An Introduction to Chemistry - Structure - The Valence Shell Electron Pair Repulsion Model
The geometry adopted by groups around an atom can be predicted by using a particularly simple model known as the valence shell electron pair repulsion model (VSEPR). This model is based on the simple idea formulated by Lewis and others that electrons tend to move as far away from one another as possible (like charges repel one another). Because electrons tend to pair with one another if their spins are opposed, we can modify the idea to say that pairs of electrons tend to adopt a geometry that minimizes repulsions. We have noted earlier that only the electrons in the valence shell are involved in bonding, so we only need to worry about those electrons.
Let us consider some examples. Carbon dioxide, a crucial part of photosynthesis, has the electron-dot structure
If we want to know the structure of this compound, we might first consider some possibilites. There are only two of them; either the three atoms lie on a straight line or they do not. That is, the compound can have only two different geometries--linear or bent. The geometry is determined by the tendency of the electron pairs around the central atom to minimize repulsions. How many pairs of electrons are there at the carbon? Clearly, the electron dot formula shows no lone pairs; it does show two sigma-bonded pairs and two 1-bonded pairs. It turns out that the 1-bonds do not influence the geometry, so the sigma-bonded (and lone pairs) are the sole determinants of geometry. Hence, only the two sigma-bonded pairs around the carbon of CO2 need be considered. How should two pairs of electrons be arranged around an atom in order to minimize the repulsions between them? The answer is clear--at the opposite ends of a straight line. Hence, we can conclude that CO2 is a linear molecule.
Now consider the nitrite ion. Reference to the electron-dot formula given above shows that there is one lone pair and two sigma-bonded pairs at the central nitrogen. How are three pairs of electrons arranged to minimize repulsions? Again, the answer is quite reasonable--at the corners of a triangle as shown in Figure 38. At the ends of two of the pairs are the oxygens; the other pair of electrons is the lone pair on the central nitrogen. Because the angle between the oxygens is less than 180°, the geometry of the ion is described as bent. Other geometries are summarized in Table 4. It is important to understand that the geometry is determined by the positions of the atoms, not all of the electron pairs. For example, even though the geometry of the electron pairs around the oxygen in water is tetrahedral, it is the position of the atoms that leads to the description of bent for the geometry of water.
Figure 38. The geometry of the nitrite ion.
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| Number of sigma bonding and nonbonding electron pairs about central atom | Number of nonbonding pairs | Examples | Shape |
|---|---|---|---|
| 2 | 0 | N3-, CO2 | linear |
| 3 | 0 | BCl3, CO32- | trigonal planar |
| 3 | 1 | NO2- | bent |
| 4 | 0 | CH4, SO42- | tetrahedral |
| 4 | 1 | NH3, PCl3 | pyramidal |
| 4 | 2 | H2O | bent |
| 5 | 0 | PCl5 | trigonal bipyramidal |
| 5 | 1 | SF4 | see-saw |
| 5 | 2 | BrF3 | T-shaped |
| 5 | 3 | I3- | linear |
| 6 | 0 | SiF62- | octahedral |
| 6 | 1 | BrF5 | square pyramidal |
| 6 | 2 | ICl4-, XeF4 | square planar |
Problem Six
Identify each of the following geometric figures:
From left to right--tetrahedron, trigonal bipyramid, and octahedron.
Problem Seven
Inscribe carbon tetrachloride in a tetrahedron and then translate the drawing to a "wedge and line" formula.
Problem Eight
Identify the geometry of each of the following molecules:
From left to right--trigonal planar, pyramidal, square planar.
Problem Nine
Identify the geometry of each of the following molecules:
From left to right--trigonal bipyramid, see-saw, T-shaped. The geometry of a molecule is based on the position of the atoms, not the lone pairs. All of these molecules are based upon the trigonal bipyramidal geometry of the electron pairs, both sigma and lone pairs, but the descriptions of the molecules are not the same.
Problem Ten
Make a drawing of sulfur tetrafluoride shown above to convince yourself that see-saw is a reasonable description of the geometry:
The drawing on the left is the same as that above. In the middle it has been rotated 90° to the right. One the right it has been redrawn without the line to the lone pair and with a better 3-D perspective of the bottom fluorines. Notice also that the drawing on the right uses a dotted line rather than the hatched wedge.