Describe the valence bond (VB) approach to chemical bonding
Demonstrate hybridization of atomic orbitals for VB
Correlate the molecular shape to the hybrid atomic orbitals of some central atoms.
Combine the concepts of hybrid orbitals, valence bond theory, VSEPR,
resonance structures, and octet rule to describe the shapes
and structures of some common molecules.
Valence Bond Theory and Hybrid Atomic Orbitals
This picture is an image of a Centaur from
Sphinx Stargate.
The Centaur is a race of monsters in Greek mythology, hybrid animal
having the head, arms and torso of a man united to the body and legs
of a horse. Mixing a number of atomic orbitals
to form the same number of hybrid orbitals to explain chemical bonding
and shapes and molecular structures is a rather recent myth.
The most significant development in the first half of the 20th century
is the human's ability to understand the structure of atoms and molecules.
Computation has made mathematical concepts visible to the extent that we
now can see the atomic and molecular orbitals. On the other hand,
Using everyday encountered materials or toys can also generate
beautiful illustrations of hybrid atomic orbitals.
The valence bond (VB) approach is different from the
molecular orbital (MO) theory.
Despite their differences, most of their results are
the same, and they are interesting.
The valence bond (VB) theory
The valence-bond approach considers the overlap of the atomic
orbitals (AO) of the participation atoms to form a chemical bond.
Due to the overlapping, electrons are localized in the bond region.
The overlapping AOs can be of different types, for example, a sigma bond
may be formed by the overlapping the following AOs.
Chemical bonds formed due to overlap of atomic orbitals
s-s
s-p
s-d
p-p
p-d
d-d
H-H Li-H
H-C H-N H-F
H-Pd in palladium hydride
C-C P-P S-S
F-S in SF6
Fe-Fe
However, the atomic orbitals for bonding may not be "pure" atomic orbitals
directly from the solution of the Schrodinger Equation. Often, the bonding
atomic orbitals have a character of several possible types of orbitals.
The methods to get an AO with the proper character for the bonding is called
hybridization. The resulting atomic orbitals are called
hybridized atomic orbitals or simply hybrid orbitals.
We shall look at the shapes of some hybrid orbitals first, because these
shapes determine the shapes of the molecules.
Hybridization of atomic orbitals
The solution to the Schrodinger Equation provides the wavefunctions
for the following atomic orbitals:
1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.
For atoms containing two or more electrons, the energy levels are shifted
with respect to those of the H atom.
An atomic orbital is really the energy state of an electron bound to an
atomic nucleus. The energy state changes when one atom is bonded to
another atom.
Quantum mechanical approaches by combining the wave functions to give new
wavefunctions are called hybridization of atomic orbitals. Hybridization
has a sound mathematical fundation, but it is a little too complicated to
show the details here. Leaving out the jargons, we can say that an
imaginary mixing process converts a set of atomic orbitals to a new set
of hybrid atomic orbitals or hybrid orbitals.
At this level, we consider the following hybrid orbitals:
sp
sp2 sp3 sp3d sp3d2
The sp hybrid atomic orbitals
The sp hybrid atomic orbitals are possible states of electron
in an atom, especially when it is bonded to others. These electron states
have half 2s and half 2p characters. From a mathematical view
point, there are two ways to combine the 2s and 2p atomic
orbitals:
sp1 = 2s + 2p sp2 = 2s - 2p
These energy states (sp1 and sp2)
have a region of high electron probability each, and the two atomic orbitals
are located opposite to each other, centered on the atom. The sp hybrid
orbitals are represented by this photograph.
H-Be-H
1s 1s
H sp1Besp2 H
1s 1s
For example, the molecule H-Be-H is formed due to the overlapping of
two 1s orbitals of 2 H atoms and the two sp hybridized
orbitals of Be. Thus, the H-Be-H molecule is linear.
The diagram here shows the overlapping of AOs in the molecule H-Be-H.
The ground state electronic configuration of Be is
1s22s2, and one
may think of the electronic configuration "before" bonding as
1s2sp2. The two electrons in
the sp hybrid orbitals have the same energy.
Linear molecules
ClBeCl
HCCH
HCN
O=C=O
You may say that the concept of hybridizing AOs for the bonding
is just a story made up to explain the molecular shape of Cl-Be-Cl.
You are right! The story is lovely and interesting, though.
In general, when two and only two atoms bond to a third atom and the third
atom makes use of the sp hybridized orbitals, the three atoms are
on a straight line. For example, sp hybrid orbitals are used in
the central atoms in the molecules shown on the right.
The sp2 hybrid orbitals
The energy states of the valence electrons in atoms of the second period are
in the 2s and 2p orbitals. If we mix two of the 2p
orbitals with a 2s orbital, we end up with three sp2
hybridized orbitals. These three orbitals lie on a plane, and they point to
the vertices of a equilateral triangle as shown here.
When the central atom makes use of sp2 hybridized orbitals,
the compound so formed has a trigonal shape. BF3 is such a
molecule:
Molecules with sp2 Hybrid orbitals
F | B / \ F F
. . -2 :O: | C / \\
:O:: O
. N // \\ O O
. . O // \\ O O
. . S // \\ O O
Not all three sp2 hybridized orbitals have to be used
in bonding. One of the orbitals may be occupied by a pair or a single
electron. If we do not count the unshared electrons, these molecules are
bent, rather than linear. The three molecules shown together with the
BF3 molecule are such molecules.
Carbon atoms also makes use of the sp2 hybrid orbitals
in the compound H2C=CH2. In this molecule, the
remaining p orbital from each of the carbon overlap to form the
additional pi, p, bond.
Planar molecules with sp2 Hybrid orbitals
H H
\ /
C = C
/ \
H H
O 2-
\
C = O
/
O
O 1-
\
N = O
/
O
Other ions such as CO32-, and NO3-,
can also be explained in the same way.
The sp3 hybrid orbitals
Mixing one s and all three p atomic orbitals produces a set of
four equivalent sp3 hybrid atomic orbitals.
The four sp3 hybrid orbitals points towards
the vertices of a tetrahedron, as shown here in this photograph.
When sp3 hybrid orbitals are used for the central
atom in the formation of molecule, the molecule is said to have the shape
of a tetrahedron.
The typical molecule is CH4, in which the 1s orbital of a
H atom overlap with one of the sp3 hybrid orbitals to form
a C-H bond. Four H atoms form four such bonds, and they are all equivalent.
The CH4 molecule is the most cited molecule to have a tetrahedral
shape. Other molecules and ions having tetrahedral shapes are
SiO44-, SO42-,
As are the cases with sp2, hybrid orbitals, one or two of
the sp3 hybrid orbitals may be occupied by non-bonding
electrons. Water and ammonia are such molecules.
Tetrahedral arrangements of CH4,
NH3E and OH2E2
H H \ /
C / \ H H
H H \ /
N / \ : H
H H \ /
O / \ : :
The C, N and O atoms in CH4, NH3, OH2 (or H2O)
molecules use the sp3 hybrid orbitals, however, a lone pair
occupy one of the orbitals in NH3, and two lone pairs occupy
two of the sp3 hybrid orbitals in OH2.
The lone pairs must be considered in the VSEPR model, and we can represent
a lone pair by E, and two lone pairs by E2. Thus, we have
NH3E and OH2E2 respectively.
The VSEPR number is equal to the number of bonds plus the number of
lone pair electrons. Does not matter what is the order of the bond, any
bonded pair is considered on bond. Thus, the VSEPR number is 4 for
all of CH4, :NH3, ::OH2.
According the the VSEPR theory, the lone electron pairs require more space,
and the H-O-H angle is 105 deegrees, less than the ideal tetrahedral angle
of 109.5 degrees.
The dsp3 hybrid orbitals
The five dsp3 hybrid orbitals resulted when one 3d,
one 3s, and three 3p atomic orbitals are mixed. When an atom
makes use of fice dsp3 hybrid orbitals to bond to five
other atoms, the geometry of the molecule is often a trigonalbipyramidal. For example,
The molecule PClF4 displayed here forms such a structure.
In this diagram, the Cl atom takes up an axial position of the
trigonalbipyramid. There are structures in which the Cl atom may take up
the equatorial position. The change in arrangement is accomplished by simply
change the bond angles. This link discusses this type of configuration
changes of this molecule.
Some of the dsp3 hybrid orbitals may be occupied by electron
pairs. The shapes of these molecules are interesting. In TeCl4,
only one of the hybrid dsp3 orbitals is occupied by
a lone pair. This structure may be represented by TeCl4E,
where E represents a lone pair of electrons. Two lone pairs occupy two
such orbitals in the molecule BrF3, or BrF3E2.
These structures are given in
a VSEPR table of 5 and 6 coordinations.
The compound SF4 is another AX4E type, and many
interhalogen compounds ClF3 and IF3 are
AX3E2 type. The ion I3-
is of the type AX2E3.
The d2sp3 hybrid orbitals
The six d2sp3 hybrid orbitals resulted when
two 3d, one 3s, and three 3p atomic orbitals are mixed.
When an atom makes use of six d2sp3 hybrid
orbitals to bond to six other atoms, the molecule takes the shape of an
octahedron, in terms of
molecular geometry. The gas compound SF6 is a typical
such structure. This link provides other shapes as well.
There are also cases that some of the d2sp3
hybrid orbitals are occupied by lone pair electrons leading to the
structures of the following types:
AX6, AX5E, AX4E2
AX3E3 and AX2E4
IOF5, IF5E, XeF4E2
No known compounds of AX3E3 and AX2E4
are known or recognized, because they are predicted to have a T shape and
linear shape respectively when the lone pairs of electrons are ignored.
Molecular shapes of compounds
While the hybridized orbitals were introduced, in the foregoing discussion,
Valence-shell Electron-pair Repulsion (VSEPR) Model were included to
suggest the shapes of various molecules. Specifically, the VSEPR model
counts unshared electron pairs and the bonded atoms as the VSEPR
number. A single-, double- and tripple-bond is considered as 1.
After having considered the hybridized orbitals and the VSEPR model,
we can not take a systematic approach to rationalize the shapes of
many molecules based on the number of valence electrons.
A summary in the form of a table is given here to account for
the concepts of hybrid orbitals, valence bond theory, VSEPR,
resonance structures, and octet rule. In this table,
the geometric shapes of the molecules are described by linear,
trigonal planar, tetrahedral, trigonal bypyramidal, and octahedral.
The hybrid orbitals use are sp, sp2, sp3,
dsp3, and d2sp3.
The VSEPR number is the same for all molecules of each group.
Instead of using NH3E, and OH2E2,
we use :NH3, ::OH2 to emphasize the unshared (or lone)
electron pairs.
A summary of hybrid orbitals, valence bond theory, VSEPR,
resonance structures, and octet rule.
This table correlates a lot of interesting chemical concepts in order to
understand the molecular structures of these compounds or ions.
There are some intriqueing chemical relationships among the molecules
in each column for you to ponder.
Only Be and C atoms are involved in linear molecules. In gas phase, BeH2
and BeF2 are stable, and these molecules do not satisfy the octet
rule. The element C makes use of sp hybridized orbitals and it has the
ability to form double and triple bonds in these linear molecules.
Carbon compounds are present in trigonal planar and tetrahedral molecules,
using different hybrid orbitals. The extra electron in nitrogen for its
compounds in these groups appear as lone unpaired electron or lone electron
pairs. More electrons in O and S lead to compounds with lone electron pairs.
The five-atom anions are tetrahedral, and many resonance structures can
be written for them.
Trigonal bipyramidal and octahedral molecules have 5 and 6 VSEPR pairs.
When the central atoms contain more than 5 or 6 electrons, the extra
electrons form lone pairs. The number of lone pairs can easily be
derived using Lewis
dot structures for the valence electrons.
In describing the shapes of these molecules, we often ignore the lone pairs.
Thus, •NO2, N3-,
:OO2 (O3), and :SO2 are bent molecules
whereas :NH3, :PF3, and :SOF2 are pyramidal.
You already know that ::OH2 (water) and ::SF2 are bent
molecules.
The lone electron pair takes up the equatorial location in :SF4,
which has the same structure as :TeF4 described earlier. If you
lay a model of this molecule on the side, it looks like a butterfly.
By the same reason, ::ClF3 and ::BrF3 have a T
shape, and :::XeF2, :::I3-,
and :::ICl2- are linear.
Similarly, :BrF5 and :IF5 are square pyramidal
whereas ::XeF4 is square planar.
The Center Atom
A nice student asked a brilliant question.
Which atom in the formula is usually the center atom?
Usually, the atom in the center is more electropositive than the terminal
atoms. However, the H and halogen atoms are usually at the terminal
positions because they form only one bond.
Take a look at the chemical formulas in the table, and see if the above
statement is true.
However, the application of VSEPR theory can be expanded to complicated
molecules such as
H H H O
| | | //
H-C-C=C=C-C=C-C-C
| | \
H N O-H
/ \
H H
By applying the VSEPR theory, one deduces the following results:
H-C-C bond angle = 109o
H-C=C bond angle = 120o, geometry around C trigonal planar
C=C=C bond angle = 180o, in other words linear
H-N-C bond angle = 109o, tetrahedral around N
C-O-H bond angle = 105 or 109o, 2 lone electron pairs around O
Confidence Building Questions
In terms of valence bond theory, how a chemical bond is formed?
Discussion -
Molecular orbital theory considers the energy states of the molecule.
When one s and two p atomic orbitals are used to generate
hybrid orbitals, how many hybrid orbitals will be generated?
Discussion -
Number of orbitals does not change in hybridization of atomic orbitals.
In the structures of SO2 and NO2, what are the values
of the bond angles?
Discussion -
Since the lone electron pair in :SO2 and lone electron in
•NO2 takes up more space, we expect the structure to distort
leaving a smaller angle than 120 between the bonds.
What is the geometrical shape of the molecule CH4,
methane?
Discussion -
The 4 H atoms form a tetrahedron, and methane has a tetrahedral shape.
What do you expect the bond angles to be in the NH4+
ion?
Discussion -
The structure of this ion is very similar to that of CH4.
What hybrid orbitals does the C atom use in the compound
H-CºC-H, in which the molecule is linear?
Discussion -
Sigma (s) bonds are due to sp hybrid orbitals,
and 2 p orbitals are used for pi (p)
bonds. The two sigma bonds for each C are due to overlap of sp
hybrid orbitals of each C atom.
What hybrid orbitals does C use in the molecule:
H
O=C<
H
This is a trigonal planar molecule. It is called formaldehyde, a solvent
for preserving biological samples. The compound has an unpleasant smell.
Skill -
The C atom has 3 sigma (s) bonds by
using three sp2) hybrid orbitals and a pi
(p) bond, due to one 2p orbital.
What is the shape of the molecule SF6?
Discussion -
Since the S atom uses d2sp3 hybrid orbitals,
you expect the shape to be octahedral. The F atoms form an octahedron
around the sulfur.
Phosphorus often forms a five coordinated compound PX5.
What hybrid orbitals does P use in these compounds?
Discussion -
A total of 5 atomic orbitals are used in the hybridization: one 3d,
one 3s and three 3p orbitals.
The dsp3 hybrid orbitals of P give rise to a
trigonalbipyramidal coordination around the P atom.
The energy of d orbitals in N is not compatible with 2s and
2p orbitals for hybridization.
Thus, you seldom encounter a compound with formula NX5
with N as the central atom.
This picture is an image of a Centaur from
Sphinx Stargate.
The Centaur is a race of monsters in Greek mythology, hybrid animal
having the head, arms and torso of a man united to the body and legs
of a horse. Mixing a number of atomic orbitals
to form the same number of hybrid orbitals to explain chemical bonding
and shapes and molecular structures is a rather recent myth.
The sp hybrid atomic orbitals are possible states of electron
in an atom, especially when it is bonded to others. These electron states
have half 2s and half 2p characters. From a mathematical view
point, there are two ways to combine the 2s and 2p atomic
orbitals:
The energy states of the valence electrons in atoms of the second period are
in the 2s and 2p orbitals. If we mix two of the 2p
orbitals with a 2s orbital, we end up with three sp2
hybridized orbitals. These three orbitals lie on a plane, and they point to
the vertices of a equilateral triangle as shown here.
Mixing one s and all three p atomic orbitals produces a set of
four equivalent sp3 hybrid atomic orbitals.
The four sp3 hybrid orbitals points towards
the vertices of a tetrahedron, as shown here in this photograph.
The five dsp3 hybrid orbitals resulted when one 3d,
one 3s, and three 3p atomic orbitals are mixed. When an atom
makes use of fice dsp3 hybrid orbitals to bond to five
other atoms, the geometry of the molecule is often a trigonalbipyramidal. For example,
The molecule PClF4 displayed here forms such a structure.
In this diagram, the Cl atom takes up an axial position of the
trigonalbipyramid. There are structures in which the Cl atom may take up
the equatorial position. The change in arrangement is accomplished by simply
change the bond angles. This link discusses this type of configuration
changes of this molecule.
The six d2sp3 hybrid orbitals resulted when
two 3d, one 3s, and three 3p atomic orbitals are mixed.
When an atom makes use of six d2sp3 hybrid
orbitals to bond to six other atoms, the molecule takes the shape of an
octahedron, in terms of
molecular geometry. The gas compound SF6 is a typical
such structure. This link provides other shapes as well.