The VSEPR Model of Molecular Geometry

The VSEPR Model of Molecular Geometry

by Ronald J Gillespie, Istvan Hargittai

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This authoritative reference, written by the developer of Valence Shell Electron Pair Repulsion (VSEPR) theory, features extensive coverage of structural information as well as theory and applications. Helpful data on molecular geometries, bond lengths, and bond angles appear in tables and other graphics. Suitable for courses in molecular geometry and


This authoritative reference, written by the developer of Valence Shell Electron Pair Repulsion (VSEPR) theory, features extensive coverage of structural information as well as theory and applications. Helpful data on molecular geometries, bond lengths, and bond angles appear in tables and other graphics. Suitable for courses in molecular geometry and chemistry. 1991 edition.

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The VSEPR Model of Molecular Geometry

By Ronald J. Gillespie, István Hargittai

Dover Publications, Inc.

Copyright © 2012 Ronald J. Gillespie and István Hargittai
All rights reserved.
ISBN: 978-0-486-31052-7


Molecular Geometry

This book is concerned with the geometry of molecules and with the interpretation and prediction of molecular geometry using the valence-shell electron-pair repulsion (VSEPR) model. In this chapter we review some basic ideas and concepts concerning the geometry of molecules. In the following chapter we briefly discuss the more important methods by means of which the geometry of a molecule may be determined. Then in the succeeding chapters we give a detailed discussion of the VSEPR model and use it to discuss the geometry of a wide variety of molecules. In the last chapter we consider the theoretical basis of the model and compare it with other models for rationalizing and predicting molecular geometry.


A molecule consists of a discrete group of two or more atoms held together in a definite geometrical arrangement. Whenever two or more atoms are held together sufficiently strongly to form a molecule, we say that there are chemical bonds between each atom and its close neighbors. The geometry of a molecule has a profound influence on its properties, and so ever since van't Hoff and le Bel proposed in 1874 that the bonds formed by a carbon atom have a tetrahedral arrangement the geometry of molecules has been of great interest. Chemists have for a long time represented a bond by a single line. We draw structures for molecules that indicate how it is believed that the atoms are connected together by bonds. We will use the term structure in this sense to indicate simply the connectivity of the atoms, while by geometry we mean the actual three-dimensional arrangement of the atoms.

Each atom in a molecule consists of a positively charged nucleus surrounded by a number of negatively charged electrons. Thus there are two important and closely related questions that we can ask about a molecule:

1. What are the relative positions of the nuclei in space? In other words, what is the geometry of the molecule? The geometry of a molecule is usually described in terms of the distances between the atomic nuclei that are bonded together (that is, the bond lengths), the angles between the bonds formed by each atom (that is, the bond angles), and the angles between the bonds on adjacent atoms (that is, the torsional angles).

2. How are the electrons arranged? Because electrons are in constant motion and because their paths cannot be precisely defined, the arrangement of the electrons in a molecule is described in terms of an electron density distribution. The electrons in an atom are arranged in successive shells surrounding the nucleus. The nucleus and the inner shells of electrons usually remain unchanged in molecule formation, and it is only the outer shell, known as the valence shell, that is modified. Thus the atomic nucleus and the inner electron shells are considered to constitute the core of the atom so that a molecule is thought of as consisting of two or more positively charged atomic cores held together by the electrostatic attraction of a negatively charged electron density distribution derived from the valence-shell electrons of the constituent atoms. Thus the relationship between the arrangement of the electrons, that is, the electron density distribution, and the bonds that are imagined to hold atoms together in a molecule is of fundamental importance to the understanding of molecular geometry.

The arrangement of the nuclei in a molecule may be determined by several different experimental methods, the most important of which is X-ray diffraction by crystalline solids, as will be described in Chapter 2. The geometry of a molecule may also be found, at least in principle, by determining by quantum mechanical calculations the arrangement of the nuclei that has the minimum energy, as will be discussed in Chapters 2 and 7.

The electron density distribution of a molecule can be determined by the same quantum mechanical calculations as are used to find the energy and geometry of a molecule. But in practice it is only possible to carry out these calculations to a reasonable accuracy for small molecules consisting of light atoms.

The electron density distribution can also, at least in principle, be determined by X-ray diffraction studies on crystalline solids. X-rays are diffracted by the periodically varying electron density distribution in a crystal; but most of the electron density is concentrated in the atomic cores, and so, although it is relatively simple to determine the positions of the atomic cores and therefore of the nuclei, it is often very difficult to detect the small changes in the electron density distribution that occur on molecule formation.


The arrangement of the electrons in an atom is usually described in terms of its electron configuration as deduced from atomic spectroscopy, ionization energies, and the periodic table, and also from quantum mechanics (Chapter 7). The electron configurations of the elements are given in Table 1.1.

One of the earliest models of the arrangement of the electrons in molecules is that published by G. N. Lewis in 1916, although it had been used by him in teaching for a number of years before. Chemists have found this model so convenient that it is still today the most widely used simple model. Lewis represented the core of an atom by its symbol and the valence-shell electrons by the appropriate number of dots. Lewis dot diagrams for the main-group elements of the first six periods are given in Figure 1.1.

Lewis proposed that in compound formation atoms achieve noble gas electron configurations either by electron loss or gain or by the sharing of one or more electron pairs. Because each of the noble gases, except helium, has eight electrons in its outer or valence shell, Lewis's proposal is often called the octet rule. Electrons are readily removed from the valence shell of an atom of a metal to give an ion with a noble gas electron configuration; for example,

Na(2s22s22p63s1) -> Na+(1s22s22p6) + e-

Nonmetals tend to gain electrons to give negative ions that have a noble gas configuration; for example,

O(1s22s22p4) + 2e- -> O2-(1s22s22p6)

The positive and negative ions thus formed are attracted to each other by electrostatic forces to form ionic compounds, and such compounds are said to have ionic bonds.

Lewis also proposed that atoms may be held together by sharing one or more electron pairs. A shared electron pair constitutes a single covalent bond between the atoms, as in the Cl2 molecule:


Similar Lewis diagrams can be written for many molecules in which each of the atoms has an octet of electrons in its valence shell. For example, the Lewis diagrams for carbon tetrafluoride, nitrogen trifluoride, oxygen difluoride, and fluorine are

Lewis Structures


In a completed valence shell all the electrons may be considered to be arranged in pairs, either bonding pairs or nonbonding pairs. Nonbonding pairs are also frequently called lone pairs or unshared pairs. Lewis diagrams are usually simplified by representing each bonding pair of electrons, that is, each covalent bond, by a single line, as follows:


Hydrogen is an exception to the octet rule in that the corresponding noble gas, helium, has only two electrons in its valence shell. Thus in the Lewis diagrams of compounds of hydrogen there are only two electrons in the valence shell of each hydrogen, as, for example, in methane, ammonia, water, and hydrogen fluoride:


In some molecules two or three electron pairs may be shared between two atoms, thereby forming double and triple bonds. Double bonds are found, for example, in ethene and carbon dioxide:


Triple bonds are found for example in ethyne and hydrogen cyanide:


Although in the vast majority of covalent compounds atoms are held together by one or more shared pairs of electrons, there are many exceptions to the octet rule. For example, the central atoms in BeCl2(g) and in BCl3 have only two and three electron pairs, respectively, in their valence shells:


There are also many molecules in which a central nonmetal atom from period 3 and beyond in the periodic table has five, six, or even more electron pairs in its valence shell. Examples include sulfur tetrafluoride, SF4, chlorine trifluoride, ClF3, and sulfur hexafluoride, SF6:



The concept of the covalent bond as consisting of a pair of shared electrons led to a great step forward in the understanding of chemical bonding and molecular structure, but Lewis could not explain why electrons are arranged in pairs nor why two shared electrons could bind two nuclei together. A full understanding of the covalent bond had to await the development of quantum mechanics, as we will discuss in Chapters 3 and 7. We will see that in the formation of a covalent bond there is a small increase in the electron density in the region between the atomic cores, and it is the electrostatic attraction between this increased electron density and the positively charged atomic cores that holds the two atomic cores together.

No sharp distinction can be drawn between covalent and ionic bonds, and in many molecules the bonds have an intermediate character. In fact, a pure covalent bond is only possible between atoms of the same kind, that is, atoms of the same element. Atoms of different elements attract the bonding electron pair to different extents, so there is some transfer of electron density from one atom to the other; that is, the bond is not purely covalent but has some ionic character. Similarly, there can be no pure ionic bond, because whenever two oppositely charged ions are attracted together there is inevitably at least a small amount of sharing of electron density between them. Molecules containing predominately ionic bonds are not common because normally, when oppositely charged ions are attracted together, they form a crystalline solid that consists of a regular periodic arrangement of ions in which no discrete molecules can be recognized (Figure 1.2). The whole crystal may be regarded as one giant molecule or as a polymer of essentially infinite size. Small molecules in which the bonding is predominately ionic are usually found only in the gas phase when an ionic solid is vaporized at high temperature.

The ability of an atom to attract the electrons of a covalent bond is called its electronegativity. Values of the electronegativities of the elements have been obtained by different authors by several different methods. Table 1.2 gives the values determined by A. L. Allred and E. G. Rochow. These can only be regarded as approximate average values because the electronegativity of an atom depends to some extent on the atoms that are attached to it and its oxidation state.

We also recognize a third type of bond, the metallic bond, in which a large number of atomic cores are held together by a delocalized electron cloud, and no discrete bonds between individual pairs of atoms and no molecules can be distinguished. Again, no sharp distinction can be drawn between metallic bonds and covalent and ionic bonds, and in many compounds the bonds have an intermediate character. However, since metallic bonding is a property of a large assembly of atoms, it is not found in the relatively small molecules with which we are primarily concerned in this book.

Both ionic bonding and metallic bonding are nondirectional in nature, and so the structures of ionic and metallic substances are determined primarily by the ways in which ions and atoms of different sizes may be packed together. In contrast, covalent bonds are highly directional in character, and it is the tendency for atoms to form bonds in specific directions that is the most important factor in determining the structures of covalent molecules and crystals.


The discussion of molecular geometry in this book is based on the valence-shell electron-pair repulsion (VSEPR) model, which in turn is based on Lewis's description of the electron arrangement in a molecule. The basic assumption of the VSEPR model is that the electron pairs in the valence shell of an atom, both bonding and nonbonding, adopt that arrangement that keeps them as far apart as possible; that is, they behave as if they repel each other. From the arrangement of the electron pairs in the valence shell of an atom the geometry of the covalent bonds that it forms can be easily predicted. In this book we are therefore mainly concerned with covalent molecules.


Some simple molecules are linear and some others are planar, but most molecules are three dimensional. It is particuarly convenient to describe the structures of many three-dimensional molecules in terms of an appropriate polyhedron. So we now describe some of the more important polyhedra.

A polyhedron encloses a portion of three-dimensional space with four or more polygons. A polygon encloses a portion of a plane with three or more straight lines. A polygon is convex if each interior angle is less than 180°, and it is regular if it has equal interior angles and equal sides. In principle, there is an infinite number of regular polygons with the circle as a limiting case (Figure 1.3). A polyhedron is convex if every dihedral angle is less than 180°. A dihedral angle is formed by two polygons joined along a common edge. A convex polyhedron is regular if its faces are equal regular polygons and if each of its vertices has the same surroundings.

There are only five regular convex polyhedra: the tetrahedron, cube (hexahedron), octahedron, dodecahedron, and icosahedron. They are shown in Figure 1.4. Their characteristic parameters are given in Table 1.3. The regular convex polyhedra are called Platonic solids because they were an important part of Plato's natural philosophy.

The same polyhedron may be used to describe the shapes of two rather different types of molecule. For example, As4 and B4Cl4 are described as tetrahedral molecules. In both these cases, there are atoms at the corners of a tetrahedron, and each of these atoms is bonded to each of its three neighbors so that there are bonds along all six edges of the tetrahedron (Figure 1.5). In contrast, methane, CH4, and silane, SiH4, are also both described as tetrahedral molecules. In these molecules there are atoms at each of the corners of the tetrahedron, but these atoms are not bonded together; rather they are bonded to an atom at the center of the tetrahedron (Figure 1.6). To distinguish these two types of tetrahedral molecules, we will call the latter type centered tetrahedral molecules. The other type of tetrahedral molecule in which the atoms are at the corners of a polyhedron and there is no central atom are often described as cage or cluster molecules. An example of an octahedral molecule without a central atom is the borane B6H2-6 (Figure 1.7). There are many octahedral molecules with a central atom. Examples are SF6 and PCl-6 (Figure 1.7).

The regular convex polyhedra are highly symmetrical. There are various other families of less symmetrical polyhedra. The semiregular polyhedra are similar to the Platonic solids in that all their faces are regular and all their vertices have the same surroundings, but their faces are not all polygons of the same kind.

Prisms and antiprisms are also important polyhedra. A prism has two identical and parallel faces that are joined by a set of parallelograms. An antiprism also has two identical and parallel faces, but they are joined by a set of triangles. There is an infinite number of prisms and antiprisms and some of them are shown in Figure 1.8. The cube is a special case of a prism in which the two parallel faces are squares that are also joined by squares, and the octahedron is a special case of an antiprism in which the two parallel faces are equilateral triangles that are also joined by equilateral triangles.

Of the endless number of less regular polyhedra, two more kinds deserve special mention, the pyramids and bipyramids. The most symmetrical pyramids and bipyramids have a regular base. The tetrahedron is a special case of the trigonal pyramid with a regular triangular base and three regular triangles as side faces. A bipyramid is a double pyramid, which may be thought of as obtained from a single pyramid by reflection with respect to its base. Examples are shown in Figure 1.9. A trigonal bipyramid is not a regular polyhedron as it has two sets of nonequivalent vertices, at two of which three edges meet and at the other three four edges meet. The tetragonal bipyramid, however, becomes an octahedron when all its faces are regular triangles. Among the pyramids and bipyramids, the square pyramid and the trigonal bipyramid are important molecular shapes (Figure 1.10).


Excerpted from The VSEPR Model of Molecular Geometry by Ronald J. Gillespie, István Hargittai. Copyright © 2012 Ronald J. Gillespie and István Hargittai. Excerpted by permission of Dover Publications, Inc..
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