Ronald Gillespie, Hamilton ON
Do not believe everything you read in the Grade 12 textbook — it may not be correct and in some cases is almost certainly
wrong. If there is any topic that you feel you do not understand, seek further information by looking the topic up in more
advanced books or by going on-line — Google or Wikipedia, for example. Do not attempt to teach something you do not
thoroughly understand, you will almost certainly reveal your lack of understanding to your students as well as very probably giving them
incorrect information. Do your best to dissuade them from memorizing material they do not understand.
This advice applies particularly to theoretical ideas such a quantum mechanics. Much of what is in the textbooks concerning orbital
explanations of bonding and geometry, for example, is incorrect or at least very misleading. Moreover these ideas are very difficult for
most students at this level because they are too abstract for them — stick to simple models such as VSEPR. You are not helping your
students by attempting to prepare them for university by trying to cover the material that is, and should be, taught at the university level.
You will only convince many of them that chemistry is too difficult for them. Keep high school chemistry interesting, relevant and above all
simple — you need to convince students that it is an exciting subject and one that everybody today needs to understand at a basic level.
The chemical bond, electron pair domains and the VSEPR model
reprinted from Chem 13 News, April 1995
[Another reprint by Ronald Gillespie called “Some applications of
the Electron Pair Domain Models” published in Chem 13 News,
May 98 can be found at www.chem13news.uwaterloo.ca.]
Discussions of the chemical bond that go beyond Lewis structures
are usually based on the orbital model at both the high school
and introductory university levels. The orbital model is certainly
of great importance in chemistry but it presents many difficulties
for the beginning student. The purpose of this article is to
present an alternative model that is particularly useful in
introductory courses because it avoids most of the difficulties
associated with the presentation of the orbital model at the
elementary level.
An orbital is a wave function that is a solution to the Schrödinger
equation for the system under consideration. This equation
cannot be understood by students in introductory courses so the
form of its solutions for the H atom are usually presented without
explanation and must therefore be memorized by students
without any understanding. That the wave function must be
squared to obtain the probability of finding an electron is a
mystery for the student. And the mathematical process of
hybridization, still often treated as if it were a physical
phenomenon, is another mystery.
Chemistry students certainly need to be exposed to a full
treatment of the orbital model but in my opinion this is not
necessary for the vast majority of students in introductory
courses. Indeed, this conventional approach to bonding is one
of the topics in the introductory course that does much to
persuade students that chemistry is a very abstract,
mathematical subject that is much too difficult for them.
The Pauli principle
The VSEPR model (valence shell electron pair repulsion model)
of molecular geometry has proved to be very successful in introductory courses because of its simplicity and its usefulness. By
looking at the physical basis of this model we can, as we will
see, develop a bonding model that is not only quantum
mechanically sound but is as simple and appealing as the
14 Chem 13 News/March 2009
VSEPR model itself. The Pauli principle is fundamental to an
understanding of the chemical bond. It describes a fundamental
property of electrons that we have to accept just as we have to
accept that an electron has a charge and a mass. The Pauli
principle can be stated in various ways. In the context of the
orbital model it is stated in the form that
no orbital can contain more than two electrons, which must
be of opposite spin.
In a more general form it states that
electrons of the same spin have a low probability of being
found close together and a high probability of being found as
far apart as possible while electrons of opposite spin may be
found close together and even at the same point.1,2
That electrons behave in this way is not as easy for students to
accept as the fact that an electron has a mass and a charge, but
it is not more difficult than the concept that an orbital can contain
only two electrons of opposite spin; and if we use the Pauli
principle in this more general form it leads to a very simple
model of the chemical bond and also to the VSEPR model.
The chemical bond, electron pair domains, and the
VSEPR model
Electrons are moving at high speeds but in accordance with the
uncertainty principle the paths that they take cannot be
determined. We can find only the probability that an electron will
be found at any particular point in a region to which it is
confined. Thus an electron is often represented by a probability
density distribution or charge cloud that is most dense at those
positions where it will most probably be found and less dense at
those positions where it is less likely to be found.
Let us consider the very common case in a molecule of an atom
that has eight electrons in its valence shell, in other words an
atom that obeys the octet rule. Let us label the spins of the
electrons α and β so there are four electrons of α spin and four
electrons of β spin. According to the Pauli principle the most
probable arrangement of the four α electrons will be when they
are as far apart as possible, that is when they are at the corners
of a tetrahedron. And the most probable arrangement of the β
electrons will also be when they are at the corners of a
tetrahedron (Fig. 1). The electrons are not to be thought of as
located at these tetrahedral positions, rather we imagine that
there are four charge clouds each of which is most dense at one
of these tetrahedral positions. If we are dealing with a free atom
or ion such as the neon atom or an oxide ion there will in
general be no relation between the two tetrahedral sets of
electrons which may have any orientation with respect to each
other giving an overall spherical electron distribution.
and they are at approximately the tetrahedral angle. Also we
see that as a consequence of the formation of the two OH bonds
and the tetrahedral distribution of the α electrons and of the β
electrons the remaining non-bonding electrons form pairs of
opposite spin. In other words, two lone pairs are formed, also at
approximately the tetrahedral angle.
The two electrons of a bonding pair have a high probability of
being found in the internuclear region, in other words the total
charge cloud of these two electrons is mostly located in the
internuclear region. We call a region in an atom where there is
a high probability of finding two electrons of opposite spin an
electron pair domain.3,4 So in the water molecule there are
two bonding electron pair domains and two nonbonding electron
pair domains (Fig. 2). According to this model a single covalent
bond consists of a pair of electrons of opposite spin occupying
an electron pair domain situated between two atomic cores
which they hold together by electrostatic attraction. In this way
we arrive very simply at the concept of a chemical bond that
extends the Lewis model of a pair of shared electrons, and also
at the concept of the VSEPR model. Four electron pair domains
in a valence shell have a tetrahedral arrangement whether two
of them are bonding as in the water molecule, three of them are
bonding as in the ammonia molecule or four of them are
bonding as in the methane molecule. So water is an angular
molecule, ammonia a pyramidal molecule and methane a
tetrahedral molecule (Fig. 2).
Fig. 1. (a) Most probable arrangement of four valence shell
electrons with spin α.
(b) Most probable arrangement of four electrons with spin β.
(c) In the water molecule the two tetrahedra are brought into
approximate coincidence forming two bonding electron
pairs and two nonbonding electron pairs.
(d) Two-dimensional representation of the "tetrahedral"
arrangement of the charge clouds of four α spin electrons.
(e) Two-dimensional representation of the "tetrahedral"
arrangement of the charge clouds of four β spin electrons.
(f)
Two-dimensional representation of the charge clouds or
electron pair domains in the water molecule.
Fig. 2. (a)
Electron pair domain models of AX4, AX3E, and AX2E2
molecules. S is a single bond pair domain; L is a lone pair
However, our interest is in molecules. So let us see what
happens if we allow two protons to approach an oxide ion to
form a water molecule. Each proton attracts electrons but it can
attract at most two electrons into the region close to it, and these
electrons must be of opposite spin (because of the Pauli
principle). The two electrons repel each other electrostatically
but the attraction of the proton is strong enough to bring them
fairly close together. At a certain internuclear distance — the
equilibrium OH bond distance — the attractive forces just
balance the repulsive forces. These two electrons of opposite
spin then constitute the chemical bond between the oxygen
atom and the hydrogen atom. Thus two OH bonds are formed
main.
(b)
Corresponding conventional structural diagrams.
For a valence shell with only two α electrons and two β electrons
each set of two will have a most probable arrangement in which
they are 180o apart so that in an AX2 molecule such as BeCl2
the two electron pair domains are at 180o to each other giving a
linear molecule (Fig. 3). In a valence shell with only three α and
three β electrons each set will have a most probable triangular
arrangement giving a triangular arrangement of electron pair
domains in a molecule such as BF3 which therefore has a
triangular shape (Fig. 3).
March 2009/Chem 13 News 15
In the domain version of the VSEPR model we can replace this
statement by the simpler statement that:
lone-pair domains are larger than bond-pair domains
Fig. 3.
Electron pair domain models of AX2 and AX3 molecules.
The shapes and sizes of electron pair domains
In Fig. 2 and 3 we have assumed that each electron pair domain
or charge cloud has a spherical shape. This is only a very rough
but, nevertheless, a very useful first approximation. If, for
example, we use styrofoam spheres to represent electron pair
domains we can easily show that the tetrahedral arrangement of
four spheres around a much smaller sphere, representing the
core of an atom, is the arrangement that packs them as closely
as possible around this point and is therefore the minimum
energy arrangement. Some years ago Henry Bent used the
same idea of representing an electron pair by a sphere in what
he called the tangent sphere model.5 We will see, however, that
it is convenient to modify this shape to represent different types
of electron pairs.
Because a bonding pair is largely confined to the region
between the two nuclei and is concentrated along the
internuclear axis, it is conveniently represented by a prolate
ellipsoidal shape rather than by a sphere. [A prolate ellipsoid of
revolution has the shape of a North American football.] In
contrast a nonbonding pair is under the attraction of only one
atomic core and it therefore tends to spread out around this core
so that is conveniently represented by a "jelly doughnut" or
oblate ellipsoidal shape (Fig. 4). So we see that a nonbonding
pair domain takes up more space in the valence shell of an atom
than a bonding pair domain. Hence we arrive at the conclusion
that the angle between a nonbonding pair domain and a bonding
pair domain will be larger than the angle between two bonding
pair domains. Consequently the bond angles in water and
ammonia are smaller than the tetrahedral angle. In the original
version of the VSEPR model it was assumed that repulsions
between electron pairs decrease in the order:
lone-pair - lone-pair > lone-pair - bond-pair
> bond-pair - bond-pair
This statement is not only simpler than the original statement but
the justification for it is more easily understood, and moreover it
is easier to apply. For example, in AX4E, AX3E2, and AX2E3
molecules such as SF4, ClF3, and XeF2 the lone pairs always
occupy the equatorial positions of a trigonal bipyramidal
arrangement of five electron pairs (Fig. 5). The explanation for
this in terms of the original statement regarding the relative
strengths of repulsions between electron pairs is not quite
straightforward, but it is very simple in terms of the relative sizes
of electron pair domains. Since an axial vertex in a trigonal
bipyramid has three close neighboring vertices at 90o, whereas
an equatorial vertex has only two close neighbouring vertices at
90o, there is more space available at an equatorial position than
at an axial position; in other words, an equatorial position is less
crowded than an axial position. Hence a larger lone pair domain
always occupies an equatorial position.
Fig. 5.
The structures of some AX4E, AX3E, and AX2E3 molecules in
which the lone pair always occupies an equatorial position as a
consequence of the larger size of a lone pair domain than a
single bond domain.
Summary
On the basis of two fundamental properties of electrons — the
uncertainty principle and the Pauli principle — from which we
derive the concept of an electron pair domain, we can give a
simple but quantum mechanically sound picture of the chemical
bond and we can also derive the VSEPR model. Moreover this
concept makes the VSEPR model even easier to understand
and apply than the original points-on-a sphere version of the
model. And it emphasizes that the true basis of the model lies in
the Pauli principle and that it is not just a consequence of the
electrostatic repulsion between electrons as has often been
incorrectly assumed.
References
1. P.W. Atkins, Quanta, 2nd edition, Oxford University Press, 1991,
page 268.
2. J.W. Linnett, The Electronic Structure of Molecules, John Wiley &
Sons, New York, 1964.
3. R.J. Gillespie, I. Hargittai, The VSEPR Model of Molecular
Fig. 4.
Electron pair domain model of an AX3E molecule with one
Geometry, Prentice-Hall, New Jersey, 1991.
prolate ellipsoidal lone pair domain, L, and three single bond
4. R.J. Gillespie, Chemical Society Reviews, 1991, volume 21, page 59.
domains, S.
5. H.A. Bent, Journal of Chemical Education, 1963, vol 40, pages 446
and 523; 1965, vol 42, pages 302 and 348; 1967, vol 44, page 512.
16 Chem 13 News/March 2009
An Update from Ron Gillespie — VSEPR and the depiction of lone pairs
In this reprint lone pairs are depicted by a typical sp3 orbital
shape. This shape is convenient for illustrations as it is
available in many drawing programs, however, it is only a very
approximate representation of the domain of an electron pair,
that is to say, the electron density distribution associated with an
electron pair. A slightly improved representation is given in Fig.
4 of the April 1995 article. This shows that the lone pair is more
spread out around the central core and takes up more angular
space than any of the bonding pairs, however it gives the
misleading impression that it occupies a considerably larger
volume of space than the bonding pairs. A lone pair domain is
not necessarily larger than a bond pair domain; the important
point is that it is attracted only by the core of the central atom,
whereas a bonding pair is attracted not only by the core of the
central atom but also by the cores of the ligands which stretches
out the electron density towards the ligands. In other words a
lone pair takes up more angular space in the valence shell than
any of the bonding pairs but does not necessarily occupy a
larger overall volume. This is the reason that bond angles are
smaller than the tetrahedral angle in the presence of a lone pair.
from the central core on the bonding side and closer to the core
on the bonding side. The recognition of the unsymmetrical
density of an oxygen or nitrogen atom in its molecules has some
important consequences. It explains why a molecule such as
B(OH)4- does not have a truly tetrahedral geometry with Td
symmetry but rather a distorted tetrahedral geometry with S4
symmetry and it enables one to predict which of the three
possible conformers of a molecule such as CH2(OH)2 is the
most stable (has the lowest energy), as will be discussed in an
article to be submitted to the Journal of the American Chemical
Society and in an article to be submitted to Chem 13 News.
This latter article will also briefly describe other recent
improvements to the VSEPR model including the closely related
Ligand Close Packing (LCP) model. For further information on
some of these topics see Ref. 1.
I have attempted to give an improved depiction of a lone pair in
Fig. 1. Such a figure shows that the electron density on the lone
pair(s) side of the central atom is closer to the core than on the
bonding side, so that the central atom does not have a spherical
electron density but rather has an unsymmetrical density, further
Fig. 1.
A representation of the lone pair domains in the NH3
molecule.
Reference
1. R. J. Gillespie and I. Hargittai, Chemical Bonding and Molecular
Geometry, Oxford University Press, New York, 2001.
∎
MERLAN AD
March 2009/Chem 13 News 17