9.1
Molecular Shapes
A molecule's shape can play an important role in determining its chemical properties.
Although Lewis structures are useful, they do not indicate the shapes of molecules. The
Lewis structure of a carbon tetrachloride molecule looks as though the atoms all lie in the
same plane. In fact, the atoms form a shape called a tetrahedron.
Lewis structures and the valence-shell electron-pair repulsion (VSEPR) model. This
model is based on the idea that the best arrangement of a given number of electron pairs
is the one that minimizes the repulsions among them. We will apply the model first to
polyatomic molecules of the general formula ABn (n can equal 2 through 6), where A is
the central atom and is bonded to 2, 3, 4, 5, or 6 B atoms. Carbon tetrachloride is an
example of an AB4 molecule where A is carbon and B is chlorine.
The shapes of ABn molecules depend on the value of n and the number of nonbonding
pairs of electrons on the central atom.
9.2
The VSEPR Model
The VSEPR model is based on the electrostatic repulsion between like charges. The
electron pairs in a molecule can be bonding pairs, which are shared by atoms in bonds,
or nonbonding pairs (lone pairs). Both are negatively charged regions of electron
density, and both will be referred to as electron domains. In fact, we will use the term
electron domain to refer to a lone pair or a bond—whether that bond is single, double, or
triple.
The electron domains in molecules, being negatively charged regions, tend to be as far
away from each other as possible. The resulting arrangements around the central atom
depend on the total number of electron domains. Table 9.1 shows the most stable
arrangements of 2 through 6 electron domains around a central atom.
The arrangement of electron domains about a central atom of an ABn molecule is called
the electron-domain geometry. The molecular geometry of a molecule (or ion) refers to
the arrangement of the atoms. It is important to understand the difference between these
two terms.
To determine the molecular geometry (or shape) of a molecule or polyatomic ion, we
follow a four-step procedure.
1. Sketch the Lewis structure of the molecule or ion.
2. Count the total number of electron domains around the central atom, and arrange
them in the way that minimizes the repulsion among them.
3. Describe the molecular geometry in terms of the angular arrangement of the
bonded atoms.
4. A double or triple bond is counted as one electron domain when predicting.
Although we consider only the positions of the atoms in determining molecular
geometry, lone pairs on the central atom help determine the molecular geometry because
they are electron domains. The table below shows how the molecular geometries of ABn
molecules depend on the number of lone pairs on the central atom.
VSEPR -- The Basic Molecular Configurations
In each of the generic models below, lone pairs of electrons are simulated as the white
balls.
Total
Electron
Domains
Electron-Domains
Geometry
2
Linear
Bonding Nonbonding
Domains Domains
2
Molecular
Geometry
0
Example
CO2
Linear
3
3
0
BF3
Trigonal Planar
Trigonal Planar
2
NO2-
1
Bent
4
0
CH4
Tetrahedral
4
Tetrahedral
3
1
NH3
Trigonal
Pyramidal
2
2
H2O
Bent
5
0
PCl5
Trigonal
Bipyramidal
5
Trigonal
Bipyramidal
4
1
SF4
Seesaw
3
2
ClF3
T-shaped
2
3
XeF2
Linear
6
0
SF6
Octahedral
6
Octahedral
5
1
BrF5
Square
Pyramidal
4
2
XeF4
Square Planar
9.3 Polarity of Polyatomic
Molecules
In eChapter 8.5 you learned how to calculate the dipole moment of a polar bond. In this
section we will take a somewhat more qualitative look at the overall polarity of ABn
molecules.
The bond in H–F is polar because of the electronegativity difference between hydrogen
and fluorine. Whenever two electrical charges of equal magnitude but opposite sign are
separated by a distance, a dipole is established. Thus the H–F molecule has a dipole. The
bond dipole is the dipole moment due only to the two atoms bonded together. Because
there is only one bond in the H–F molecule, its bond dipole is the molecule's dipole.
Let's consider the CO2 molecule. The Lewis structure and VSEPR theory tell us that it is
a linear molecule. Clearly the C=O bonds are polar, owing to the difference in
electronegativity of carbon and oxygen. But the molecule overall is nonpolar. The
polarity of a bond can be denoted with an arrow like those shown below on CO2. The
arrowhead points toward the more electronegative atom.
Because the C=O bonds are identical, the bond dipoles are equal in magnitude. The bond
dipoles are equal in magnitude, yet exactly opposite one another, and they cancel each
other out. The overall dipole moment is zero. Even though the bonds in CO2 are polar,
the geometry of the molecule makes it nonpolar overall. The same is true for BCl3.
Although it may not be immediately apparent, the vectors corresponding to these three
polar bonds cancel completely also.
9.4 Covalent Bonding and Orbital
Overlap
We now take a closer look at covalent bonding between atoms. Using both the Lewis
theory of electron-pair bonds and the idea of atomic orbitals, we arrive at a model of
chemical bonding called valence-bond theory. In valence-bond theory we envision
atomic orbitals overlapping as atoms approach one another, which corresponds nicely to
the VSEPR model. The region of orbital overlap provides the space in which bonding
electron pairs reside. Figure 9.11 shows the valence-bond explanation of the formation of
the bonds in H2, Cl2, and HCl.
Figure 9.11. The overlap of orbitals to form covalent bonds. (a) The
bond in H2 results from the overlap of two 1s orbitals from two H
atoms. (b) The bond in HCl results from the overlap of a 1s orbital of
H and one of the lobes of a 3p orbital of Cl. (c) The bond in Cl2
results from the overlap of two 3p orbitals from two Cl atoms.
Note that each bond in the figure forms as the result of overlap of an atomic orbital
(containing only one electron) on one atom with an atomic orbital (also containing only
one electron) on another atom. Valence-bond theory does not explain how molecules
such as BCl3 form. To explain that, we must take our molecular bonding theory to the
next level.
9.5
Hybrid Orbitals
The VSEPR model correctly predicts that the BeF2 molecule is linear. Valence-bond
theory, however, does not provide an easy way to describe the formation of two covalent
bonds, as beryllium has no unpaired electrons in its ground-state electron configuration.
To explain how beryllium forms two covalent bonds, let's envision the promotion of an
electron from the 2s orbital to one of the empty 2p orbitals.
In this excited state the beryllium atom has the two unpaired electrons it needs to form
two covalent bonds. There is still a problem, though. If the Be–F bonds were to form by
overlap of two different types of orbitals (s and p), the bonds would differ from one
another in length and strength. Experimentally, the Be–F bonds are found to have
identical lengths and identical strengths.
To explain this, we introduce the concept of hybridization—where hybrid orbitals are
formed by mixing two or more atomic orbitals on an atom. We envision the 2s and
occupied 2p orbitals blending to form two hybrid orbitals, which we designate sp hybrid
orbitals.
The sp hybrid orbitals are shaped like lopsided p orbitals with one small lobe and one
large lobe. Each contains a single electron and can be considered an electron domain. As
such, they orient themselves about the beryllium atom just as any two-electron domains
would orient themselves about a central atom. They point in opposite directions,
imparting a linear geometry.
Now we can visualize the formation of two identical bonds in BeF2.
We can extend this model to explain the bonding in a molecule such as BCl3. The boron
atom has only one unpaired electron in its ground state. By promoting one of the 2s
electrons to an empty 2p orbital, we get the three unpaired electrons needed to form three
covalent bonds.
These hybrid orbitals are designated sp2 because they result from the hybridization of one
s orbital and two p orbitals. They have shapes similar to those of sp hybrid orbitals, and
they arrange themselves as any three electron domains would about a central atom—in a
trigonal plane with 120° angles between them.
As with the other hybrid orbitals, sp3 orbitals have one small lobe and one large lobe.
They orient themselves in a tetrahedron about the carbon atom.
The bonding in molecules with expanded octets can also be explained using
hybridization. Consider the PCl5 molecule. Phosphorus has only three unpaired electrons
in its ground state. In this case, promotion of an electron from 3s to 3p would not yield an
additional unpaired electron. (Remember, that's why we do the promotion step—to
increase the number of unpaired electrons.) Phosphorus, however, occurs in the third
period where d orbitals are present. We can envision promotion of an electron to an
empty d orbital, which would provide the necessary five unpaired electrons to explain the
bonding in this molecule. Hybridization of one s orbital, three p orbitals, and one d orbital
gives rise to five equivalent sp3d orbitals.
Similarly, six equivalent bonds in a molecule such as SF6 can be explained. In this case,
to obtain the necessary number of unpaired electrons, we envision promotion of two
electrons: one from the 3s orbital and one from a 3p orbital. Hybridization of one s, three
p, and two d orbitals gives rise to six equivalent sp3d2 hybrid orbitals.
So far, we've considered only hybrid orbitals that contain a single, unpaired electron. It is
also possible for a hybrid orbital to contain a lone pair. Consider the water molecule.
We know from VSEPR theory that the central oxygen atom in a water molecule has four
electron domains around it. Only two of the electron domains are bonds, though. It is
important to recognize that the number of hybrid orbitals about a central atom is dictated
by the number of electron domains that surround it in a Lewis structure. Four electron
domains require four equivalent hybrid orbitals.
In this case promotion of an electron would not yield an additional unpaired electron, so
we skip that step. (We already have the number of unpaired electrons needed to explain
the two covalent bonds in a water molecule.)
To end up with four hybrid orbitals, we must start with four atomic orbitals. So all four of
the orbitals shown are hybridized.
The orbitals on oxygen in a water molecule are sp3 hybridized. Two of the hybrid orbitals
contain lone pairs. The other two contain unpaired electrons that can form covalent bonds
to two hydrogen atoms.
9.6
Multiple Bonds
We now take a closer look at the bonding in molecules with multiple bonds. Let's
consider the ethylene molecule, C2H4. Its Lewis structure has a double bond between the
carbon atoms and single bonds between carbon and hydrogen atoms. The single bonds
are called sigma ( ) bonds. In a bond the shared electron density lies directly along the
axis between the two bonded nuclei (called the internuclear axis). A double bond actually
consists of a s bond and a bond. A pi ( ) bond is a covalent bond in which the overlap
regions lie above and below the internuclear axis. Unlike a bond, in a bond there is no
probability of finding the electron on the internuclear axis; in other words, the electron
density does not lie directly between the atoms.
Each carbon atom can be considered a separate "central" atom. Each has three electron
domains around it. In order to accommodate three electron domains, we need three
hybrid orbitals, which means we must hybridize three atomic orbitals. The hybridization
then involves the 2s orbital and two of the 2p orbitals.
The bonds from each carbon to the hydrogen atoms result from overlap of 2sp2 hybrid
orbitals on carbon and 1s orbitals on the hydrogen atoms. The bond between the carbon
atoms results from the overlap of two 2sp2 orbitals. This time, though, we have a leftover
atomic p orbital with an electron in it. The p orbital is perpendicular to the plane in which
the carbon and hydrogen atoms lie.
This occupied atomic orbital helps explain the double bond in this molecule.
Figure 9. 22. The bond in ethylene is formed by overlap of the
unhybridized 2p orbitals on each C atom. The electron density in the
bond is above and below the axis, whereas in the bonds, the
electron density lies on the bond axes. The two lobes constitute one
bond.
Triple bonds can be considered the combination of a bond and two
bonds.
Figure 9. 23. Formation of two bonds in acetylene, C2H2, from the
overlap of two sets of unhybridized carbon 2p orbitals.
9.7
Molecular Orbitals
Valence-bond theory and hybridization provide a means by which we can explain the
bonding in many molecules and polyatomic ions. Some observations cannot be explained
by these theories, however, and require the development of a new theory. This is the
scientific method at work.
Some aspects of bonding are better explained by another model called the molecular
orbital theory. This theory considers the set of orbitals involved in bonding (the
molecular orbitals or MOs) to be an attribute of the molecule rather than of the
individual atoms. Atomic orbitals overlap to form molecular orbitals. When two atomic
orbitals of equal energy overlap, they produce two molecular orbitals. One of the
molecular orbitals produced is lower in energy than the original atomic orbitals. This is
the bonding MO, designated . The bonding MO concentrates electron density between
the nuclei, drawing them closer by electrostatic attraction. The other MO formed is
higher in energy than the original atomic orbitals and has very little electron density
between the nuclei. This is the antibonding MO, designated *. Electrons in antibonding
orbitals tend to diminish the attraction between nuclei.
Figure 9.31 displays the MOs of a hydrogen molecule and the original atomic orbitals of
the two hydrogen atoms on an energy-level diagram.
Figure 9. 31.
As with atomic orbitals, MOs can hold up to two electrons, and electrons are placed in
the lowest energy orbitals first. A hydrogen molecule has a total of two electrons, both of
which reside in the bonding MO, 1s, generated by the overlap of atomic orbitals. The
antibonding MO in hydrogen, 1s*, is empty. Electrons in bonding MOs are referred to as
bonding electrons. Electrons in antibonding MOs are referred to as antibonding
electrons.
Figure 9. 32. Energy-level diagram for (a) the H2 molecule and (b)
the hypothetical He2 molecule.
A measure of the strength (and stability) of a bond in a diatomic molecule is the bond
order. Bond order is determined by
Applying this formula to the H2 and He2 molecules, we get a bond order of 1 for diatomic
hydrogen and a bond order of 0 for diatomic helium. A bond order of 0 indicates that the
molecule doesn't exist, which is what we would have predicted for helium. The
hydrogen's bond order of 1 corresponds to the single bond between hydrogen atoms in
the Lewis structure of H2. In general, the larger the bond order, the stronger the bond
between two atoms.
9.8 Second-Row Diatomic
Molecules
We have seen how 1s orbitals overlap to produce bonding and antibonding MOs. 2s
orbitals combine in the same way to produce 2s and 2s* MOs. The energy-level diagram
for Li2 shows the distribution of electrons in the MOs that result from overlap of 1s and
2s atomic orbitals on the lithium atoms.
The bond order of the dilithium molecule is 1. We could draw a similar energy-level
diagram for Be2. The diberyllium molecule has two more electrons than the dilithium
molecule. These additional electrons would be placed in the 2s* MO, giving Be2 a bond
order of 0, meaning that diberyllium does not exist.
To apply MO theory to the remaining elements in the second period, we must consider
how p atomic orbitals interact to form MOs.
1. The number of MOs formed equals the number of atomic orbitals combined.
2. Atomic orbitals combine most effectively with other atomic orbitals of similar
energy.
3. The effectiveness with which two atomic orbitals combine is proportional to their
overlap with one another; that is, as the overlap increases, the bonding MO is
lowered in energy and the antibonding MO is raised in energy.
4. Each molecular orbital can accommodate, at most, two electrons, with their spins
paired (Pauli exclusion principle).
5. When MOs have the same energy, one electron enters each orbital (with the same
spin) before spin pairing occurs (Hund's rule).
When three p orbitals on one atom interact with three p orbitals on another atom, the
interactions do not all produce the same type of MO. If we designate the z axis as the one
that connects the atoms, we see that the pz atomic orbitals point toward each other and
can overlap quite effectively, forming and * MOs. The px orbitals on the two atoms are
parallel to one another as are the py orbitals. They can't overlap as effectively, and they
give rise to and * MOs.
We can now consider the bonding in homonuclear diatomic molecules of elements in the
second period. Considering point 3 above, we expect the bonding MOs resulting from pz
overlap (the 2pz MO) to be lower in energy than the bonding MOs resulting from px and
py overlap (the 2px and 2py MOs). We also expect the antibonding 2pz* MO to be
higher in energy than the 2px* and 2py* MOs. This results in the energy-level diagram
in Figure 9.36. This is the general energy-level diagram for diatomic molecules of the
second period.
Figure 9. 36.
In boron, carbon, and nitrogen molecules, we see a slightly different ordering of MOs.
Because of their smaller nuclear charges, these early second-row elements exhibit some
bonding interaction between 2s and 2p orbitals. (Larger nuclei have a stronger hold on
their electrons and constrain them sufficiently to prevent such interactions.) The
interaction of 2s and 2p orbitals causes the energies of the 2s and 2p MOs to become
more disparate in energy. The energy of the 2s MO is decreased while the energy of the
2pz MO is raised. The increase in the energy of the 2pz MO is enough to put it at a
higher energy than the 2px,y MOs. Thus, the order of MOs for B2, C2, and N2, reverses
the positions of the 2p and 2px,y MOs. The energy-level diagrams for both are shown
below. (Only the valence electrons are shown.)
The energy-level diagrams and MO electron configurations are shown in Figure 9.39.
Figure 9.39.
Note that several of the molecules shown have unpaired electrons. Unpaired electrons
cause a molecule to be attracted to a magnetic field. This type of magnetic behavior is
known as paramagnetism. Part of the strength of MO theory is that it predicts that
molecules such as O2 and B2 will exhibit paramagnetism. Valence-bond theory did not
predict any unpaired electrons in molecular oxygen. Molecules without unpaired
electrons are weakly repelled from a magnetic field, and this type of magnetic behavior is
called diamagnetism.