions in the interpretation of the C–C single bond length changes in a series of molecules.other example, in Figure 3-32, the C–C bond lengthening is related tothe increasing number of nonbonded interactions. Of course, the 1,3intramolecular nonbonded radii (Table 3-5) are purely empirical, butso are the other kinds of radii. Thus, the 1,3-nonbonded radii may beupdated from time to time.Of the observations of constancy of nonbonded distances, herewe single out one [86].
The O···O nonbonded distances in XSO2 Ysulfones have been found to be remarkably constant at 248 pm ina relatively large series of compounds. At the same time the S=Obond lengths vary up to 5 pm and the O=S=O bond angles up to 5◦depending on the nature of the X and Y ligands. The geometrical variations in the sulfone series could be visualized (Figure 3-33) as if thetwo oxygen ligands were firmly attached to two of the four vertices ofthe ligand tetrahedron around the sulfur atom, and this central atomwere moving along the bisector of the OSO angle depending on the Xand Y ligands.
The sulfuric acid, H2 SO4 , or (HO)SO2 (OH), moleculehas its four oxygens around the sulfur at the vertices of a nearly regularFigure 3-33. Tetrahedral sulfur configurations; from the left: sulfones; sulfuric acid;alkali sulfates.3.7. Polyhedral Molecular Geometries139tetrahedron. Compared with the differences in the various OSO angles(up to 20◦ ) and in the two kinds of SO bonds (up to 15 pm), the largestdifference among the six O···O nonbonded distances is only 7 pm [87].The alkali sulfate molecules used to appear in old textbooks withthe following structural formula:However, the SO4 groups have nearly regular tetrahedral configuration in such molecules.
The metal atoms are located on axes perpendicular to the edges of the SO4 tetrahedron. Thus, this structure isbicyclic as shown in Figure 3-33.3.7.5. The VSEPR ModelNumerous examples of molecular structures have been introduced inthe preceding sections. They are all confirmed by modern experimentsand/or calculations. We would like to know, however, not only thestructure of a molecule and its symmetry, but also, why a certain structure with a certain symmetry is realized.It has been a long-standing goal in chemistry to determine theshape and measure the size of molecules, and also to calculate theseproperties. Today, quantum chemistry is capable of determining thestructure of molecules of ever growing complexity, starting from themere knowledge of the atomic composition, and without using anyempirical information.
Such calculations are called ab initio. Theprimary results from these calculations are, however, wave functionsand energies which may also be considered “raw measurements,”similar to some experimental data. At the same time there is a desireto understand molecular structures in simple terms—such as, forexample, the localized chemical bond—that have proved so useful tochemists’ thinking. There is a need for a bridge between the measurements and calculations on one hand, and simple qualitative ideas, onthe other hand.
There are several qualitative models for molecularstructure that serve this purpose well. These models can explain, forexample, why the methane molecule is regular tetrahedral, Td , whyammonia is pyramidal, C3v , why water is bent, C2v , and why the xenon1403 Molecular Shape and GeometryFigure 3-34.
Molecular configuration of OPF3 (C3v ) and OClF3 (Cs ).tetrafluoride molecule is square planar, D4h . It is also important tounderstand why seemingly analogous molecules like OPF3 and OClF3have so different symmetries, the former C3v , and the latter Cs , as seenin Figure 3-34.The structure of a series of the simplest AXn type molecules willbe examined in terms of one of these useful and successful qualitativemodels. A is the central atom, the Xs are the ligands, and not necessarily all n ligands are the same.Qualitative models simplify. They usually consider only a few, ifnot just one, of the many effects that are present and are interactingin a most complex way.
The measure of the success of a qualitativemodel is in its ability to create consistent patterns for interpreting individual structures and structural variations in a series of molecules and,above all, in its ability to correctly predict the structures of molecules,not yet studied or not even yet prepared.One of the simplest models [88] is based on the following postulate: The geometry of the molecule is determined by the repulsionsamong the electron pairs in the valence shell of its central atom. Thevalence shell of an atom may have bonding pairs and other electronpairs that do not participate in bonding and belong to this atom alone.The latter are called unshared or lone pairs of electrons.
The abovepostulate emphasizes the importance of both bonding pairs and lonepairs in establishing the molecular geometry. The model is appropriately called the Valence Shell Electron Pair Repulsion or VSEPRmodel. The bond configuration around atom A in the molecule AXnis such that the electron pairs of the valence shell are at maximumdistances from each other. Thus, the situation may be visualized insuch a way that the electron pairs occupy well-defined domains of the3.7.
Polyhedral Molecular Geometries141Table 3-6. Arrangements of Two to Six ElectronPairs That Maximize Their Distances ApartNumber of electron pairsArrangementin the valence shell23456LinearEquilateral triangleTetrahedronTrigonal bipyramidOctahedronspace around the central atom corresponding to the concept of localized molecular orbitals.If it is assumed that the valence shell of the central atom retainsits spherical symmetry in the molecule, then the electron pairs will beat equal distances from the nucleus of the central atom.
In this casethe arrangements at which the distances among the electron pairs areat maximum, will be those listed in Table 3-6. If the electron pairsare represented by points on the surface of a sphere, then the shapesshown in Figure 3-35 are obtained by connecting these points. Of thethree polyhedra appearing in Figure 3-35, only two are regular, viz.,the tetrahedron and the octahedron. The trigonal bipyramid is not aregular polyhedron; although its six faces are equivalent, its edges andvertices are not. Incidentally, the trigonal bipyramid is not a uniquesolution to the five-point problem.
Another, and only slightly lessadvantageous arrangement, is the square pyramidal configuration.Figure 3-35. Molecular shapes from a points-on-the-sphere model.1423 Molecular Shape and GeometryThe repulsions considered in the VSEPR model may be expressedby the potential energy termsVi j = k/rinjwhere k is a constant, rij is the distance between the points i and j; andthe exponent n is large for strong, or “hard,” repulsion interactionsand small for weak, or “soft,” repulsion interactions. This exponentn is generally much larger than it would be for simple electrostaticCoulomb interactions.
Indeed, when n is larger than 3, the resultsbecome rather insensitive to the value of n. That is very fortunatebecause n is not really known. This insensitivity to the choice of nis what provides the wide applicability of the VSEPR model.3.7.5.1. AnalogiesIt is easy to illustrate the three-dimensional consequences of theVSEPR model with examples from our macroscopic world.
We needonly to blow up a few balloons that children play with. If groups oftwo, three, four, five, and six balloons, respectively, are connected atthe ends near their openings, the resulting arrangements are shown inFigure 3-36. Obviously, the space requirements of the various groupsof balloons acting as mutual repulsions, determine the shapes andsymmetries of these assemblies. The balloons here play the role ofthe electron pairs of the valence shell.Another beautiful analogy with the VSEPR model, and one founddirectly in nature, is demonstrated in Figure 3-37.
These are hardshell fruits growing together. The small clusters of walnuts, e.g., haveexactly the same arrangements for two, three, four, and five walnutsin assemblies as predicted by the VSEPR model or as those shown bythe balloons. The walnuts—when they grow close to each other—areFigure 3-36. Shapes of groups of balloons.3.7. Polyhedral Molecular Geometries143Figure 3-37.
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