To use the VSEPR model to predict molecular geometries. To predict whether a molecule has a dipole moment.

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The Lewis electron-pair approach can be used to predict the number and types of bonds between the atoms in a substance, and it indicates which atoms have lone pairs of electrons. This approach gives no information about the actual arrangement of atoms in space, however. We continue our discussion of structure and bonding by introducing the valence-shell electron-pair repulsion (VSEPR) model (pronounced “vesper”), which can be used to predict the shapes of many molecules and polyatomic ions. Keep in mind, however, that the VSEPR model, like any model, is a limited representation of reality; the model provides no information about bond lengths or the presence of multiple bonds.


The VSEPR Model

The VSEPR model can predict the structure of nearly any molecule or polyatomic ion in which the central atom is a nonmetal, as well as the structures of many molecules and polyatomic ions with a central metal atom. The premise of the VSEPR theory is that electron pairs located in bonds and lone pairs repel each other and will therefore adopt the geometry that places electron pairs as far apart from each other as possible. This theory is very simplistic and does not account for the subtleties of orbital interactions that influence molecular shapes; however, the simple VSEPR counting procedure accurately predicts the three-dimensional structures of a large number of compounds, which cannot be predicted using the Lewis electron-pair approach.

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Figure \(\PageIndex{1}\): Common Structures for Molecules and Polyatomic Ions That Consist of a Central Atom Bonded to Two or Three Other Atoms. (CC BY-NC-SA; anonymous)

We can use the VSEPR model to predict the geometry of most polyatomic molecules and ions by focusing only on the number of electron pairs around the central atom, ignoring all other valence electrons present. According to this model, valence electrons in the Lewis structure form groups, which may consist of a single bond, a double bond, a triple bond, a lone pair of electrons, or even a single unpaired electron, which in the VSEPR model is counted as a lone pair. Because electrons repel each other electrostatically, the most stable arrangement of electron groups (i.e., the one with the lowest energy) is the one that minimizes repulsions. Groups are positioned around the central atom in a way that produces the molecular structure with the lowest energy, as illustrated in Figures \(\PageIndex{1}\) and \(\PageIndex{2}\).

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Figure \(\PageIndex{2}\): Electron Geometries for Species with Two to Six Electron Groups. Groups are placed around the central atom in a way that produces a molecular structure with the lowest energy, that is, the one that minimizes repulsions.(CC BY-NC-SA; anonymous)

In the VSEPR model, the molecule or polyatomic ion is given an AXmEn designation, where A is the central atom, X is a bonded atom, E is a nonbonding valence electron group (usually a lone pair of electrons), and m and n are integers. Each group around the central atom is designated as a bonding pair (BP) or lone (nonbonding) pair (LP). From the BP and LP interactions we can predict both the relative positions of the atoms and the angles between the bonds, called the bond angles. Using this information, we can describe the molecular geometry, the arrangement of the bonded atoms in a molecule or polyatomic ion.


We will illustrate the use of this procedure with several examples, beginning with atoms with two electron groups. In our discussion we will refer to Figure \(\PageIndex{2}\) and Figure \(\PageIndex{3}\), which summarize the common molecular geometries and idealized bond angles of molecules and ions with two to six electron groups.

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Figure \(\PageIndex{3}\): Common Molecular Geometries for Species with Two to Six Electron Groups. Lone pairs are shown using a dashed line.(CC BY-NC-SA; anonymous)

Two Electron Groups

Our first example is a molecule with two bonded atoms and no lone pairs of electrons, \(BeH_2\).


AX2 Molecules: BeH2

1. The central atom, beryllium, contributes two valence electrons, and each hydrogen atom contributes one. The Lewis electron structure is

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Figure \(\PageIndex{2}\) that the arrangement that minimizes repulsions places the groups 180° apart.(CC BY-NC-SA; anonymous)

3. Both groups around the central atom are bonding pairs (BP). Thus BeH2 is designated as AX2.

4. From Figure \(\PageIndex{3}\) we see that with two bonding pairs, the molecular geometry that minimizes repulsions in BeH2 is linear.


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Three Electron Groups


AX3 Molecules: BCl3

1. The central atom, boron, contributes three valence electrons, and each chlorine atom contributes seven valence electrons. The Lewis electron structure is

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Figure \(\PageIndex{2}\)):(CC BY-NC-SA; anonymous)

3. All electron groups are bonding pairs (BP), so the structure is designated as AX3.

4. From Figure \(\PageIndex{3}\) we see that with three bonding pairs around the central atom, the molecular geometry of BCl3 is trigonal planar, as shown in Figure \(\PageIndex{2}\).



AX3 Molecules: CO32−

1. The central atom, carbon, has four valence electrons, and each oxygen atom has six valence electrons. As you learned previously, the Lewis electron structure of one of three resonance forms is represented as

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Figure \(\PageIndex{2}\)).

3. All electron groups are bonding pairs (BP). With three bonding groups around the central atom, the structure is designated as AX3.

4. We see from Figure \(\PageIndex{3}\) that the molecular geometry of CO32− is trigonal planar with bond angles of 120°.


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api/deki/files/141660/imageedit_91_9146022588.png?revision=1" />Figure \(\PageIndex{2}\)):(CC BY-NC-SA; anonymous)

3. There are two bonding pairs and one lone pair, so the structure is designated as AX2E. This designation has a total of three electron pairs, two X and one E. Because a lone pair is not shared by two nuclei, it occupies more space near the central atom than a bonding pair (Figure \(\PageIndex{4}\)). Thus bonding pairs and lone pairs repel each other electrostatically in the order BP–BP 2, we have one BP–BP interaction and two LP–BP interactions.

4. The molecular geometry is described only by the positions of the nuclei, not by the positions of the lone pairs. Thus with two nuclei and one lone pair the shape is bent, or V shaped, which can be viewed as a trigonal planar arrangement with a missing vertex (Figures \(\PageIndex{2}\) and \(\PageIndex{3}\)). The O-S-O bond angle is expected to be less than 120° because of the extra space taken up by the lone pair.

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Figure \(\PageIndex{4}\): The Difference in the Space Occupied by a Lone Pair of Electrons and by a Bonding Pair.(CC BY-NC-SA; anonymous)

As with SO2, this composite model of electron distribution and negative electrostatic potential in ammonia shows that a lone pair of electrons occupies a larger region of space around the nitrogen atom than does a bonding pair of electrons that is shared with a hydrogen atom.


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Four Electron Groups

One of the limitations of Lewis structures is that they depict molecules and ions in only two dimensions. With four electron groups, we must learn to show molecules and ions in three dimensions.


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2. There are four electron groups around the central atom. As shown in Figure \(\PageIndex{2}\), repulsions are minimized by placing the groups in the corners of a tetrahedron with bond angles of 109.5°.

3. All electron groups are bonding pairs, so the structure is designated as AX4.

4. With four bonding pairs, the molecular geometry of methane is tetrahedral (Figure \(\PageIndex{3}\)).

2. There are four electron groups around nitrogen, three bonding pairs and one lone pair. Repulsions are minimized by directing each hydrogen atom and the lone pair to the corners of a tetrahedron.

3. With three bonding pairs and one lone pair, the structure is designated as AX3E. This designation has a total of four electron pairs, three X and one E. We expect the LP–BP interactions to cause the bonding pair angles to deviate significantly from the angles of a perfect tetrahedron.

4. There are three nuclei and one lone pair, so the molecular geometry is trigonal pyramidal. In essence, this is a tetrahedron with a vertex missing (Figure \(\PageIndex{3}\)). However, the H–N–H bond angles are less than the ideal angle of 109.5° because of LP–BP repulsions (Figure \(\PageIndex{3}\) and Figure \(\PageIndex{4}\)).


AX2E2 Molecules: H2O

1. Oxygen has six valence electrons and each hydrogen has one valence electron, producing the Lewis electron structure

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Five Electron Groups

In previous examples it did not matter where we placed the electron groups because all positions were equivalent. In some cases, however, the positions are not equivalent. We encounter this situation for the first time with five electron groups.


AX5 Molecules: PCl5

1. Phosphorus has five valence electrons and each chlorine has seven valence electrons, so the Lewis electron structure of PCl5 is

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Once again, we have a compound that is an exception to the octet rule.

2. There are five groups around the central atom, three bonding pairs and two lone pairs. We again direct the groups toward the vertices of a trigonal bipyramid.

3. With three bonding pairs and two lone pairs, the structural designation is AX3E2 with a total of five electron pairs. Because the axial and equatorial positions are not equivalent, we must decide how to arrange the groups to minimize repulsions. If we place both lone pairs in the axial positions, we have six LP–BP repulsions at 90°. If both are in the equatorial positions, we have four LP–BP repulsions at 90°. If one lone pair is axial and the other equatorial, we have one LP–LP repulsion at 90° and three LP–BP repulsions at 90°:

2. There are five electron groups about the central atom in I3−, two bonding pairs and three lone pairs. To minimize repulsions, the groups are directed to the corners of a trigonal bipyramid.

3. With two bonding pairs and three lone pairs, I3− has a total of five electron pairs and is designated as AX2E3. We must now decide how to arrange the lone pairs of electrons in a trigonal bipyramid in a way that minimizes repulsions. Placing them in the axial positions eliminates 90° LP–LP repulsions and minimizes the number of 90° LP–BP repulsions.


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AX5E Molecules: BrF5

1. The central atom, bromine, has seven valence electrons, as does each fluorine, so the Lewis electron structure is


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The relationship between the number of electron groups around a central atom, the number of lone pairs of electrons, and the molecular geometry is summarized in Figure \(\PageIndex{6}\).

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Figure \(\PageIndex{6}\): Overview of Molecular Geometries



Example \(\PageIndex{1}\)

Using the VSEPR model, predict the molecular geometry of each molecule or ion.

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PF5 (phosphorus pentafluoride, a catalyst used in certain organic reactions) H3O+ (hydronium ion)

Given: two altoalsimce.orgical species

Asked for: molecular geometry

Strategy:

Draw the Lewis electron structure of the molecule or polyatomic ion. Determine the electron group arrangement around the central atom that minimizes repulsions. Assign an AXmEn designation; then identify the LP–LP, LP–BP, or BP–BP interactions and predict deviations in bond angles. Describe the molecular geometry.

Solution:

A The central atom, P, has five valence electrons and each fluorine has seven valence electrons, so the Lewis structure of PF5 is
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