VSEPR Theory

Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular geometry, including approximate bond angles around a central atom, of a molecule from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding pairs or nonbonding lone pairs. The electrostatic repulsion of these electrons is reduced when they assume positions as far away from each other as possible.

As a simple example of VSEPR theory, let us predict the structure of a gaseous BeF₂ molecule. The Lewis structure of BeF₂ (Figure 1) shows only two electron pairs around the central beryllium atom. With two bonds and no lone pairs of electrons on the central atom, the bonds are as far apart as possible, and the electrostatic repulsion between these regions of high electron density is reduced to a minimum when they are on opposite sides of the central atom. The F-Be-F bond angle is 180° (Figure 1) in the BeF₂ molecule resulting in a linear geometry.

Table 1 illustrates electron region geometries that minimize the repulsions between regions of high electron density (bonds and/or lone pairs). Two regions of electron density around a central atom in a molecule form a linear geometry; three regions form a trigonal (or triangular) planar geometry; and four regions form a tetrahedral geometry.

Table 1: The basic electron region geometries predicted by VSEPR theory maximize the space around any region of electron density (bonds or lone pairs).

Number of Electron Domains (bonds and/or nonbonding electron pairs)	Two Regions	Three Regions	Four Regions
Spatial Arrangement
Dash-Wedge Notation
Electron Region Geometry	Linear 180º angle	Trigonal Planar 120º angle	Tetrahedral 109.5º angle

Electron Region Geometry versus Molecular Geometry

It is important to note that electron region geometry around a central atom is not the same thing as its molecular geometry. The electron region geometries shown in Table 1 describe all regions where electrons are located. Bonds and lone pairs are treated equally. Molecular geometry describes the location of the atoms, not the lone pairs of electrons. The electron region geometries will be the same as the molecular geometries when there are no lone pairs of electrons around the central atom, but they will be different when there are lone pairs present on the central atom.

For example, the methane molecule, CH₄, which is the major component of natural gas, has four bonding pairs of electrons around the central carbon atom; the electron region geometry is tetrahedral, as is the molecular geometry (Figure 2). On the other hand, the ammonia molecule, NH₃, also has four electron pairs associated with the nitrogen atom, and thus has a tetrahedral electron region geometry. However, one of these regions is a lone pair and this lone pair influences the shape of the molecule, giving it a molecular geometry of trigonal pyramidal (Figure 3).

Table 2: The molecular geometries are identical to the electron region geometries when there are no lone pairs present (first column). For a particular number of electron pairs (row), the molecular geometries for one or more lone pairs are determined based on modifications of the corresponding electron region geometry.

Electron Regions	Electron Region Geometry	Bond Angles	Nonbonding Lone Pairs	Molecular Geometry	Picture
2	Linear	180º	0	Linear
3	Trigonal (or Triangular) Planar	~120º	0	Trigonal Planar
			1	Bent
4	Tetrahedral	~109.5º	0	Tetrahedral
			1	Trigonal Pyramidal
			2	Bent

Molecular Geometry for Multicenter Molecules

When a molecule or polyatomic ion only has one central atom, the molecular geometry completely describes the shape of the molecule. Larger molecules do not have a single central atom, but are connected by a chain of interior, central atoms that each possess a “local” geometry. The way these local structures are oriented with respect to each other also influences the molecular shape, but such considerations are largely beyond the scope of this introductory discussion. For our purposes, we will only focus on determining the local geometries of single atoms.

Molecular Polarity and Dipole Moment

As discussed previously, polar covalent bonds connect two atoms with differing electronegativities, leaving one atom with a partial positive charge (δ+) and the other atom with a partial negative charge (δ–), as the electrons are pulled toward the more electronegative atom. This separation of charge gives rise to a bond dipole moment. This bond dipole moment can be represented as a vector, a quantity having both direction and magnitude (Figure 4). Dipole vectors are shown as arrows pointing along the bond from the less electronegative atom toward the more electronegative atom. A small plus sign is drawn on the less electronegative end to indicate the partially positive end of the bond. The length of the arrow is proportional to the magnitude of the electronegativity difference between the two atoms. For this class, you should memorize these trends of electronegativity: F > O > N > Cl >> … > C > … > H > metals

A whole molecule may also have a dipole moment, depending on its molecular geometry and the polarity of each of its bonds. If the molecule does have a dipole moment, the molecule is said to be a polar molecule; otherwise the molecule is said to be nonpolar. The molecular dipole moment measures the net charge separation in the whole molecule. We determine the molecular dipole moment by adding all of the bond dipole moments in three-dimensional space.

Homonuclear diatomic molecules, such as Br₂ and N₂, have bond and molecular dipole moments equal to zero, because the two component atoms have equal electronegativity. For heteronuclear molecules, such as CO or HF, the molecular dipole moment is equal to the bond dipole moment, which is determined by the magnitude of difference between the two electronegativity values.

When a molecule contains more than one bond, the geometry must be taken into account. If the bonds in a molecule are arranged such that their bond dipole moments cancel (vector sum equals zero), then the molecule is nonpolar. This is the situation in CO₂ (Figure 5). Each of the C=O bonds are polar, but the molecule as a whole is nonpolar. From the Lewis structure and using VSEPR theory, we determine that the CO₂ molecule is linear with polar C=O bonds on opposite sides of the carbon atom. The bond dipole moments cancel because they are pointed in opposite directions. In the case of the water molecule (Figure 5), the Lewis structure shows that there are two bonds to a central atom, and the electronegativity difference between oxygen and hydrogen indicates that each of these O-H bonds has a nonzero bond dipole moment. In this case, however, the molecular geometry is bent because of the lone pairs on oxygen, and the two bond dipole moments do not cancel out. Therefore, water does have a net molecular dipole moment and is therefore a polar molecule.

The OCS molecule has a structure similar to CO₂, but a sulfur atom has replaced one of the oxygen atoms. To determine if this molecule is polar, we first draw the molecule with the correct geometry. VSEPR theory predicts a linear molecule:

The C-O bond is considerably polar. Although C and S have very similar electronegativity values, S is slightly more electronegative than C, and so the C-S bond is just slightly polar. Even though these bond dipole moments are pointing in opposite directions, they will not fully cancel because they have different magnitudes. Since oxygen is more electronegative than sulfur, the overall molecular dipole moment will point towards the oxygen end of the molecule.

Chloromethane, CH₃Cl, is another example of a polar molecule. Although the polar C–Cl and C–H bonds are arranged in a tetrahedral geometry, the C–Cl bond has a larger bond dipole moment than the C–H bonds, and the bond dipole moments do not cancel each other out. All of the dipoles have an upward component in the orientation shown, since carbon is more electronegative than hydrogen and less electronegative than chlorine, giving an overall molecular dipole moment going from the hydrogens through the chlorine:

Note that there is a small electronegativity difference between carbon and hydrogen and a C-H bond is slightly polar; however, the difference is quite small, and C-H bonds are often categorized as nonpolar.

The highly symmetrical molecules BF₃ (trigonal planar) and CH₄ (tetrahedral), in which all the polar bonds are identical and symmetrical, are nonpolar. The bonds in these molecules are arranged such that their bond dipoles cancel. However, just because a molecule contains identical bonds does not mean that the dipoles will always cancel. Many molecules that have identical bonds and lone pairs on the central atoms have bond dipoles that do not cancel. Examples include H₂O, H₂S, and NH₃. A hydrogen atom is at the positive end and a nitrogen or sulfur atom is at the negative end of the polar bonds in these molecules:

In summary, to be polar, a molecule must:

1. Contain at least one polar covalent bond.
2. Have a molecular geometry such that the sum of the vectors of each bond dipole moment does not equal zero.

The hybridization of an atom is determined based on the number of regions of electron density that surround it. The geometrical arrangements characteristic of the various sets of hybrid orbitals are shown in Figure 25. These arrangements are identical to those of the electron region geometries predicted by VSEPR theory. VSEPR theory predicts the shapes of molecules, and hybrid orbital theory provides an explanation for how those shapes are formed. To find the hybridization of a central atom, we can use the following guidelines:

1. Determine the Lewis structure of the molecule.
2. Determine the number of regions of electron density around an atom using VSEPR theory, in which single bonds, multiple bonds, radicals, and lone pairs each count as one region.
3. Assign the set of hybridized orbitals from Figure 25 that corresponds to this geometry.

It is important to remember that hybridization was devised to rationalize experimentally observed molecular geometries. The model works well for molecules containing small central atoms, in which the valence electron pairs are close together in space. However, for larger central atoms, the valence-shell electron pairs are farther from the nucleus and there are fewer repulsions. Their compounds exhibit structures that are often not consistent with VSEPR theory and hybridized orbitals are not necessary to explain the observed data. For example, we have discussed the H–O–H bond angle in H₂O (in red below), 104.5°, which is more consistent with sp³ hybrid orbitals (109.5°) on the central atom than with 2p orbitals (90°). Sulfur is in the same group as oxygen, and H₂S (in yellow) has a similar Lewis structure. However, it has a much smaller bond angle (92.1°), which indicates much less hybridization on sulfur than oxygen. Continuing down the group, tellurium (in brown) is even larger than sulfur, and for H₂Te, the observed bond angle (90°) is consistent with overlap of the 5p orbitals, without invoking hybridization. We invoke hybridization where it is necessary to explain the observed structures.

Key Concepts and Summary

In this section, we review many of the topics you are expected to be familiar with that are the foundation of organic chemistry. The first review topic is VSEPR Theory of two, three, and four electron regions. These electron region and molecular geometries enable us to predict molecular shape and bond angles. Using these molecular shapes, we can take a closer look at the electronegative of the atoms within a molecule to predict if a molecule is polar. A molecule’s polarity determines many of its physical properties, like melting point.

Glossary

bond dipole moment
the separation of charge that results when two atoms with differing electronegativites are bonded together, leaving a δ+ charge on the less electronegative atom and a δ- charge on the more electronegative atom

electron region geometry
geometry based on all regions where electrons are located (bonds and lone electron pairs)

hybridization
a widely accepted model that uses quantum mechanics to mathematically combine valence orbitals and create new hybrid orbitals. This model explains the observed bond angles in water, and many other molecules

hybrid orbitals
the new orbitals created after hybridization

molecular (overall) dipole moment
the net charge separation in a molecule

molecular geometry
geometry only based o the location of atoms, not lone electron pairs

nonpolar molecule
a molecule without a dipole moment

polarizability
the measure of how easy or difficult it is for another electrostatic charge (a nearby ion or molecule) to distort a molecule’s electron cloud

polar molecule
a molecule with a dipole moment

valence shell electron-pair repulsion theory (VSEPR theory)
a theory to predict the molecular geometry, including approximate bond angles around a central atom, of a molecule from an examination of the number of bonds and lone electron pairs in its Lewis structure

vector
a quantity having both direction and magnitude