The Structure of Methane and Ethane: sp3 Hybridization
** The (s) and (p) orbitals used in the
quantum mechanical description of the carbon atom,
were based on
calculations for hydrogen atoms. These simple (s) and (p) orbitals do not, when
taken alone, provide a satisfactory model for the tetravalent–tetrahedral carbon
of methane.
** However, a
satisfactory model of methane’s structure that is based on quantum mechanics can
be obtained through an approach called orbital
hybridization.
** Orbital
hybridization, in its simplest terms, is nothing more than a mathematical
approach that involves the combining of individual wave functions for (s) and (p)
orbitals to obtain wave functions for new orbitals. The new orbitals have, in
varying proportions, the properties of the original orbitals taken separately.
These new orbitals are called hybrid atomic
orbitals.
** According to
quantum mechanics, the electronic configuration of a carbon atom in
its lowest
energy state—called the ground state—is that
given here:
 |
| Fig (1) |
** The valence
electrons of a carbon atom (those used in bonding) are those of the outer
level, that is,
the (2s) and (2p) electrons.
The
Structure of Methane
** Hybrid atomic
orbitals that account for the structure of methane can be derived from carbon’s
second-shell (s) and (p) orbitals as follows (Fig.2):
(1) Wave
functions for the (2s, 2px, 2py, and 2pz) orbitals
of ground state carbon are mixed to form four new and equivalent 2sp3 hybrid
orbitals.
(2) The
designation (sp3) signifies that the hybrid orbital has one part (s)
orbital character and three parts (p) orbital character.
 |
| Figure (2) |
(3) The mathematical result is that the four (2sp3) orbitals are oriented at angles of 109.5o with respect to each other. This is precisely the orientation of the four hydrogen atoms of methane. Each H-C-H bond angle is 109.5o.
** If, in our
imagination, we visualize the hypothetical formation of methane from an (sp3) hybridized carbon atom and four hydrogen atoms, the process might be like that shown
in Fig.3. For simplicity we show only the formation of the bonding
molecular orbital for each carbon–hydrogen bond. We see that an sp3-hybridized
carbon gives a tetrahedral structure for methane, and one with four equivalent C-H
bonds.
 |
| Figure (3) |
** In addition
to accounting properly for the shape of methane, the orbital hybridization model
also explains the very strong bonds that are formed between carbon and hydrogen.
To see how this is so, consider the shape of an individual (sp3) orbital
shown in Fig.4. Because an (sp3) orbital has the character of a p
orbital, the positive lobe of an sp3 orbital is large and extends relatively
far from the carbon nucleus.
** It is the
positive lobe of an sp3 orbital that overlaps with the positive (1s)
orbital of hydrogen to form the bonding molecular orbital of a carbon–hydrogen bond
(Fig.5).
** Because the
positive lobe of the sp3 orbital is large and is extended into
space, the overlap
between it and
the 1s orbital of hydrogen is also large, and the resulting carbon–hydrogen
bond is quite
strong.
** The bond
formed from the overlap of an sp3 orbital and a 1s orbital is an example of a sigma
(s) bond (Fig. 6).
(1) A sigma (σ)
bond has a circularly symmetrical orbital cross section when viewed along the bond
between two atoms.
(2) All purely single
bonds are sigma bonds.
** From this
point on we shall often show only the bonding molecular orbitals because they
are the ones that contain the electrons when the molecule is in its lowest
energy state. Consideration of antibonding orbitals is important when a
molecule absorbs light and in explaining certain reactions. We shall point out
these instances later.
** In Fig.7
we show a calculated structure for methane where the tetrahedral geometry derived
from orbital hybridization is clearly apparent.
Figure (7)
(a) In this
structure of methane, based on quantum mechanical calculations, the inner solid
surface represents a region of high electron density. High electron density is
found in each bonding region. The outer mesh surface represents approximately
the furthest extent of overall electron density for the molecule.
(b) This
ball-and-stick model of methane is like the kind you might build with a molecular
model kit.
(c) This structure is how you would draw methane.
Ordinary lines are used to show the two bonds that are in the plane of the
paper, a solid wedge is used to show the bond that is in front of the paper,
and a dashed wedge is used to show the bond that is behind the plane of the
paper.
The Structure of Ethane
** The bond angles
at the carbon atoms of ethane, and of all alkanes, are also tetrahedral like those in
methane. A satisfactory model for ethane can be provided by sp3-hybridized carbon atoms.
Figure 8 shows how we might imagine the bonding molecular orbitals of an ethane
molecule being constructed from two sp3-hybridized carbon atoms and
six hydrogen atoms.
|
| Figure (8) |
Figure (8)
The hypothetical formation of the bonding
molecular orbitals of ethane from two sp3-hybridized carbon atoms
and six hydrogen atoms. All of the bonds are sigma bonds. (Antibonding sigma
molecular orbitals—called s* orbitals—are formed in each instance as well, but
for simplicity these are not shown.)
** The carbon–carbon
bond of ethane is a sigma bond with cylindrical symmetry, formed by two
overlapping sp3 orbitals. (The carbon–hydrogen bonds are also sigma bonds.
They are formed from overlapping carbon sp3 orbitals and hydrogen s orbitals.)
** Rotation of
groups joined by a single bond does not usually require a large amount of
energy.
** Consequently,
groups joined by single bonds rotate relatively freely with respect to one another.
In Fig. 1.20 we show a calculated structure for ethane in which the tetrahedral
geometry derived from orbital hybridization is clearly apparent.
Figure (9)
(a) In this
structure of ethane, based on quantum mechanical calculations, the inner solid surface
represents a region of high electron density. High electron density is found in
each bonding region. The outer mesh surface represents approximately the
furthest extent of overall electron density for the molecule.
(b) A ball-and-stick
model of ethane, like the kind you might build with a molecular model kit.
(c) A
structural formula for ethane as you would draw it using lines, wedges, and
dashed wedges to show in three dimensions its tetrahedral geometry at each
carbon.
Reference: Organic chemistry / T.W. Graham Solomons , Craig B.Fryhle , Scott A.snyder , / ( eleventh edition) / 2014.
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