Valence Shell Electron Pair Repulsion (VSPER) Theory

The valence shell electron pair repulsion model is often abbreviated as VSEPR (pronounced "vesper") and is a model to predict the geometry of molecules. Specifically, VSEPR models look at the bonding and molecular geometry of organic molecules and polyatomic ions. It is useful for nearly all compounds that have a central atom that is not a metal.

Lewis structures only tell the number and type of bonds between atoms, as they are limited to two dimensions. The VSEPR model predicts the 3-D shape of molecules and ions but is ineffective in providing any specific information regarding the bond length or the bond itself.

VSEPR models are based on the concept that electrons around a central atom will configure themselves to minimize repulsion, and that dictates the geometry of the molecule.

It can predict the shape of nearly all compounds that have a central atom, as long as the central atom is not a metal. Each shape has a name and an idealized bond angle associated with it.

The following terms are commonly used in discussing the shapes of molecules:

1. bond angle: the angle between a bonded atom, the central atom, and another bonded atom
2. lone pair: a pair of valence electrons that are not shared with another atom
3. molecular geometry: the 3-D arrangement of bonded atoms in a polyatomic ion or molecule
4. electron pair geometry: the 3-D arrangement of electron pairs around the central atom of a polyatomic ion or molecule.

The main difference between molecular geometry and electron pair geometry is that molecular geometry does not include unpaired electrons, whereas electron pair geometry includes both bonded atoms and unpaired electrons. If there are no unpaired electrons in the compound being assessed, the molecular and electron pair geometries will be the same.

Molecules with the same electron pair geometry may have different molecular geometries.^[7]

1. Draw a Lewis structure for the ion or molecule in question.
2. Determine the number of electron groups around the central atom. Each lone pair of electrons counts as a single group. Each bond counts as a single group, even if it is a double or triple bond. Find the corresponding electron geometry from the table.
3. Determine the number of lone pairs and the number of bonding pairs around the central atom, and use that to find the molecular geometry.

What is the shape of the rare $\ce{I_3}?$

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The central atom has a total of 5 electron pairs, giving it the trigonal bipyramidal geometry. Due to the 3 lone pairs at the 3 equatorial bond positions, the $\ce{I}$ atoms occupy the central and axial positions. Hence it is linear in shape.

VSEPR notation gives a general formula for classifying chemical species based on the number of electron pairs around a central atom. Note, however, that not all $AB_n$ species have the same molecular geometry. For example, carbon dioxide and sulfur dioxide are both $AB_2$ species, but one is linear and the other is bent. Sometimes, the notation is expanded to $AB_nE_m$ to include lone pair electrons. This can get confusing, because water can be referred to as an $AB_2$ species or an $AX_2E$ species, depending on the conventions the author or text chooses.

In general,

• $A$ is used to represent the central atom;
• $B$ or $X$ is used to represent the number of atoms bonded to the central atom;
• $E$ represents the number of lone pairs on the central atom (ignore lone pairs on bonded atoms).

Use VSEPR notation to represent the molecules $\ce{O_3,~O_2, ~CCl_4, ~NaCl},~\text{and}~ \ce{H2O}.$

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We have

$$\begin{aligned} \ce{O_3}&=\ce{AB_2E}\\ \ce{O_2}&=\ce{ABE_2}\\ \ce{CCl_4}&=\ce{AB_4}\\ \ce{NaCl} &= \text{ none--it's ionic}\\ \ce{H_2O}&=\ce{AB_2E_2}. \end{aligned}$$

The VSEPR model is not a theory. It does not explain or attempt to explain any observations or predictions. Rather, it is an algorithm that accurately predicts the structures of a large number of compounds.

VSEPR is simple and useful but does not work for all chemical species. First, the idealized bond angles do not always match the measured values. For example, VSEPR predicts that $H_2O$ and $H_2S$ will have the same bond angles, but structural studies have shown the bonds in the two molecules are different by 12 degrees. VSEPR also predicts that group-2 halides such as $BaF_2$ will be linear when they are actually bent. Quantum mechanics and atomic orbitals can give more sophisticated predictions when VSEPR is inadequate.

1. , . Linear-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Linear-3D-balls.png
2. , . Trigonal-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Trigonal-3D-balls.png
3. , . Tetrahedral-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Tetrahedral-3D-balls.png
4. , . Trigonal-bipyramidal-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Trigonal-bipyramidal-3D-balls.png
5. , . Octahedral-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Octahedral-3D-balls.png
6. , . Pentagonal-bipyramidal-3D-balls. Retrieved August 24, 2016, from https://commons.wikimedia.org/wiki/File:Pentagonal-bipyramidal-3D-balls.png
7. Frey, R. VSEPR geometries. Retrieved August 24, 2016, from https://en.wikibooks.org/wiki/Structural_Biochemistry/Molecular_Geometry#/media/File:VSEPR_geometries.PNG