CHAPTER 2: VALENCE BOND THEORY
HOMONUCLEAR DIATOMIC MOLECULES: VALENCE
BOND (VB) THEORY
The word homonuclear is used in two ways:
• A homonuclear covalent bond is formed between
atoms of the same element, e.g. the H – H bond in
H2, the O = O bond in O2 and the O – O bond in
H2 O2 .
• A homonuclear molecule contains
one type of element, e.g. H2, N2 and
F2 and larger molecules such as O3,
P4, S8 and C60.
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Before discussing covalent bonding, we consider the following:
• For an atom X, the value of the single bond covalent radius, rcov, is half the
internuclear separation in a homonuclear X – X bond.
• The van der Waals radius, rv, of an atom X is half of the distance of closest
approach of two non-bonded atoms of X
In covalent bonding, as two nuclei approach each other their atomic orbitals
overlap.
• As the amount of overlap increases, the energy of the interaction decreases.
• At some distance the minimum energy is reached.
• The minimum energy corresponds to the bonding distance (or bond length).
• As the two atoms get closer, their nuclei begin to repel and the energy
increases.
At the bonding distance, the attractive forces between nuclei and electrons just
balance the repulsive forces (nucleus-nucleus, electron-electron).
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A covalent bond forms when the orbitals of two atoms overlap and the overlap
region, which is between the nuclei, is occupied by a pair of electrons.
A set of overlapping orbitals has a maximum of two electrons that must have
opposite spins.
The greater the orbital overlap, the stronger (more stable) the bond.
The valence atomic orbitals in a molecule are different from those in isolated
atoms.
There is a hybridization of atomic orbitals to form molecular orbitals.
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HYBRIDIZATION
The number of hybrid orbitals obtained equals the number of atomic orbitals
mixed.
The type of hybrid orbitals obtained varies with the types of atomic orbitals
mixed.
sp hybrid orbital
atomic
orbitals
hybrid
orbitals
The sp hybrid orbitals in gaseous BeCl2.
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orbital box diagrams with orbital contours
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sp2 hybrid orbitals
When we mix n atomic orbitals we must get n hybrid orbitals.
sp2 hybrid orbitals are formed with one s and two p orbitals, therefore, there
is one unhybridized p orbital remaining.
The large lobes of sp2 hybrids lie in a trigonal plane.
All molecules with trigonal planar electron pair geometries have sp2 orbitals
on the central atom.
The sp2 hybrid orbitals in BF3.
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sp3 hybrid orbitals
sp3 hybrid orbitals are formed from one s and three p orbitals, therefore, there
are four large lobes.
Each lobe points towards the vertex of a tetrahedron.
The angle between the large lobes is 109.5
The sp3 hybrid orbitals in CH4.
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The sp3 hybrid orbitals in NH3.
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The sp3 hybrid orbitals in H2O.
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Geometrical arrangements characteristic of hybrid orbital sets
Atomic orbital Hybrid orbital
set
set
Geometry
Examples
s, p
Two sp
BeF2, HgCl2
s, p, p
Three sp2
BF3, SO3
s, p, p, p
Four sp3
CH4, NH3,
H2O, NH4+
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Composition and orientation of orbitals
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MULTIPLE BONDS
Have  and -bonds.
In -bonds, the electron density lies on the axis between the nuclei. All single
bonds are -bonds.
-Bonds: electron density lies above and below the plane of the nuclei.
A double bond consists of one -bond and one bond.
A triple bond has one -bond and two bonds.
Often, the p-orbitals involved in -bonding
come from unhybridized orbitals.
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Ethane, C2H6
both Cs are sp3
hybridized
s-sp3 overlaps to σ
bonds
relatively even distribution of
electron density over all σ bonds
sp3-sp3 overlap to
form a σ bond
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Ethylene, C2H4
One - and one -bond with both C atoms being sp2 hybridized.
Both C atoms with trigonal planar electron pair and molecular geometries.
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overlap in one position - σ
p overlap - π
electron density
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Acetylene, C2H2
In acetylene:
• the electron pair geometry of each C is linear,therefore, the C atoms are
sp hybridized.
• the sp hybrid orbitals form the C-C and C-H -bonds.
• there are two unhybridized p-orbitals.
• both unhybridized p-orbitals form the two -bonds, one -bond is
above and below the plane of the nuclei and the other -bond is in
front and behind the plane of the nuclei.
When triple bonds form (e.g. N2), one  bond is always above and below
and the other is in front and behind the plane of the nuclei.
Electron density and bond order.
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EXAMPLE
Describe the types of bonds and orbitals in acetone, (CH3)2CO
SOLUTION
Use the Lewis structures to ascertain the arrangement of groups and shape at
each central atom. Postulate the hybrid orbitals taking note of the multiple
bonds and their orbital overlaps.
O
H
H
C
H
C
O
H
C
H
H
C
H3 C
σ bonds
CH3
π bonds
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Delocalized π bonding
So far all the bonds we have encountered are localized between two nuclei.
In the case of benzene:
• there are 6 C-C  bonds, 6 C-H  bonds.
• each C atom is sp2 hybridized.
• there are 6 unhybridized p orbitals on each C atom.
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In benzene there are two options for the 3  bonds:
• localized between C atoms or
• delocalized over the entire ring (i.e. the  electrons are shared by all 6 C
atoms).
Experimentally, all C-C bonds are the same length in benzene, therefore, all CC bonds are of the same type (recall single bonds are longer than double
bonds).
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Restricted rotation of π-bonded molecules in C2H2Cl2
cis-
trans-
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General conclusions on multiple bonds
•
•
•
•
Every two atoms share at least 2 electrons.
Two electrons between atoms on the same axis as the nuclei are  bonds.
 bonds are always localized.
If two atoms share more than one pair of electrons, the second and third
pair form  bonds.
• When resonance structures are possible, delocalization is also possible.
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