2.1 Valence Shell Electron Pair Repulsion (VSEPR) Theory: Three-Dimensional Geometry

To understand many aspects of molecular geometry, chemists routinely work with two models. One, which we discuss here, is valence shell electron pair repulsion (VSEPR) theory. The other, which we discuss in Chapter 3, uses the concepts of hybridization and molecular orbital (MO) theory. Although hybridization and MO theory constitute a more powerful model than VSEPR theory, VSEPR theory remains extremely useful because of its simplicity: Its concepts are easier to grasp and it allows us to arrive at answers much more quickly.

2.1a Basic Principles of VSEPR Theory

The basic ideas of VSEPR theory are as follows:

 1. Electrons in a Lewis structure are viewed as groups.

 ● A lone pair of electrons, a single bond, a double bond, and a triple bond each constitute one group of electrons (Table 2-1).

 2. The negatively charged electron groups strongly repel one another, so they tend to arrange themselves as far away from each other as possible.

 ● Two electron groups tend to be 180° apart (a linear configuration).

 ● Three groups tend to be 120° apart (a trigonal planar configuration).

 ● Four groups tend to be 109.5° apart (a tetrahedral configuration).

 3. Electron geometry describes the orientation of the electron groups about a particular atom. These configurations are summarized in Table 2-2.

 4. Molecular geometry describes the arrangement of atoms about a particular atom. Because atoms must be attached by bonding pairs of electrons, an atom’s molecular geometry is governed by its electron geometry.

Table 2-1 Various Types of Electron Groups in VSEPR Theory

Type of Group

Total Number of e–

Number of Groups

1 Lone pair

2

1

1 Single bond

2

1

1 Double bond

4

1

1 Triple bond

6

1
Table 2-2 is titled, correlations between electron geometry and bond angle in VSEPR theory. The table has three columns and four rows. The rows represent the data for different electron groups. The columns represent the electron geometry and approximate bond angles for different numbers of electron groups. Data are included in the accompanying table. | Number of electron groups Electron geometry Approximate bond angle | 2 A central atom with two single bonds in a linear orientation. 180 degrees | 3 A central atom with three single bonds in a trigonal planar orientation. 120 degrees | 4 A central atom with four single bonds in a tetrahedral orientation. 109.5 degrees

The common molecular geometries, which are summarized in Table 2-3, lead to the following conclusions:

Table 2-3 is titled, molecular geometry in VSEPR theory superscript a. The table has four columns and five rows. The rows represent the data for different number of bonded atoms or groups. The columns represent the corresponding electron geometry. A note below the table reads, �Superscript a: Bonding electron groups are depicted with gray sticks; nonbonding electron groups are depicted as yellow sticks terminating in a red lone pair.� Data are included in the accompanying table. | Empty cell Electron geometry Electron geometry Electron geometry | Number of bonded atoms or groups Linear (180 degrees) Trigonal planar (120 degrees) Tetrahedral (109.5 degrees) | 2 A central atom bonded to two other atoms on either side in a linear arrangement. A central atom with one lone pair of electrons, bonded to two other atoms on either side in a bent arrangement. A central atom with two lone pairs of electrons, bonded to two other atoms on either side in a bent arrangement. | 3 Empty cell A central atom bonded to three other atoms in a trigonal planar arrangement. A central atom with one lone pair of electrons, bonded to three other atoms in a trigonal pyramidal arrangement. | 4 Empty cell Empty cell A central atom bonded to four other atoms in a tetrahedral arrangement.

● If all the electron groups are bonds (depicted in gray), then there is an atom attached to each electron group and the molecular geometry is the same as the electron geometry.

●  If one or more of the electron groups is a lone pair (depicted in yellow and red), then the molecular geometry is different than the electron geometry.

Connections 2-Aminoethanol (Fig. 2-2) is commonly used in the production of a variety of industrial compounds, including shampoos and detergents. It is also used as an injectable treatment for hemorrhoids.

Some examples of molecules containing central atoms without lone pairs are shown in Figure 2-1. For these atoms, the electron and molecular geometries are the same.

Three illustrations show Lewis structures and ball-and-stick models of ethanenitrile, propanone, and ethane. The structural formulas represent the electron geometry of the compounds, while the ball-and-stick models represent the molecular geometry. The structural formula of ethanenitrile, also known as acetonitrile, shows a linear two-carbon chain where carbon 1 is bonded by a triple bond to a nitrogen atom with a lone pair and carbon 2 is bonded to three hydrogen atoms. The ball-and-stick model of acetonitrile also has a linear orientation, with the angle between the C-C and C-N bonds being 180 degrees. The structural formula of propanone, also known as acetone, shows a central carbon atom bonded by a double bond to an oxygen atom with two lone pairs and to another carbon on each side in a trigonal planar manner. The ball-and-stick model of propanone also has a trigonal planar orientation, with the angle between the C-C and C-O bonds being 120 degrees. The structural formula of ethane shows a linear two-carbon chain where each carbon is bonded to three hydrogen atoms in a tetrahedral manner. The ball-and-stick model of ethane also has a tetrahedral orientation, with the angle between the C-C and C-H bonds being 109.5 degrees approximately. The caption reads, �Compounds in which the central atom lacks lone pairs: Because there are no lone pairs about the central atom, the molecular geometries of acetonitrile, acetone, and ethane are identical to their electron geometries.�
FIGURE 2-1 Compounds in which the central atom lacks lone pairs Because there are no lone pairs about the central atom, the molecular geometries of acetonitrile, acetone, and ethane are identical to their electron geometries.

YOUR TURN 2.1
SHOW ANSWERS

How many electron groups surround

(a) the triply bonded C in Figure 2-1a, (b) the central C in Figure 2-1b, and (c) each C atom in Figure 2-1c?

(a) Two electron groups surround the triply bonded C in Figure 2-1a, which has one single bond and one triple bond.(b) The central C in Figure 2-1b has two single bonds and one double bond, thus three groups of electrons.(c) Each C atom in Figure 2-1c has four single bonds, thus four groups of electrons.

Connections Acetonitrile (Fig. 2-1a) is a polar organic solvent used in the manufacture of DNA oligonucleotides and numerous pharmaceuticals. Acetone (Fig. 2-1b) is another organic solvent and is the active ingredient in nail polish remover. Ethane (Fig. 2-1c) is a gas that is important in the petrochemical industry.

A photo shows nail paint being removed with a ball of cotton.

In 2-aminoethanol (ethanolamine, Fig. 2-2, next page), the N and O atoms have molecular geometries that are different than their electron geometries. The electron geometry of the N atom is tetrahedral because it is surrounded by four electron groups: three single bonds and one lone pair. Its molecular geometry, however, which describes only the orientation of the three single bonds, is trigonal pyramidal. Likewise, the O atom of the OH group has a tetrahedral electron geometry (two single bonds and two lone pairs), but its molecular geometry is bent.

Lewis structure and ball-and-stick model of 2-aminoethanol. The structural formula represents the electron geometry of the compound, while the ball-and-stick model represents the molecular geometry. The structure shows two carbons bonded in a linear manner. Carbon 1 is bonded in a bent fashion to a hydroxyl group, where the oxygen atom has two lone pairs arranged around it in a tetrahedral orientation. Carbon 2 is bonded in a bent fashion to an amine group, where the nitrogen atom has one lone pair arranged around it in a tetrahedral orientation. The ball-and-stick model of 2-aminoethanol also has a similar structure, except that the molecular geometry of the hydroxyl group is bent and of the amine group is trigonal pyramidal. The caption reads, �Lewis structure and VSEPR geometries about the atoms in 2-aminoethanol: The electron geometries about the NH2 nitrogen and the OH oxygen atoms are both tetrahedral, but they have different molecular geometries because N has one lone pair and O has two.�
FIGURE 2-2 Lewis structure and VSEPR geometries about the atoms in 2-aminoethanol The electron geometries about the NH2 nitrogen and the OH oxygen atoms are both tetrahedral, but they have different molecular geometries because N has one lone pair and O has two.

Solved Problem 2.1

Imines, which are characterized by a C═N double bond, are commonly used as intermediates in organic synthesis. Use VSEPR theory to predict the electron and molecular geometries about the nitrogen atom in the acetone imine molecule shown.

An illustration shows the Lewis structure of an acetone imine molecule. The Lewis structure shows a central carbon atom bonded to two methyl groups by single bonds and an amine group by double bonds. The amine group has a lone pair of electrons.

Think
SHOW SECTION

How many electron groups surround the N atom? Are any of them lone pairs?

Solve
SHOW SECTION

There are three groups of electrons around the nitrogen atom: one double bond, one single bond, and one lone pair. According to VSEPR theory, therefore, its electron geometry is trigonal planar, and its molecular geometry is bent.

An illustration shows the ball-and-stick model of a molecule. The model shows a bent three-carbon chain, where the carbon atoms are represented by black spheres. Carbons 1 and 3 are each bonded to three hydrogen atoms, represented by white spheres, and carbon 2 is bonded to an amine group by a double bond. The nitrogen atom in the amine group is represented by a blue sphere. The angle between the double bond and the nitrogen-hydrogen bond is marked as 120 degrees approximately. An arrow pointing to the structure reads, �Electron equals trigonal planar. Molecular equals bent.�

problem 2.2 Prop-2-yn-1-ol (propargyl alcohol) is used as an intermediate in organic synthesis and can be polymerized to make poly(propargyl alcohol). Use VSEPR theory to predict the electron and molecular geometries about each nonhydrogen atom in the molecule.

An illustration shows the line structure of Prop-2-yn-1-ol. The line structure of Prop-2-yn-1-ol, also known as Propargyl alcohol shows an inverted V with one end being longer than the other. The shorter end of the structure is bonded to a hydroxyl group by single bonds and the longer end features triple bonds.

The rules of VSEPR theory apply equally well to ions. Figure 2-3a shows, for example, that the methyl cation, , has a trigonal planar electron geometry, consistent with a carbon atom that is surrounded by three groups of electrons (i.e., three single bonds). The methyl anion (Fig. 2-3b), on the other hand, is surrounded by four groups of electrons (i.e., three single bonds and a lone pair). Its electron geometry, therefore, is tetrahedral, and its molecular geometry is trigonal pyramidal.

Lewis structure and ball-and-stick model of methyl cation and methyl anion. The structural formula represents the electron geometry of the ion, while the ball-and-stick model represents the molecular geometry. The structure of the methyl cation and anion both show a central carbon atom bonded to three hydrogen atoms. The carbon atom carries a positive charge in the cation, and a negative charge with a lone pair in the anion. The electron geometry and molecular geometry of the methyl cation are both trigonal planar, while in the methyl anion, the electron geometry is tetrahedral and the molecular geometry is trigonal pyramidal. The caption reads, Lewis structures and three-dimensional geometries of the methyl cation and methyl anion: The central C atom in CH13 is surrounded by three single bonds only with no lone pairs, so its electron and molecular geometries are the same. The central C atom in CH23, on the other hand, is surrounded by three single bonds and one lone pair, so its electron and molecular geometries are different.
FIGURE 2-3 Lewis structures and three-dimensional geometries of the methyl cation and methyl anion The central C atom in CH3+ is surrounded by three single bonds only (i.e., no lone pairs), so its electron and molecular geometries are the same. The central C atom in CH3-, on the other hand, is surrounded by three single bonds and one lone pair, so its electron and molecular geometries are different.

YOUR TURN 2.2
SHOW ANSWERS

Circle each electron group in the Lewis structures of and in Figure 2-3.

has three single bonds and no lone pairs, thus three groups. has three single bonds and one lone pair, thus four groups.

An illustration shows Lewis structures of methyl cation and methyl anion. The structure of the methyl cation shows a central carbon atom with a positive charge is single bonded to three hydrogen atoms. The carbon bonds are circled and labeled as, �C equals 3 groups�. The structure of the methyl anion shows a central carbon atom with a negative charge carrying a lone pair of electrons is single bonded to three hydrogen atoms. The carbon bonds are the lone pair are circled and labeled as, �C equals 4 groups�.

2.1b Angle Strain

Geometric constraints can force an atom to deviate significantly from its ideal bond angle—that is, the bond angle predicted by VSEPR theory. Most commonly this happens in ring structures. For example, the carbon atoms in a molecule of cyclopropane (Fig. 2-4a) should have an ideal bond angle of 109.5°, given that each carbon is surrounded by four groups of electrons (four single bonds). To form the ring, however, the C—C—C bond angles must be 60°. Similarly, each carbon atom of cyclobutadiene (Fig. 2-4b) has an ideal bond angle of 120°, but geometric constraints force the angles in the ring to be 90°.

Condensed structural formulas and ball-and-stick models of cyclopropane and cyclobutadiene. The structural formula and ball-and-stick model of cyclopropane show three carbon atoms bonded in a triangular manner. A note below the illustrations reads: �Ideal bond angle equals 109.5 degrees. Real bond angle equals 60 degrees.� The structural formula and ball-and-stick model of cyclobutadiene show four carbon atoms bonded in a square fashion with alternating single and double bonds. A note below the illustrations reads: �Ideal bond angle equals 120 degrees. Real bond angle equals 90 degrees.� The caption reads, Examples of angle strain: In cyclopropane, the ideal C-C-C bond angle is 109.5 degrees, but the actual angle is 60 degrees. In cyclobutadiene, the ideal C-C-C bond angle is 120 degrees but the actual angle is 90 degrees.
FIGURE 2-4 Examples of angle strain In cyclopropane (a), the ideal C—C—C bond angle is 109.5° but the actual angle is 60°. In cyclobutadiene (b), the ideal C—C—C bond angle is 120° but the actual angle is 90°.

The deviation of a bond angle from its ideal angle results in an increase in energy, called angle strain. Angle strain weakens bonds and makes a species more reactive. In some cases, excessive angle strain can preclude the existence of a molecule altogether.