The VSEPR Model

The structures of molecules play a very important role in determining their properties. For example, as we can see in the Chemistry In Your World feature, taste is directly related to molecular structure. Structure is particularly important for biological molecules a slight change in the stmcture of a large biomolecule can completely destroy its usefulness to a cell and may even change the cell from a normal one to a cancerous one. 

Many experimental methods now exist for determining the molecular stmcture of a molecule—that is, the three-dimensional arrangement of the atoms. These methods must be used when accurate information about the stmcture is required. However, it is often useful to be able to predict the approximate molecular structure of a molecule. Now we will consider a simple model that allows us to do this. The valence shell electron pair repulsion (VSEPR) modei is useful for predicting the molecular structures of molecules formed from nonmetals. The main idea of this model is that 

The structure around a given atom is determined by minimizing 

This means that the bonding and nonbonding electron pairs (lone pairs) around a given atom are positioned as far apart as possible. 

Two Pairs of Electrons To see how this model works, we will first consider the molecule BeC, which has the following Lewis stmcture (it is an exception to the octet rule)  

Imagine tying two identical balloons together at their ends. As shown in FIGURE 9.5, the two balloons naturally orient themselves to point away from each other that is, they try to get out of each other s way as much as possible. If we add a third balloon, the balloons orient themselves toward the vertices of an equilateral triangle, and if we add a fourth balloon, they adopt a tetrahedral shape. We see that an optimum geometry exists for each number of balloons. 

Each multiple bond in a molecule also constitutes a single electron domain. Thus, the resonance structure for O3 has three electron domains around the central oxygen atom (a single bond, a double bond, and a nonbonding pair of electrons)  

In general, each nonbonding pair, single bond, or multiple bond produces a single electron domain around the central atom in a molecule. 

Does this structure follow the octet rule How many electron domains are there 

TABLE 9.1 Electron-Domain Geometries as a Function of Number of Electron Domains 

Numerous examples of molecular structures have been introduced in the preceding sections. They are all confirmed by modern experiments and/or calculations. We would like to know, however, not only what is the structure of a molecule and its symmetry, but also, why a certain structure with a certain symmetry is realized. 

The structure of a series of the simplest AX type molecules will be examined in terms of one of these useful and successful qualitative models. A is the central atom, the X s are the ligands, and not necessarily all n ligands 

Qualitative models simplify. They usually consider only a few, if not just one, of the many effects which are obviously present and are interacting in a most complex way. The measure of the success of a qualitative model 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. 

If it is assumed that the valence shell of the central atom retains its spherical symmetry in the molecule, then the electron pairs will be at equal distances from the nucleus of the central atom. In this case the arrangements at 

The repulsions considered in the VSEPR model may be expressed by the potential energy terms 

The arrangement of electron domains about the central atom of an AB molecule or ion is called its electron-domain geometry. In contrast, the molecular geometry is 

Electron-Domain Predicted Geometry Bond Angles 

In order to determine shape, we must. start with a correct Lewis stracture and apply the VSEPR model. 

Recall that the electrons in the valence shell are the ones involved in chemical bonding [M Section 8.1], 

The basis of the VSEPR model is that electron pairs in the valence shell of an atom repel one another. As we learned in Chapter 8, there are two types of electron pairs bonding pairs and nonbonding pairs (also known as lone pairs). Furthermore, bonding pairs may be found in single bonds or in multiple bonds. For clarity, we will refer to electron domains instead of electron pairs when we use the VSEPR model. An electron domain in this context is a lone pair or a bond, regardless of whether the bond is single, double, or triple. Consider the following examples  

Total number of electron domains on central atom 

2 double bonds 1 single bond 1 double bond -1- 1 lone pair 3 single bonds -1- 1 lone pair 5 single bonds 4 single bonds + 2 lone pairs 

Lone pair Singie bond Doubie bond Tripie bond 

Total number 2 electron 3 electron 4 electron 5 electron 6 electron 

Student Annotation Note that you cannot tell the shape of a molecule or ion simply from its formula—you must apply VSEPR theory. 

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The tetrahedral geometry of methane is often explained with the valence shell electron pair repulsion (VSEPR) model The VSEPR model rests on the idea that an electron pair either a bonded pair or an unshared pair associated with a particular atom will be as far away from the atom s other electron pairs as possible Thus a tetrahedral geomehy permits the four bonds of methane to be maximally separated and is charac terized by H—C—H angles of 109 5° a value referred to as the tetrahedral angle... 

Multiple bonds are treated as a single unit m the VSEPR model Formaldehyde is a trigonal planar molecule m which the electrons of the double bond and those of the two single bonds are maximally separated A linear arrangement of atoms m carbon diox ide allows the electrons m one double bond to be as far away as possible from the elec Irons m the other double bond... 

R. J. Gillespie and I. Hargittai The VSEPR Model of Molecular Geometry, Allyn and Bacon, 1991. 

The major features of molecular geometry can be predicted on the basis of a quite simple principle—electron-pair repulsion. This principle is the essence of the valence-shell electron-pair repulsion (VSEPR) model, first suggested by N. V. Sidgwick and H. M. Powell in 1940. It was developed and expanded later by R. J. Gillespie and R. S. Nyholm. According to the VSEPR model, the valence electron pairs surrounding an atom repel one another. Consequently, the orbitals containing those electron pairs are oriented to be as far apart as possible. 

Figure 7.5 (page 177) shows the geometries predicted by the VSEPR model for molecules of the types AX2 to AX. The geometries for two and three electron pairs are those associated with species in which the central atom has less than an octet of electrons. Molecules of this type include BeF2 (in the gas state) and BF3, which have the Lewis structures shown below ... 

In many molecules and polyatomic ions, one or more of the electron pairs around the central atom are unshared. The VSEPR model is readily extended to predict the geometries of these species. In general—... 

Geometries of molecules such as these can be predicted by the VSEPR model The results are shown in Figure 7.8 (page 181). The structures listed include those of all types of molecules having five or six electron pairs around the central atom, one or more of which may be unshared. Note that—... 

The VSEPR model is readly extended to species in which double or triple bonds are present A simple principle applies Insofar as molecular geometry is concerned, a multiple bond behaves like a single bond. This makes sense. The four electrons in a double bond, or the six electrons in a triple bond, must be located between the two atoms, as are the two electrons in a single bond. This means that the electron pairs in a multiple bond must occupy the same region of space as those in a single bond. Hence the extra electron pairs in a multiple bond have no effect on geometry. 

The VSEPR model applies equally well to molecules in which there is no single central atom. Consider the acetylene molecule, C2H2. Recall that here the two carbon atoms are joined by a triple bond ... 

The VSEPR model was first explored by the British chemists Nevil Sidgwick and Herbert Powell and has been developed by the Canadian chemist Ronald Gillespie. 

A molecule with only two atoms attached to the central atom is BeCl2. The Lewis structure is CI — Be — CE, and there are no lone pairs on the central atom. To be as far apart as possible, the two bonding pairs lie on opposite sides of the Be atom, and so the electron arrangement is linear. Because a Cl atom is attached by each bonding pair, the VSEPR model predicts a linear shape for the BeCL molecule, with a bond angle of 180° (4). That shape is confirmed by experiment. 

A sulfur hexafluoride molecule, SF6, has six atoms attached to the central S atom and no lone pairs on that atom (8). According to the VSEPR model, the electron arrangement is octahedral, with four pairs at the corners of a square on the equator and the remaining two pairs above and below the plane of the square (see Fig. 3.2). An F atom is attached to each electron pair, and so the molecule is predicted to be octahedral. All its bond angles are either 90° or 180°, and all the F atoms are equivalent. 

The second rule of the VSEPR model concerns the treatment of multiple... 

According to the VSEPR model, regions of high electron concentration take up positions that maximize their separations electron pairs in a multiple bond are treated as a single unit. The shape of the molecule is then identified from the relative locations of its atoms. 

STRATEGY For the electron arrangement, draw the Fewis structure and then use the VSEPR model to decide how the bonding pairs and lone pairs are arranged around the central (nitrogen) atom (consult Fig. 3.2 if necessary). Identify the molecular shape from the layout of atoms, as in Fig. 3.1. 

When there is more than one central atom in a molecule, we concentrate on each atom in turn and match the hybridization of each atom to the shape at that atom predicted by VSEPR. For example, in ethane, C2H6 (38), the two carbon atoms are both central atoms. According to the VSEPR model, the four electron pairs around each carbon atom take up a tetrahedral arrangement. This arrangement suggests sp hybridization of the carbon atoms, as shown in Fig. 3.14. Each... 

STRATEGY Use the VSEPR model to identify the shape of the molecule and then assign the hybridization consistent with that shape. All single bonds are cr-bonds and multiple i bonds are composed of a cr-bond and one or more TT-bonds. Because the C atom is attached to three atoms, we anticipate that its hybridization scheme is sp1 and that one unhybridized p-orbital remains. Finally, we form cr- and Tr-bonds by allowing the 1 orbitals to overlap. 

Use the VSEPR model to identify The C atom is bonded to 3 atoms and has no lone the electron arrangements around pairs therefore, it has a trigonal planar arrangement,... 

Explain the basis of the VSEPR model of bonding in terms of repulsions between electrons (Section 3.1). 

Using the VSEPR model, predict the shapes of each of the following molecules and identify the member of each pair with the higher boiling point (a) PBr3 or PF3 (b) S02 or C02 ... 

Consider the structure of p-azoxyanisole (14). (a) Using the VSEPR model, draw a picture that represents the shape of the molecule and predict the CNN bond angles, (b) What features of the bonding of this molecule give rise to its rodlike nature ... 

Si044, and deduce the formal charges and oxidation numbers of the atoms. Use the VSEPR model to predict the shape of the ion. 

Use the VSEPR model to estimate the Si—O—Si bond angle in silica. 

If the central atom has different groups or atoms around it, or if one or more of the vertices of the polyhedron is occupied by a lone pair, then variations in bond angles will occur such that distorted polyhedral arrangements are obtained. In its quantitative forms, the VSEPR model parameterizes each individual interaction and makes very accurate predictions of the distortions which are to be expected. 

Having introduced methane and the tetrahedron, we now begin a systematic coverage of the VSEPR model and molecular shapes. The valence shell electron pair repulsion model assumes that electron-electron repulsion determines the arrangement of valence electrons around each inner atom. This is accomplished by positioning electron pairs as far apart as possible. Figure 9-12 shows the optimal arrangements for two electron pairs (linear),... 

Tetrahedral geometry may be the most common shape in chemistry, but several other shapes also occur frequently. This section applies the VSEPR model to four additional electron group geometries and their associated molecular shapes. 

The carbon atom in CO2 has two groups of electrons. Recall from our definition of a group that a double bond counts as one group of four electrons. Although each double bond includes four electrons, all four are concentrated between the nuclei. Remember also that the VSEPR model applies to electron groups, not specifically to electron pairs (despite the name of the model). It is the number of ligands and lone pairs, not the number of shared eiectrons, that determines the steric number and hence the molecular shape of an inner atom. 

Each of the steric numbers described in Sections 94 and 94 results in electron groups separated by well-defined bond angles. If the VSEPR model is accurate, the actual bond angles found by experimental measurements on real molecules should match the optimal angles predicted by applying the model. 

According to the VSEPR model developed in Chapter 9, an inner atom with a steric number of 4 adopts tetrahedral electron group geometry. This tetrahedral arrangement of four electron groups is very common, the only important exceptions being the hydrides of elements beyond the second row, such as H2 S and PH3. Thus,... 

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