M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 23
Текст из файла (страница 23)
Walnut clusters (photographs by the authors).required to accommodate themselves to each other’s company andfind the arrangements that are most advantageous considering thespace requirements of all. Incidentally, the balloons and the walnutsmay take us one step further in analogies as they may be considered as “soft” and “hard” objects, with weak and strong interactions,respectively.3.7.5.2. Molecular ShapesUsing the VSEPR model, it is simple to predict the shape andsymmetry of a molecule from the total number of bonding pairs, n,and lone pairs, m, of electrons in the valence shell of its central atom.The molecule may then be written as AXn Em where E denotes a lonepair of electrons.
Only a few examples will be described here for illustration. For a comprehensive coverage see, e.g., the monograph [89].First, we consider the methane molecule, shown in the second rowof Figure 3-38, together with ammonia and water. Originally, therewere four electrons in the carbon valence shell, and these formedfour C–H bonds, with the four hydrogens contributing the other fourelectrons. Thus, methane is represented as AX4 and its symmetry is,accordingly, regular tetrahedral. In ammonia, originally there were1443 Molecular Shape and GeometryFigure 3-38. Bond configurations with 2, 3, 4, 5, and 6 electron pairs in the valenceshell of the central atom [90].five electrons in the nitrogen valence shell, and the formation of thethree N–H bonds added three more. With the three bonding pairs andone lone pair in the nitrogen valence shell, ammonia may be writtenas AX3 E, and, accordingly, the arrangement of the molecule is relatedto a tetrahedron.
However, only in three of its four directions do wefind bonds, and consequently ligands, while in the fourth there is alone pair of electrons. Hence a pyramidal geometry is found for theammonia molecule. The bent configuration of the water molecule canbe similarly deduced.In order to establish the total number of electron pairs in the valenceshell, the number of electrons originally present and the number of3.7. Polyhedral Molecular Geometries145bonds formed need to be considered.
A summary of molecular shapesbased on the arrangements of two to six valence shell electron pairs isshown in Figure 3-38.The molecular shape to a large extent determines the bond angles.Thus, the bond angle X–A–X is 180◦ in the linear AX2 molecule,it is 120◦ in the trigonal planar AX3 molecule, and 109◦ 28’ in thetetrahedral AX4 molecule. The arrangements shown in Figure 3-38correspond to the assumption that the strengths of the repulsions fromall electron pairs are equal.
In reality, however, the space requirements and, accordingly, the strengths of the repulsions from variouselectron pairs may be different depending on various circumstancesas described in the following three subrules [91]:1. A lone pair, E, in the valence shell of the central atom has a greaterspace requirement in the vicinity of the central atom than doesa bonding pair. Thus, a lone pair exercises a stronger repulsiontowards the neighboring electron pairs than does a bonding pair, b.The repulsion strengths weaken in the following order:E/E > E/b > b/bThis order is well illustrated by the various angles in sulfur difluoride in Figure 3-39 as determined by ab initio molecular orbitalcalculations [92]. This is also why, for example, the bond anglesH–N–H of ammonia, 106.7◦ , are smaller than the ideal tetrahedral value, 109.5◦ .
Unless stated otherwise, the parameters in thepresent discussion are taken from the Landolt Börnstein Tables[93].Figure 3-39. The angles of sulfur difluoride as determined by ab initio molecularorbital calculations [94].2. Multiple bonds, bm , have greater space requirements than dosingle bonds and thus exercise stronger repulsions toward the1463 Molecular Shape and Geometryneighboring electron pairs than do single bonds. The repulsionstrengths weaken in the following order:bm /bm > bm /b > b/bA consequence of this is that the bond angles will be largerbetween multiple bonds than between single bonds.
The structureof dimethyl sulfate in Figure 3-40 provides a good example in thatit has three different types of OSO bond angles, and they decreasein the following order [95]:S = O/S = O > S = O/S−O > S−O/S−OFigure 3-40. The three different kinds of oxygen–sulfur–oxygen bond angles in thedimethyl sulfate molecule as determined by electron diffraction [96].3. A more electronegative ligand decreases the electron density in thevicinity of the central atom as compared with a less electronegative ligand.
Accordingly, the bond to a less electronegative ligand,bX , has a greater space requirement than the bond to a more electronegative ligand, bY . The repulsion strengths then weaken in thefollowing order:bX /bX > bX /bY > bY /bYConsequently, the bond angles are smaller for more electronegativeligands than for less electronegative ligands. An example of thiseffect can be seen in a comparison of sulfur difluoride (98◦ ) andsulfur dichloride (103◦ ).It is interesting to compare the implications expressed by thesesubrules with the depiction of some localized molecular orbitals inFigure 3-41 [97].
The lone pair of electrons occupies more space thando the bonding pairs in the vicinity of the central atom. Also, a bond toa more electronegative ligand such as fluorine occupies less space in3.7. Polyhedral Molecular Geometries147Figure 3-41. Localized molecular orbitals represented by contour lines denotingelectron densities of 0.02, 0.04, 0.06, etc.
electron/bohr3 from theoretical calculations for the S–H, S–F, and S=O bonds and the lone pair on sulfur [98].the vicinity of the central atom than does a bond to a less electronegative ligand such as hydrogen. Finally, a double bond occupies morespace than a single bond. The angular ranges of the correspondingcontours in the electron density plots are all in good qualitative agreement with the postulates of the VSEPR model.The VSEPR model has a fourth subrule that concerns the relativeavailability of space in the valence shell:4. There is less space available in a completely filled valence shellthan in a partially filled valence shell. Accordingly, the repulsionsare stronger and the possibility for angular changes are smaller inthe filled valence shell than in the partially filled one.
Thus, forexample, the bond angles of ammonia (107◦ ) are closer to the idealtetrahedral value than are those of phosphine (94◦ ).Thus, the differences in the electron pair repulsions may accountfor the bond angle variations in various series of molecules.
The question now arises as to whether these differences have any effect on thesymmetry choice of the molecules. In the four-electron-pair systemsthe differences in the electron pair repulsions have a decisive role inthe sense that the AX4 , EBX3 , E2 CX2 molecules have Td , C3v , and C2vsymmetries, respectively. Within each series, however, the symmetryis preserved regardless of the changes in the ligand electronegativities.For example, only the bond angles change in the molecules EBX3 , andEBY3 ; the symmetry remains the same.1483 Molecular Shape and GeometryLigand electronegativity changes may have decisive effects,however, on the symmetry choices of various bipyramidal systems,of which the trigonal bipyramidal configuration is the simplest.When five electron pairs are present in the valence shell of thecentral atom, the trigonal bipyramidal configuration is usually found,although a tetragonal pyramidal arrangement cannot be excluded insome cases.
Even intermediate arrangements between these two mayappear to be the most stable in some special structures. The trigonal bipyramidal configuration with an equilateral triangle in theequatorial plane has D3h symmetry while the square pyramidal hasC4v symmetry. The intermediate arrangements have C2v symmetryor nearly so. Indeed, rearrangements often occur in trigonal bipyramidal structures performing low-frequency large-amplitude motion.Such rearrangements will be illustrated later.The positions in the D3h trigonal bipyramid are generally not equivalent, and the axial ligand position is further away from the centralatom than the equatorial one. This has no effect on the symmetryof the AX5 structures, and this is comforting from the point of viewof the applicability of the VSEPR model in establishing the pointgroup symmetries of such molecules. On the other hand, when thereis inequality among the electron pairs, the differences in the axialand equatorial positions do have importance for symmetry considerations.
The PF5 molecule, as an AX5 system, shows unambiguouslyD3h symmetry in its trigonal bipyramidal configuration. However, theprediction of the symmetry of the SF4 molecule, which may be writtenas AX4 E, is less obvious. For SF4 the problem is where will the lonepair of electrons occur?An axial position in the trigonal bipyramidal arrangement has threenearest neighbors at 90◦ away and one more neighbor at 180◦ . Foran equatorial position there are two nearest neighbors at 90◦ and twofurther ones at 120◦ .
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
