7.7 VSEPR Theory

VSEPR Theory

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.

In 1956, British scientists R.J. Gillespie and R.S. Nyholm recognized that the current model for explaining bond angles did not work well. The theory at that time relied on hybrid orbitals to explain all aspects of bonding. The problem was that the theory gave incorrect prediction of bond angles for many compounds. They developed a new approach based on earlier work by other scientists that incorporated a consideration of electron pairs in predicting three-dimensional structure.

The valence shell is the outermost electron-occupied shell of an atom. The valence shell holds the electrons that are involved in bonding and are the electrons shown in a Lewis structure. The acronym VSEPR stands for the valence-shell electron pair repulsion model. The model states that electron pairs will repel each other such that the shape of the molecule will adjust so that the valence electron-pairs stay as far apart from each other as possible. Molecules can be systematically classified according to the number of bonding pairs of electrons as well as the number of nonbonding or lone pairs around the central atom. For the purposes of the VSEPR model, a double or triple bond is no different in terms of repulsion than a single bond. It is important to note here that shape of the molecule is determined by electronic arrangement of central atom only!

So in summary, VSEPR theory allows more accurate predictions of molecular shape by predicting the arrangement of electron pairs around each central atom and, usually, the correct arrangement of atoms in a molecule. We should understand, however, that the theory only considers electron-pair repulsions. Other interactions, such as nuclear-nuclear repulsions and nuclear-electron attractions, are also involved in the final arrangement that atoms adopt in a particular molecular structure.

VSEPR theory predicts the order of repulsions and an order of the amount of space occupied by different electron pairs. The order of electron-pair repulsions from greatest to least repulsion is:

lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair

As a simple example of VSEPR theory, let us predict the structure of a gaseous BeF₂ molecule. The Lewis structure of BeF₂ as in the following Figure 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 bond angle is 180°.

Figure 7.78: BeF₂

Ref: commons/Wikimedia.org/

In the above Figure, the BeF2 molecule adopts a linear structure in which the two bonds are as far apart as possible, on opposite sides of the Be atom.

Carbon dioxide, CO₂

In the CO₂ molecule, each oxygen is double bonded to the central carbon, as the Lewis structure on the left shows. VSEPR predicts that the molecule will be linear because that’s the configuration that moves the C=O bonds as far apart as possible.

Figure 7.79 Linear CO₂ molecule

The actual picture is really more like that shown on the right, because each oxygen atom has two lone electron pairs.

Notice that even these lone pairs, which don’t really contribute to what we think of as the structure of the molecule, orient in such a way as to maximize the distance between them. Notice the similarity between the left-most two lone pairs and the C atom, and the shape of BF₂.

Figure 7.80 Electronic Geometry of CO₂ molecule

Generally, when we speak of the structure of a molecule, we’re talking about the location of the nuclei of atoms, but we even have to be careful there for two reasons: (1) All atoms move all of the time, so we’re always talking about average positions of atoms as they vibrate, and (2) those lone pairs can be big factors in determining the shape and properties of a molecule.

The table below shows the basic electron-pair geometries predicted by VSEPR theory maximize the space around any region of electron density:

References: https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_Chemistry_(OpenSTAX)/07%3A_Chemical_Bonding_and_Molecular_Geometry/7.6%3A_Molecular_Structure_and_Polarity

Molecular structure describes the location of the atoms, not the electrons. We differentiate between these two situations by naming the geometry that includes all electron pairs the electron-pair geometry. The structure that includes only the placement of the atoms in the molecule is called the molecular structure.

A whole molecule may also have a separation of charge, depending on its molecular structure and the polarity of each of its bonds. If such a charge separation exists, the molecule is said to be a polar molecule (or dipole); otherwise the molecule is said to be nonpolar.

It is important to note that electron-pair geometry around a central atom is not the same thing as its molecular structure. Molecular structure describes the location of the atoms, not the electrons.

We differentiate between these two situations by naming the geometry that includes all electron pairs the electron-pair geometry. The number of regions surrounding central atom is called “Electron Group Geometry” or Steric Number (SN). This includes arrangement derived using Lewis structure including bond pairs and lone pairs.

The structure that includes only the placement of the atoms in the molecule is called the molecular structure. The electron-pair geometries will be the same as the molecular structures when there are no lone electron pairs 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-pair geometry is tetrahedral, as is the molecular structure in the following Figure-A below.

Methane         

Figure 7.81 Electronic Geometry of CH₄ molecule

The above Figure-A showing the molecular structure of Methane (CH₄). The molecule structure is shown with tetrahedral arrangement of the hydrogen atoms.

VSEPR structures like this one are often drawn using the wedge and dash notation, in which solid lines represent bonds in the plane of the page, solid wedges represent bonds coming up out of the plane, and dashed lines represent bonds going down into the plane.

On the other hand, the ammonia molecule, NH₃, also has four electron pairs associated with the nitrogen atom, and thus has a tetrahedral electron-pair geometry. One of these regions, however, is a lone pair, which is not included in the molecular structure, and this lone pair influences the shape of the molecule (Figure-B).

Figure 7.82 Electronic Geometry of NH₃ molecule

Figure  7.82(a) The electron-pair geometry for the ammonia molecule is tetrahedral with one lone pair and three single bonds. (b) The trigonal pyramidal molecular structure is determined from the electron-pair geometry. (c) The actual bond angles deviate slightly from the idealized angles because the lone pair takes up a larger region of space than do the single bonds, causing the HNH angle to be slightly smaller than 109.5°.

Reference: https://youtu.be/0SJ0oprIhTU

Reference: https://www.youtube.com/watch?v=bBYlyqb7aOI

Reference: https://www.youtube.com/watch?v=_Cw0_cJzkSI&t=17s

Figure 7.83 VSEPR Chart

Ref: www.openstax.org/

Also, the table below illustrates the molecular structures which are identical to the electron-pair geometries when there are no lone pairs present at the central atom (column number 1).

Figure 7.84 VSEPR Chart

Ref: www.openstax.org/

Reference: https://www.youtube.com/watch?v=nxebQZUVvTg

Reference: https://www.youtube.com/watch?v=keHS-CASZfc

Reference: https://www.youtube.com/watch?v=3ZsqcDOBv7g

Reference: https://www.youtube.com/watch?v=v0nzeCpCb3k

Predicting Electron Pair Geometry and Molecular Structure

Thus, electron pairs will spread themselves as far from each other as possible to minimize repulsion. Using the VSEPR theory, the electron bond pairs and lone pairs on the center atom will help us predict the shape of a molecule. The shape of a molecule is determined by the location of the nuclei and its electrons.

The VSEPR theory is to determine the electron pair geometries and the molecular structures: A model used to predict the shapes of many molecules and polyatomic ions, based on the idea that the lowest-energy arrangement for a compound is the one in which its electron pairs (bonding and nonbonding) are as far apart as possible. (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. Following sections of this chapter will connect the VSEPR model to atomic and molecular orbitals.

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 VSEPR model is not a theory; it does not attempt to explain observations. Instead, it is a counting procedure that accurately predicts the three-dimensional structures of a large number of compounds, which cannot be predicted using the Lewis electron-pair approach.

So Lewis electron structures predict the number and types of bonds, whereas VSEPR can predict the shapes of many molecules and polyatomic ions.

We can use the VSEPR model to predict the geometry of most polyatomic molecules and ions by focusing on only 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 the following Figure 7.85 A and Figure 7.85 -B.

Figure-A: Common Structures for Molecules and Polyatomic Ions That Consist of a Central Atom Bonded to Two or Three Other Atoms.

Figure-B: Geometries for Species with Two to Six Electron Groups

Ref. www.libretext.org/

The following we will illustrate the several examples, beginning with atoms with two electron groups. We will also summarize the common molecular geometries and idealized bond angles of molecules and ions with two to six electron groups.

Figure 7.86 AXE groups in VSEPR

Ref. www.libretext.org/

Common Molecular Geometries for Species with Two to Six Electron Groups.

Below we will discuss each type of electron pair Geometry and molecular shape more in detail.

Trigonal molecules

In an AX₃ molecule such as BF₃, there are three regions of electron density extending out from the central atom. The repulsion between these will be at a minimum when the angle between any two is (360° ÷ 3) = 120°. This requires that all four atoms be in the same plane; the resulting shape is called trigonal planar, or simply trigonal.

Figure 7.87 Shape of BF₃ molecule

Tetrahedral coordination

Figure 7.88 Tetrahedral CH₄ molecule

Methane, CH₄, contains a carbon atom bonded to four hydrogens. What bond angle would lead to the greatest possible separation between the electron clouds associated with these bonds? In analogy with the preceding two cases, where the bond angles were 360°/2=180° and 360°/3=120°, you might guess 360°/4=90°; if so, you would be wrong. The latter calculation would be correct if all the atoms were constrained to be in the same plane (we will see cases where this happens later), but here there is no such restriction. Consequently, the four equivalent bonds will point in four geometrically equivalent directions in three dimensions corresponding to the four corners of a tetrahedron centered on the carbon atom. The angle between any two bonds will be 109.5°.

This is called tetrahedral coordination.

This is the most important coordination geometry in Chemistry: it is imperative that you be able to sketch at least a crude perspective view of a tetrahedral molecule.

It is interesting to note that the tetrahedral coordination of carbon in most of its organic compounds was worked out in the nineteenth century on purely geometrical grounds and chemical evidence, long before direct methods of determining molecular shapes were developed.

For example, it was noted that there is only one dichloromethane, CH₂Cl₂.

Figure 7.89 Shape of CH₂Cl₂

If the coordination around the carbon were square, then there would have to be two isomers of CH₂Cl₂, as shown in the pair of structures here. The distances between the two chlorine atoms would be different, giving rise to differences in physical properties would allow the two isomers to be distinguished and separated.

The existence of only one kind of CH₂Cl₂ molecule means that all four positions surrounding the carbon atom are geometrically equivalent, which requires a tetrahedral coordination geometry. If you study the tetrahedral figure closely, you may be able to convince yourself that it represents the connectivity shown on both of the “square” structures at the top. A three-dimensional ball-and-stick mechanical model would illustrate this very clearly.

Tetrahedrally-coordinated carbon chains

Carbon atoms are well known for their tendency to link together to form the millions of organic molecules that are known. We can work out the simpler hydrocarbon chains by looking at each central atom separately. Thus the hydrocarbon ethane is essentially two CH₃ tetrahedra joined end-to-end. Similar alkane chains having the general formula H₃C–(CH₂)_n–CH₃ (or C_nH_2n+2) can be built up; a view of pentane, C₅H₁₂, is shown below.

Figure 7.90 Tetrahedral chain of carbon atoms

Figure 7.91 shape of long chain carbon atoms

Notice that these “straight chain hydrocarbons” (as they are often known) have a carbon “backbone” structure that is not really straight, as is illustrated by the zig-zag figure that is frequently used to denote hydrocarbon structures.

Coordination geometry and molecular geometry

Coordination number refers to the number of electron pairs that surround a given atom; we often refer to this atom as the central atom even if this atom is not really located at the geometrical center of the molecule. If all of the electron pairs surrounding the central atom are shared with neighboring atoms, then the coordination geometry is the same as the molecular geometry. The application of VSEPR theory then reduces to the simple problem of naming (and visualizing) the geometric shapes associated with various numbers of points surrounding a central point (the central atom) at the greatest possible angles. Both classes of geometry are named after the shapes of the imaginary geometric figures (mostly regular solid polygons) that would be centered on the central atom and would have an electron pair at each vertex.

If one or more of the electron pairs surrounding the central atom is not shared with a neighboring atom (that is, if it is a lone pair), then the molecular geometry is simpler than the coordination geometry, and it can be worked out by inspecting a sketch of the coordination geometry figure.

Tetrahedral coordination with lone pairs

In the examples we have discussed so far, the shape of the molecule is defined by the coordination geometry; thus the carbon in methane is tetrahedrally coordinated, and there is a hydrogen at each corner of the tetrahedron, so the molecular shape is also tetrahedral.

It is common practice to represent bonding patterns by “generic” formulas such as AX₄, AX₂E₂, etc., in which “X” stands for bonding pairs and “E” denotes lone pairs. (This convention is known as the “AXE method“)

The bonding geometry will not be tetrahedral when the valence shell of the central atom contains nonbonding electrons, however. The reason is that the nonbonding electrons are also in orbitals that occupy space and repel the other orbitals. This means that in figuring the coordination number around the central atom, we must count both the bonded atoms and the nonbonding pairs.

The water molecule: AX₂E₂

Figure 7.92 water molecule shape

In the water molecule, the central atom is O, and the Lewis electron dot formula predicts that there will be two pairs of nonbonding electrons. The oxygen atom will therefore be tetrahedrally coordinated, meaning that it sits at the center of the tetrahedron as shown below. Two of the coordination positions are occupied by the shared electron-pairs that constitute the O–H bonds, and the other two by the non-bonding pairs. Thus although the oxygen atom is tetrahedrally coordinated, the bonding geometry (shape) of the H₂O molecule is described as bent.

Figure 7.93 bent shape of water

Figure 7.94 Tetrahedral Electronic Geometry of Water

There is an important difference between bonding and non-bonding electron orbitals. Because a nonbonding orbital has no atomic nucleus at its far end to draw the electron cloud toward it, the charge in such an orbital will be concentrated closer to the central atom. As a consequence, nonbonding orbitals exert more repulsion on other orbitals than do bonding orbitals. Thus in H₂O, the two nonbonding orbitals push the bonding orbitals closer together, making the H–O–H angle 104.5° instead of the tetrahedral angle of 109.5°.

Although the water molecule is electrically neutral, it is not electrically uniform; the non-bonding electrons create a higher concentration of negative charge (blue color) at the oxygen end, making the hydrogen side relatively positive (red).

This image was produced by a computer simulation based on the more complete molecular orbital model that we describe in the next lesson.

This charge unbalance gives rise to many of the so-called anomalous properties of water.

Figure 7.95 Charge Density of water

Ammonia: AX₃E

Figure 7.96 Shape of ammonia, NH₃

Figure 7.97 Computer-generated image of NH₃ molecule showing electrostatic potential (red=+, blue=–.) [source]

The electron-dot structure of NH₃ places one pair of nonbonding electrons in the valence shell of the nitrogen atom. This means that there are three bonded atoms and one lone pair, for a coordination number of four around the nitrogen, the same as occurs in H₂O. We can therefore predict that the three hydrogen atom will lie at the corners of a tetrahedron centered on the nitrogen atom. The lone pair orbital will point toward the fourth corner of the tetrahedron, but since that position will be vacant, the NH₃ molecule itself cannot be tetrahedral. Instead, it assumes a pyramidal shape. More precisely, the shape is that of a trigonal pyramid (i.e., a pyramid having a triangular base). The hydrogen atoms are all in the same plane, with the nitrogen above (or below, or to the side; molecules of course don’t know anything about “above” or “below”!) The fatter orbital containing the non-bonding electrons pushes the bonding orbitals together slightly, making the H–N–H bond angles about 107°.

Central atoms with five bonds

Compounds of the type AX₅ are formed by some of the elements in Group 15 of the periodic table; PCl₅ and AsF₅ are examples.

In what directions can five electron pairs arrange themselves in space so as to minimize their mutual repulsions? In the cases of coordination numbers 2, 3, 4, and 6, we could imagine that the electron pairs distributed themselves as far apart as possible on the surface of a sphere; for the two higher numbers, the resulting shapes correspond to the regular polyhedron having the same number of sides.

The problem with coordination number 5 is that there is no such thing as a regular polyhedron with five vertices.

In 1758, the great mathematian Euler proved that there are only five regular convex polyhedra, known as the platonic solids: tetrahedron (4 triangular faces), octahedron (6 triangular faces), icosahedron (20 triangular faces), cube (6 square faces), and dodecahedron (12 pentagonal faces). Chemical examples of all are known; the first icosahedral molecule, LaC₆₀ (in which the La atom has 20 nearest C neighbors) was prepared in 1986.

Besides the five regular solids, there can be 15 semi-regular isogonal solids in which the faces have different shapes, but the vertex angles are all the same. These geometrical principles are quite important in modern structural chemistry.

Figure 7.98 Electronic Geometry of Trigonal Bipyramidal

The shape of PCl₅ and similar molecules is a trigonal bipyramid. This consists simply of two triangular-base pyramids joined base-to-base. Three of the chlorine atoms are in the plane of the central phosphorus atom (equatorial positions), while the other two atoms are above and below this plane (axial positions). Equatorial and axial atoms have different geometrical relationships to their neighbors, and thus differ slightly in their chemical behavior.

In 5-coordinated molecules containing lone pairs, these non-bonding orbitals (which you will recall are closer to the central atom and thus more likely to be repelled by other orbitals) will preferentially reside in the equatorial plane. This will place them at 90° angles with respect to no more than two axially-oriented bonding orbitals.

Figure 7.99 Ball and Stick model of Trigonal Bipyramidal grometry

Using this reasoning, we can predict that an AX₄E molecule (that is, a molecule in which the central atom A is coordinated to four other atoms “X” and to one nonbonding electron pair) such as SF₄ will have a “see-saw” shape; substitution of more nonbonding pairs for bonded atoms reduces the triangular bipyramid coordination to even simpler molecular shapes, as shown below.

Figure 7.100 lone pairs in Trigonal bipyramidal geometry

• Octahedral coordination

Just as four electron pairs experience the minimum repulsion when they are directed toward the corners of a tetrahedron, six electron pairs will try to point toward the corners of an octahedron. An octahedron is not as complex a shape as its name might imply; it is simply two square-based pyramids joined base to base. You should be able to sketch this shape as well as that of the tetrahedron.

Figure 7.101 Electronic Geometry of Octahedral

The shaded plane shown in this octahedrally-coordinated molecule is only one of three equivalent planes defined by a four-fold symmetry axis. All the ligands are geometrically equivalent; there are no separate axial and equatorial positions in an AX₆ molecule. Click here to see an image that shows the symmetry of the octahedron in more detail.

At first, you might think that a coordination number of six is highly unusual; it certainly violates the octet rule, and there are only a few molecules (SF₆ is one) where the central atom is hexavalent. It turns out, however, that this is one of the most commonly encountered coordination numbers in inorganic chemistry. There are two main reasons for this:

• Many transition metal ions form coordinate covalent bonds with lone-pair electron donor atoms such as N (in NH₃) and O (in H₂O). Since transition elements can have an outer configuration of d¹⁰s², up to six electron pairs can be accommodated around the central atom. A coordination number of 6 is therefore quite common in transition metal hydrates, such as Fe(H₂O)₆³⁺.
• Although the central atom of most molecules is bonded to fewer than six other atoms, there is often a sufficient number of lone pair electrons to bring the total number of electron pairs to six.

Octahedral coordination with lone pairs

There are well known examples of 6-coordinate central atoms with 1, 2, and 3 lone pairs. Thus all three of the molecules whose shapes are depicted below possess octahedral coordination around the central atom. Note also that the orientation of the shaded planes shown in the two rightmost images are arbitrary; since all six vertices of an octahedron are identical, the planes could just as well be drawn in any of the three possible vertical orientations.

Figure 7.102 Lone pairs of Octahedral Geometry

Reference: https://www.youtube.com/watch?v=-pq2wum1uDc

Reference: https://www.youtube.com/watch?v=Moj85zwdULg

Reference: https://www.youtube.com/watch?v=umwN74a0A2g

Following CLASSROOM ACTIVITY has been adapted from Phet simulation: https://phet.colorado.edu

It’s All in the Shape:  Discovering Molecular Geometry

Structure begets function.  How molecules behave or interact with one another or other molecules is an important part of chemistry.  Molecular structure controls properties such as solubility or boiling point.  So let’s explore the simple world of molecular geometry.  

It would be helpful to build some molecular models.  If you have some toothpicks and clay, playdough, or gummy bears, you can make some models – the clay or gummy bear will be the central atom and the toothpicks will represent the electron pairs.

Predict the geometry for the three situations given in the table below.  How do you think electron pairs will behave towards each other?   This behavior will control how they arrange around a central atom depending on the number of electron pairs.

Beware of molecular roadkill (flattened molecules)!!!

Now electron pairs are repulsive to each other; hence, they minimize repulsion by maximizing distance.  They want to get away from each other!  This is the basis of valence shell electron-pair repulsion theory or VSEPR.  Let’s see how well your predictions came out above and add two more geometries to the list.  Go to the following PhET html5 simulation:

Click on the Model box as shown above.  When the screenshot below opens, follow the instructions below.

1.         Click the “Remove All” button.

2.         Check the Show Bond Angles Option

3.         Check the Name Molecular Geometry

Now if you click the single bond (top entity in the Bonding box (upper right corner), you can build the geometries in the table below around the central purple atom.  WATCH carefully as you do this and you will see repulsion in action!!!  If you click and hold in the space away from the boxes, you can rotate the molecule to examine the bond angles and general shape.

Draw the Lewis dot structures for the molecules below. 

BeCl₂                                                                                                                                                                BF₃                                                                                                                                          CH₄

PCl₅                                                                                                                                                                     SF₆

The number of electron pairs on the central atom, first atom in each formula above, determines the molecular geometry.  Predict and illustrate the molecular geometries of the structures above.

Click on the Real Molecules box at the bottom of the screen.

Check your predictions for the molecules.  Did you get the correct answers?   Revise your illustration if needed.  Some help with illustrations is on the next page!

To help with the illustration of the geometries, wedge diagrams, which are used in organic chemistry, are introduced below.  The solid triangular shape is in front of the plane of the paper and the dashed triangular shape is in back of the plane of the paper.

On these three geometries, are there any opposite positions (place where atoms are 180^o apart)?  Circle them.

The trigonal bipyramidal geometry (tbp) needs a little further explanation before we go on.  This geometry has two distinct positions – axial (180^o apart) and equatorial (120^o apart).  This will be important later.

Here is a Google Slide with four movies (<30 seconds each) rotating the various geometries, click the present button in the upper right and then click on the short movies to view.  Click here

Wedge diagrams created in ChemSketch.

Here are models of the ideal geometries that were just explored.

Source:  https://www.indigoinstruments.com/molecular_models/molymod/

For the following molecules, draw the Lewis dot structure and determine the geometry, and sketch the molecules with all atoms identified using wedge diagrams if needed.

SiH₄                                                                     AlCl₃                           

SeF₆                                                                  AsF₅

Let’s do a little carbon chemistry, where you will run across double and triple bonds. Multiple bonds are counted as one pair of electrons, so a single, double, or triple bond counts as one pair.

Determine the geometry of each carbon in the structures below.  Start with drawing the Lewis dot structures for each molecule.

CO₂                              H₂CO                            H₂C=CH₂                       HC≡CH                        CO

Draw the 3D structure of acetic acid, CH₃COOH (first carbon is tetrahedral, second carbon is trigonal planar).

Determine the molecular geometry for the following three molecules:

CH₄                                                                  NH₃                                                                  H₂O

What is different about ammonia and water compared to methane?