1
Covalent Bonding and Hybrid Orbitals
Covalent Bond
Introductory example is the hydrogen atom
Covalent bond results when two atoms approach each other and their orbitals overlap in
such a way that an orbital containing one electron from one atom overlaps with the orbital of
another atom also containing one electron. The result is a pair of electrons in overlapping
orbitals. Each electron experiences attraction to both nuclei (+ve charged nuclei & -ve
charged electrons). The electrons spend more time between the nuclei of the two atoms
and provide lower energy situation than two separate atomic orbitals.
A simple model of bonding is illustrated by forming molecular H2 from H
atoms and varying distance:
– Region I: The total energy of two isolated atoms
– Region II: The nucleus of one atom starts attracting the electrons
of the other; the energy of the system is lowered
– Region III: at 0.74 Å the attraction of electrons and nuclei exactly
balances repulsion of the two nuclei; this is the bond length of H2
– Region IV: energy of system rises as the repulsion of the two
nuclei predominates
2
Bonding in Simple Hydrocarbons
In today’s lecture we will deal with bonding in 4 simple molecules: methane, ethane, ethene
(ethylene) and ethyne (acetylene)
Key ideas:
1. Covalent Bond formed by overlap of orbitals each with one electron of opposite spin
2. Paired electrons are shared in overlapping orbitals.
3. Greater the orbital overlap the stronger the bond.
How do we explain the Tetrahedral Geometry at Carbon?
How can Carbon form 4 equal bonds that point to the corners of a tetrahedron?
Its ground state electronic configuration is 1s22s22p2 !!
What if we excited one electron to give the electronic configuration?
1s22s12p3 ?
Would this give us orbitals that point to the corners of a tetrahedron? Clearly no!
HYBRIDIZATION sp3 ORBITALS
Linus Pauling (2 Nobel Prizes) provided the explanation:One 2s and three 2p orbitals are said to mix and produce 4 hybrid orbitals - called sp3.
In methane CH4 the carbon atom is sp3 hybridized
This means that the wave functions of three 2p orbitals (2px, 2py, 2pz) are combined with the
wave function of one 2s orbital. The result of this mixing of orbitals is 4 new orbitals that
have the character of one part s orbital and three parts p orbital. The two most important
points to remember is that these orbitals have the appearance
4 of these hybrid orbitals point to the corners of a tetrahedron.
Hybrid orbitals can hold 2 electrons of opposite spin and in methane each sp3 orbital is
overlapped by the 1s orbital of the four hydrogen atoms.
Overlap of a sp3 hybrid orbital with a 1s orbital to make a
sigma C-H bond.
Four bonds of equal length and equal strength. Bond vector separated by 109.5°. This is
the angle that places the substituents around the carbon as far apart as possible.Since each
electron pair of the 4 sigma bonds will be concentrated between the C-H atoms, the bond
angle minimizes the repulsion between the electron pair of one bond and those of its 3
neighbouring bonds.
Hybrid Orbitals and Molecular Shape
sp3 hybridization
CH4
The ground state electron configuration of C is
1s2 2s2 2p2
or
1s
2s
2px
valence level
This electron configuration explains
neither the bonding capacity of C
nor the shape of CH4 .
2py
2pz
Hybrid Orbitals
Step One
Electron Promotion 2s
2p
+energy
1s
2s
2px
2py
2pz
1s
2s
ground state of C
Step Two
1s
2s 2px 2py 2pz
This set of valence
orbitals does not
explain the molecular
shape of methane.
2px 2py 2pz
excited state
Orbital Hybridization
1s
sp3 sp3 sp3 sp3
hybrid orbitals
Overview
orbital hybridization
electron promotion
+ energy
1s
2s 2px 2py 2pz
ground state for C
1s
2s 2px 2py 2pz
excited state
2px 2py 2pz
2s
2s
1s
1s
sp3 sp3 sp3 sp3
hybrid orbitals
sp3 sp3 sp3 sp3
energy
2px 2py 2pz
1s
1s
Mixing of Atomic Orbitals to Make Hybrid Orbitals
Mix 1 2s with 3 2p orbitals
get
4 sp3 orbitals
25% s character 75% p character
Sigma Bonds
Because sp3 orbital has the character of a p orbital, the positive lobe of the
sp3 orbital is large and extends out far from the carbon nucleus.
Sigma Bonds
The positive lobe of the sp3 orbital overlaps with the 1s orbital of hydrogen to
form the bonding molecular orbital of a carbon-hydrogen bond. The two
orbitals have a large overlap due to their size and shape. This large overlap
results in a very strong bond.
The bond formed from the overlap of an sp3 orbital and a 1s orbital is a
sigma (σ) bond. Sigma bonds are bonds in which the orbital overlap gives a
bond that has a circular, symmetric cross section when viewed along the
bond axis. ALL PURELY SINGLE BONDS ARE SIGMA BONDS .
The Shape of CH4
1s
H
1s
H
sp3
In-phase combination of
atomic orbitals yields
bonding molecular orbitals.
sp3
sp3
C
1s
H
sp3
H
1s
H
H
o
109.5
H
H
C
H
H
C
H
H
four sigma bonds
a tetrahedral geometry
3
Structure of Ethane
C2H6
H
H
H
C
C
H
H
H
Lewis or Dot Structure
H
H
H
H
H
H
C
C
H
H
H
Line Bond Structure
H
C
C
H
H
Sigma bond caused by
overlap of two sp3 orbitals
C
C
The Structure of Ethane
Ethane, C2H6, is the second member of the alkane family. The four
covalent bonds around each carbon are projected towards the corners of
a tetrahedron, as in methane. This shape of ethane may be predicted by
removing a C-H bond from two methanes and joining the carbons
through a C-C bond.
H
H
H
C
H
H
H
H
H
C
C
H
H
H
HH
H
H
H
H
H
This geometry
follows from the sp3
hybridization at
each carbon.
C
C
C
H
sigma
C-C bond
H
H
The C-C sigma bond results
from the in-phase combination
of sp3 orbitals. Each C-H bond is
formed from the in-phase
combination of an sp3 orbital at
carbon with the hydrogen 1s
orbital.
Rotation Around the C-C Bond
All sigma type bonds have circular symmetry along the bond which means
that there is no loss of orbital overlap when one atom is rotated.
Consequently, there is no significant energy barrier (no increase in
energy) with rotation .
For a C-H bond,
H
there is no
change in energy H
C
with rotation
around the
H
sigma bond.
H
C
H
H
For a C-C bond, there
are small energy
changes with rotation
around the bond that
lead to significant
structural properties.
4
Hybridization: The structure of Ethene or Ethylene - sp2 Hybrid Orbitals
Ethylene C2H4
Since Carbon is tetravalent ethylene must contain a carbon to carbon double bond.
Experimental evidence shows that ethylene is a flat molecule (planar) with bond angles of
120°.
Two sp2 orbitals one from each carbon atom overlap to make a sigma bond between the
carbon atoms.
The unhybridized p orbitals overlap in a sideways fashion - to form a π bond
This is a weaker/smaller overlap than sigma bond overlap which has greater overlap.
So the C-C bond has a sigma and a π bond. The Double bond is stronger than a single
bond; Sigma + a π bond. Therefore the bond length is shorter than a single sigma C-C
bond.
Alkenes: the Carbon-Carbon Double Bond
The covalent bonding possibilities to carbon
include two, four and six electron bonds.
:C:
C
4 single
bonds
: :
: :
.
.C.
.
atomic state
C ::
C=
2 single
and
1 double
bond
: C :::
C
1 single
and
1 triple
bond
Alkenes: the Carbon-Carbon Double Bond
Consider two carbon atoms coming together to
share 4 valence electrons in a covalent bond:
Lewis Structures
.
.C.
.
.
.C.
.
. .
. C .. C .
. .
a two electron
bond
. C .. .. C .
. .
a four electron
bond
The remaining valence electrons are used to form
covalent bonds to other atoms or groups. In ethene,
C2H4, four hydrogen atoms are bonded to the carbons.
:
:
H H
H:C::C:H
or
H H
H-C=C-H
Geometry of Ethene
Ethene is a planar molecule with the internal bond angles
shown below.
H
118o C
H 121o
H
C
H
This trigonal planar
arrangement of the
bonding electrons is
predicted by the valence
shell electron pair
repulsion theory.
Spatial Arrangement of the Hybrid Orbitals
sp2 hybridized carbon
valence
level
2pz
sp2
sp2
pz
sp2
sp2
sp2
C
sp2
1s
bonding orbitals
Three equivalent sp2 orbitals
are in the X-Y plane. The idealized
inter-orbital angle is 120o.
The Carbon-Carbon Double Bond
The carbon-carbon double bond results from valence level orbital
interaction between two sp2 hybridized carbons as shown below. In
this picture, the two atomic centers are brought together along an
axis that allows overlap of sp2 hybrid orbitals.
pz
pz
sp2
C
sp2
C
π
σ
C
C
π
The double bond is made
up of a σ bond from
overlapping sp2 orbitals,
and a π bond from
overlapping pz orbitals.
Trigonal Planar Geometry of Ethene
In ethene all the atoms lie in a single plane called the nodal plane
because it passes through the nodes of the p-orbitals .
H
C
C
H
nodal plane
H
H
ethene
The π-electrons lie above and below the nodal plane.
Restricted Rotation Around the Double Bond
The picture of the carbon-carbon double bond as separate σ and π
bonds is consistent with the observed large barrier (approx. 251
kJ/mol) to rotation around the C-C axis. While σ-bonds are
cylindrically symmetrical around the axis of the bond (meaning that
rotation around the bond axis does not cause loss of orbital overlap),
π-bonds are not.
A rotation of one carbon relative to the other uncouples (loss of orbital
overlap) the p-orbitals. When the p-orbitals are 90o apart, there is no
overlap and the electronic energy is the same as for an electron
residing in an isolated p-orbital.
C C
or
rotation
C C
o
90
C
C
localized
p-orbitals
o
90
view along the
C-C axis
C C
loss of orbital overlap
π-bond
The Energy Barrier to Rotation
C
C C
o
localized
p-orbitals
C C
90
o
π-bond
250
An energy barrier of close
to250 kJ/mol is estimated
during rotation around the
carbon-carbon double bond.
kJ/mol
π-electron potential energy
π-bond
90
C
0
45
90
degree of rotation
135
180
5
The structure of Acetylene - sp Hybrid Orbitals
Carbon can form triple bonds by sharing 6 electrons
H C
C
H
H
C
C
H
It is possible to mix one 2s orbital with only one p orbitals and obtain two equal sp hybrid
orbitals. The second and third p orbital remains as a p orbitals each with an unpaired
electron.
The geometry of the sp orbitals is a 180° bond angle.
The extra 4 electrons in the 4 unhybridized p orbitals overlap sideways to give a triple bond
1 sigma bond and 2 π bonds.
Triple bond is stronger than a double or single bond and the triple C-C bond length is
shorter than a double which is shorter than a sigma bond.
Linear Geometry of Ethynee
:::
H:C C:H
C2H2
or
H-C
C-H
A linear molecule as predicted by VSEPR theory.
The Hybrid Orbital Model
pz
sp hybridized carbon
py
pz
spx
spx
1s
valence
level
spx
C
spx
py
bonding orbitals
The Carbon-Carbon Triple Bond
The carbon-carbon triple bond is formed from in-phase overlap of the
orbitals of two sp-hybridized carbons positioned along the x-axis as
shown.
A sigma bond forms from overlap of two spx orbitals.
Two separate π-bonds form from overlap of the py and pz orbitals.
pz
pz
spx
C
spx
spx
py
σ
C
πy
spx
py
πz
x-axis
C
C
In ethyne, C2H2, the remaining spx
orbitals overlap with the 1s orbital
of H.
H-C C-H
• In ethyne the sp orbitals on the two carbons overlap
to form a σ bond
– The remaining sp orbitals overlap with hydrogen 1s
orbitals
• The p orbitals on each carbon overlap to form two π
bonds
• The triple bond consists of one σ and two π bonds
Orbital Hybridization, Bond Lengths
and Bond Strengths
The greater the degree of s-character in a hybrid orbital that
overlaps with another atomic orbital to form a covalent bond, the
shorter the covalent bond and the stronger the bond.
hydrocarbon
H
H
H
H
H
H
hybridization
sp3
bond lengths
C-C
C-H
ΔHo (C-H)
1.54 Å 1.10 Å
410
(kJ/mol)
(sp3 - 1s)
H
H
H
H
sp2
H
H
sp
1.34 Å 1.09 Å
452
2
(sp - 1s)
1.20 Å 1.06 Å
(sp- 1s)
523
Orbital Hybridization Influences on
C-C Bond Lengths and Bond Strengths
C
CH3
orbitals
C-C Bond Length
ΔHo (C-C)
(kJ/mol)
H3C CH3
sp3
sp3
1.54 Å
368
CH3
sp2
sp3
1.50 Å
385
CH3
sp
sp3
1.46 Å
490
CH2=CH
HC
C
Shorter bonds are generally stronger bonds.
Quiz Chapter 1 Section 14
The longest C-H bond among those
labeled in the structure above is
The strongest C-H bond among
those labeled in the structure
below is
B
A
H C
C
H
C
H
C
H
C
H
C
D
H
Valence-Shell Electron Pair Repulsion VSEPR
To Apply this idea use the following steps:1. Count electron groups on an atom.
These are of the following type
Lone Pair - one group
Any pair or set of pairs of electrons - one group.
2. Assume each group moves as far apart as possible.
Acetylene C2H2
The geometry of the molecule is linear and the
bond angle = 180°.
H
C
C
H
H
Two groups of electrons one of two and one of 6 electrons.
Molecule is linear
C
C
H
CH5N
H
H
Geometry around carbon
C
N H
H
H
Geometry around nitrogen ?
CH5N
H
H
Geometry around carbon
C
N H
H
H
Geometry around nitrogen ?
The carbon atom is surrounded by three hydrogen atoms and one N.
The Nitrogen has a lone pair is attached to one carbon and two hydrogens.
Therefore, we would predict that the carbon would have tetrahedral geometry
3
and is sp hybridized, the same for nitrogen.
C2H6O
There are two plausible Lewis or Line Bond structures.
Both are acceptable structures.
H3C
O
CH3
H3C
CH2
O
H
C2H6O
There are two plausible Lewis or Line Bond structures.
Both are acceptable structures.
H3C
O
CH3
The carbon atom is surrounded by three
hydrogen atoms and one O.
The Oxygen has two lone pairs and is
attached to two carbons.
Therefore, we would predict that the
carbon would have tetrahedral geometry
and is sp3 hybridized, the same for
oxygen with two lone pairs and two bonds
to different carbon atoms.
H3C
CH2
O
H
The carbon atoms all surrounded by 4
groups .
The Oxygen has two lone pairs and is
attached to one carbon and one hydrogen
atom.
Therefore, we would predict that the
carbon atoms would have tetrahedral
geometry and are sp3 hybridized, the
same for oxygen with two lone pairs and
two bonds to different carbon atoms.
Benzene C6H6
H
H
H
H
H
H
Geometry at this carbon?
Benzene C6H6
H
H
H
H
H
Geometry at this carbon?
H
Each carbon has an identical set of groups surround it.
one hydrogen one C-C double bond and one C-C single
bond for a total of 3 groups. Therefore, we would predict
that each carbon would be planar and sp2 hybridized
Acetonitrile C2H3N
Lewis structure?
Hybridization?
Shape?