1. science
2. mathematics
3. geometry

Topic 3
Molecular Shape and Chemical
Bonding
Content
3.1. COVALENT BONDING......................................................................................... 51
3.1.1. The octet rule .......................................................................................... 52
3.1.2. Valency ................................................................................................... 52
3.1.3. Co-ordinate covalent bonds .................................................................... 53
3.1.4. Multiple bonds ......................................................................................... 53
3.1.5. Bond polarity ........................................................................................... 54
3.2. LEWIS STRUCTURE OF MOLECULES ................................................................... 55
3.2.1. Charged and delocalized species ........................................................... 55
3.2.2. Exceptions to octet rule ........................................................................... 57
3.2.3. Bridging atoms ........................................................................................ 59
3.2.4. Bond order, bond length and bond energy .............................................. 60
3.3. MOLECULAR SHAPE .......................................................................................... 63
3.3.1. Geometry and shape ............................................................................... 63
3.3.2. VSEPR .................................................................................................... 64
3.3.3. Further examples of Lewis structure / VSEPR ........................................ 70
3.3.4. Inert pair effects ...................................................................................... 72
3.3.5. Shape and Molecular Dipoles ................................................................. 74
3.4. VALENCE BOND (VB) THEORY........................................................................... 76
3.4.1. Basis ....................................................................................................... 76
3.4.2. Hybrid Orbitals ........................................................................................ 77
3.4.3. VB construction ....................................................................................... 79
3.5. MOLECULAR ORBITAL (MO) THEORY- A BRIEF INTRODUCTION .............................. 81
Learning objectives
Basic Concepts of Chemical Bonding – chemical formulae ; ionic bonding ; covalent bonding
– octet rule, valency, bond polarity, Lewis structures, resonance, hypervalency, bond order,
length and dissociation energy ; molecular geometry – VSEPR Theory ; dipole moments ;
valence bond theory – hybrid orbitals ; molecular orbital theory.
TOPIC 3. Molecular Shape and Chemical Bonding
51
3.1. Covalent Bonding
A covalent bond is a chemical bond that involves the sharing of an electron pair between
neighbouring atoms.
Covalent bonding is energetically favoured. The bond energy is defined as the
energy that must be supplied to separate the bonded atoms to infinity.
The bond length is the distance between the two nuclei; it is the internuclear distance
for which the bond energy is minimal.
Covalent bonds are affected by the electronegativity of the connected atoms.
For two atoms with equal electronegativity, the covalent bond is non-polar.
E.g.: The hydrogen molecule: H-H; bond energy = 435 KJ mol-1; bond distance = 74 pm
1 e-
2 e-
H H
H H
H
Figure. Non-polar covalent bonding formed by the interaction of two shared bonding
electrons.
In a heteroatomic bond, the more electronegative atom tends to attract the electron
pair of the bond. The covalent bond is polar with a negative partial charge over the
more electronegative atom and a positive partial charge over the less
electronegative.
Example: The hydrochloride molecule: H-Cl
unpaired electron
lone pair
1
e-
bonding pair
+
-
1+
+
-
H Cl
H
Cl
+
H
Cl
-
Figure. Polar covalent bonding formed by the interaction of two shared bonding
electrons. The bonding pair is not shared equally but is more attracted by the more
electronegative atom (here Cl) which polarises the bond.
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TOPIC 3. Molecular Shape and Chemical Bonding
52
3.1.1. The octet rule
The octet rule states that atoms tend to be more stable when their electronic
configuration is similar to that of a noble gas. As a result, atoms tend to gain, lose or
share electrons so that their outer shell is populated by 8 electrons. (8 = octet).
This rule applies to the main group elements of low atomic number (<20), including
carbon, nitrogen, oxygen, halogens, sodium, potassium, magnesium. The number 8
correspond to a full n-shell: 2 electrons in ns-orbital plus 6 electrons in np-orbitals.
On ammonia (NH3) the nitrogen (which has 5 valence electrons) is bond to three
hydrogen atoms: each hydrogen brings one electron to the molecule - so the total
number of electron in the nitrogen's outer shell is 8 (5(N) + 3(H)).
On water molecule, the oxygen (6 valence electrons) is bond to two hydrogens. Each
hydrogen brings one electron to the oxygen's outershell, which is then populated by 8
electrons. (6(O) + 2(H))
3.1.2. Valency
The valency or valence number of an atom is the number of chemical bonds that an atom
may form to satisfy the octet rule. It is equal to the number of unpaired electron (upe). The
lone pair electrons are not counted as bonding, therefore the valency is the number of
valence electrons, less the lone pair electrons (lp).
The valency of an atom in a molecule is equal to the number of bond to the atom (single
bond count as one bond, double bond two and triple bond three).
Example:
Nitrogen, has 5 valence electrons. Two of them are organised in one lone pair and
three are available for bonding: the valency is 3.
lp
upe
N
upe
upe
Nitrogen has one lone pair (lp) and three unpaired electrons (upe)
Chlorine, has 7 valence electrons. Six electrons are organised in three lone pairs
and one electron is available for bonding: the valency is 1.
lp
lp
Cl
upe
lp
Chlorine has three lone pairs (lp) and one unpaired electron (upe)
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TOPIC 3. Molecular Shape and Chemical Bonding
53
3.1.3. Co-ordinate covalent bonds
This is also known as a dipolar bond; a dative covalent bond or a co-ordinate bond and
is a covalent bond in which the two electrons of the bond are provided by the same atom.
Example: Adduct of ammonia and boron trifluoride. The two electrons of the B-N bond are
provided by the nitrogen: as a result a positive charge appears on the nitrogen and a
negative charge on the boron.
Ground state Boron: [He] 2s22p1
lp
eo
empty orbital (eo)
upe
B
F B
upe
upe
empty orbital
Excited state Boron: [He] 2s12p2
F
H N
H
F
H
Boron trifluoride
ammonia
F
H
F B
N
F
H
H
F
H
F B
N
F
H
H
Adduct of ammonia and boron trifluoride
3.1.4. Multiple bonds
A double bond is a chemical bond involving four bonding electrons shared between two
atoms.
Example: Ethylene C2H4. Each carbon is surrounded by 8 valence electrons. The bonding
between the two carbons involves four valence electrons making a double bond.
H
H
C
H
H
H
C C
C
H
H
H
Figure. Double bond of ethylene.
A triple bond involves six bonding electrons shared by two atoms.
Example: Acetylene C2H2. Each carbon is surrounded by 8 valence electrons. The bonding
between the two carbons involves six valence electrons: a triple bond.
H C
C H
H C C H
Figure. Triple bond of acetylene.
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TOPIC 3. Molecular Shape and Chemical Bonding
54
The valency of carbon is 4 in ethylene and acetylene:
In ethylene, each carbon has four bonds: two single bonds with hydrogen plus one
double bond with carbon.
In acetylene, each carbon has four bonds: one single bond with hydrogen plus one
triple bond with carbon.
3.1.5. Bond polarity
When one of the two atoms involved in a covalent bond attracts the bonding electron pair
more than the other atom, partial charges appear and the bond is polar. A negative partial
charge ( -) appears over the atom attracting the electronic density and a positive partial
charge ( +) appears over the other one.
The ability to attract the electronic density is evaluated using the empirical value of
electronegativity . The higher the value the greater the pull on electrons and the higher the
difference in electronegativity between the two atoms bonded the higher the polarity.
The polarity scale spreads continuously from non polar (the two atoms share the electron
density equally -have equal ) to ionic (one atom takes the totality of the electron density
leaving nothing to the other atom - the difference in between the two atoms is well over
0.5). Between these two extremes the covalent bond is essentially non polar (difference less
than 0.5) or polar (difference over 0.5).
The polarity of a bond is measured by the values of the partial charge ( + and -) created.
= q x e x r (C m)
is the dipole moment measured in Debye (D)
-30
( 1D = 3.336 x 10 Cm)
q is the partial charge on the atoms
e is the charge of an electron in C (coulomb)
r is the bond length in m (metre
Example. HF has a dipole moment of 1.83 D and a bond length of 92 pm (92x10 -12m)
Calculate the value of q
q = / (e x r) = 0.41
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TOPIC 3. Molecular Shape and Chemical Bonding
55
3.2. Lewis Structure of Molecules
Lewis electron dot diagrams show the valence electrons arround the atoms of a molecule
and identify their nature as lone pair (lp), bonding pair (bp) or unpaired electrons (upe).
The molecular shape is dictated by the position of the electrons around the central atoms.
Building the Lewis structure of molecules in 5 steps: Methanol, CH 3OH
1. Start from the molecular formula. Determine for each atom the total number of
valence electrons. When dealing with an anion, add one electron per charge. For a
cation, remove one electron per charge.
2. Place the element of lowest valence around the element of highest valence. Then
assign the bonds (single double or triple) to satisfy the valency of the atoms of lowest
valency.
3. Calculate the number of valence electrons around the central atom, adding the
shared electrons from the peripheral atoms.
4. Assign the shared electrons to bond pairs (bp).
5. Assign the residual valence electrons to lone pairs (lp).
3.2.1. Charged and delocalized species
To draw the Lewis structure of negatively charged species, the general method of
construction is followed, adding one extra valence electron per negative charge.
Example. Tetrahydroborate ion: BH4-.
eo
B
Boron
Electron
H
H
H
H
H
H
B
H
H
H
B
H
Four hydrogens
H
H
Tetrahydroborate
Note: Boron is surrounded by 8 electrons. The octet rule is satisfied.
The Lewis structure of positively charged species is constructed following the general
method, removing one valence electron per positive charge.
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TOPIC 3. Molecular Shape and Chemical Bonding
56
Example. Ammonium ion: NH4+.
H
H
H
H
N
H
H
N
H
N
H
H
H
H
Nitrogen
H
Four hydrogens, of which
one had its electron
removed (proton with
positive charge)
Ammonium ion
Note: Nitrogen is surrounded by 8 electrons. The octet rule is satisfied.
When dealing with delocalised bonding: more than one Lewis structure can be
drawn. This happen when a bond pair does not have a definite position between two
atoms only but over three or more atoms. Each possible Lewis structure is called a
resonance structure; the molecular skeleton does not change but the arrangements
of the electrons change.
Example. Nitrate: [NO3]-. Three equivalent Lewis structures (resonance structures)
are possible, because one bond pair is delocalized over four atoms. The nitrogen is
positively charged and two negative charges are delocalized between the three
oxygens. Each oxygen has a charge of -2/3.
N
Three oxygens
Nitrogen
O
O
N
O
O
O
N
-2/3
O
N
O
O
O
O
O
O
N
One electron
N O
O
O
O
O
O
O
N
O
O
O
or
N
O
O
-2/3
Nitrate ion: three equivalent Lewis structure are possible
Note. The phenomenon of resonance is symbolized by double arrow between the resonance
structures.
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-2/3
TOPIC 3. Molecular Shape and Chemical Bonding
57
3.2.2. Exceptions to octet rule
Hypervalence. (more than 8 valence electrons)
A hypervalent molecule contains one or more main group elements formally bearing more
than eight electrons in their valence shells.
It can happen when:
o The central atom is a main group element with a valence shell n ≥ 3. *
o Central atom must use more than 4 valence orbitals,
o Peripheral atoms have large (O, F, Cl, …)
Example of hypervalent molecules: Phosphorus pentafluoride (PF 5), sulfur hexafluoride
(SF6), SF4,Chlorine trifluoride (CIF3), Triiodite (I3-), SOCl2, XeOF4, … ClF5, XeF6
(*) Note. The central atom must use more than 4 valence orbitals, so hypervalence is
naturally limited to valence shell, n ≥ 3.
upe
F
[He] 2s2 2p5
[Ne] 3s2 3p3 3d0
P in PF5
F
P
F
p
d
s
p
d
[Ne] 3s2 3p3 3d0
Ground state P
F
s
F
F
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TOPIC 3. Molecular Shape and Chemical Bonding
58
Figure. Hypervalent phosphorus pentafluoride (PF5). The phosphorus undergoes excitation
to promote one electron from 3s orbital to one empty 3d orbital, providing five unpaired
electrons and allowing the formation of PF 5 molecule.
I
5s
5p
5s
5p
5s
5p
5d
[Kr] 4d105s2 5p5
10
2
5d
6
ground state of I -[Kr] 4d 5s 5p
I- in I3-
5d
[Kr] 4d105s2 5p5 5d1
Lewis structure of triiodide
I
I
I
Figure. Hypervalent triiodide (I3-). The central atom is ion iodide; its extra electron is
promoted to the empty 5d orbital – allowing the formation of two single bounds. The central
atom has therefore three lone pairs.
Less than 8 valence electrons. The case of boron trifluoride.
Looking at the atomic orbitals, the central atom of boron trifluoride has only 6 valence
electrons, hence does not follow the octet rule.
2s
B
[He] 2s2 2p1
F
2s
B in BF3
2p
1
2
B
2p
F
F
[He] 2s 2p
Lewis structure of BF3
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TOPIC 3. Molecular Shape and Chemical Bonding
59
However, three resonance structures can be drawn in which one fluoride, already bonded to
the boron by a single bond, provides co-ordinate pi-bond to the central atom’s empty porbital. In these three resonance structures, the octet rule is respected (but fluorine has to
bear a positive charge).
F
F
F
F
B
B
B
F
F
F
F
F
Resonance structures of BF3
Which Lewis structure best describe BF3?
If several Lewis structure are possible; choose the one with the lowest charges
The zwitterion description shows a positive charge on fluorine (not best).
3.2.3. Bridging atoms
Bridging chloride.
If boron is stable with 6 valence electrons as in BF3, aluminium although in the same group
is not so stable in AlCl3.
Al [Ne] 3s2 3p1
Cl
high temperature, gas phase
Al
Cl
Cl
lower temperature, gas phase and liquid phase
Cl
Cl
Cl
Cl
Al
Al
Cl
Cl
Cl
Cl
Cl
Al
Al
Cl
Cl
Cl
At lower temperatures dimers form via Cl bridging using Cl lone pairs and the Al empty porbital, forming a co-ordinate covalent bond (2 centers and 2 electrons).
Note. In the solid phase, the structure is polymeric
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TOPIC 3. Molecular Shape and Chemical Bonding
60
Bridging hydrogen.
Borane, BH3 dimerises to form diborane B 2H6. Here the bridge uses bond pair: the electron
pair from BH bond is shared to make a second BH bond: 3 center 2 electrons bond.
2
1
B [He] 2s 2p
H
H
H
B
2
H
B
H
H
H
H
B
H
B
H
H
H
H
H
H
B
H
H
B
H
H
3.2.4. Bond order, bond length and bond energy
Bond order (bo) is the number of chemical bonds between two atoms.
Example:
The bond order in diatomic nitrogen (N≡N) is 3
The bond order in hydrogen chloride (H-Cl) is 1.
Covalent radius is half the internuclear distance (the bond length) in homonuclear
bond and is bond order specific.
Example:
Molecules
Bond length
Covalent radius
H3C
CH3
154 pm
77 pm
H2C
CH2
134 pm
67 pm
HC
CH
120 pm
60 pm
Bond length (bl) between two atoms is the addition of their covalent radii.
Example:
Molecules
Cl
Bond length
Covalent radius
Cl
198 pm
Clcr = 99 pm
H3C
CH3
154 pm
Ccr = 77 pm
H3C
Cl
178 pm
Clcr + Ccr = 176 pm
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B
H
H
TOPIC 3. Molecular Shape and Chemical Bonding
61
Bond energy (be) is directly correlated with bond order (bo) and inversely correlated
with bond length (bl).
Example:
Molecules
Bond order Bond length
Bond energy (kJ.mol-1)
H3C
CH3
1
154 pm
346
H2C
CH2
2
134 pm
598
HC
CH
3
120 pm
813
Bond energy is always positive: it is the energy required to break up the bond. When
a bond is made, energy is released (exothermic).
C
H
C
N
O
S
F
Cl
Br
I
H
435
416
391
464
366
570
432
366
298
C=C
C≡C
N=N
N≡N
P≡P
598
813
400
945
490
C=N
C≡N
N=O
O=O
S=S
346
285
359
272
485
327
285
213
N
Single Bonds
O
S
159
201
146
272
193
615
866
607
498
425
266
326
255
217
190
218
201
201
Multiple Bonds
C=O
C≡O
S=O (in SO2)
S=O (in SO3)
Si=O
F
Cl
Br
I
159
247
249
278
242
216
208
193
175
151
806
1072
532
469
642
Table of single and double bonds energy (in kJ .mol-1).
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TOPIC 3. Molecular Shape and Chemical Bonding
62
Exercise 1: Calculate the heat of reaction H (ie enthalpie change) for the reaction:
C2H6
C2H2 + 2H2
H
H
C
C
H
H
H
H
H
Bond broken
H
be
total
H
C
C
H
H
H
bond made
energy released
total
1
C
C
813
813
1 C
C
-346
-346
2
H
H
2 X 435
870
4 C
H
4 X -416
-1664
1683 kJ
- 2010 kJ
H = 1683 -2010 = -327 kJ
Exercise 2: Calculate the heat of reaction ( H) for the formation of sulfur bromide (S 2Br2)
from the elements in their standard states and comment on its sign.
4 S2Br2
S8 + 4 Br2
S
S
S
S
S
S
S
Br
4
Br
S
4
Br
Br
S
Bond broken
S
be
total
bond made
8 x Br
4x S
S
4 x 266
1064
4 x Br
Br
4 x 193
772
1836 kJ
H = 1836 -1736 = + 100 kJ
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S
energy released
8 x - 217
total
- 1736
- 1736 kJ
(ie reaction is endothermic)
TOPIC 3. Molecular Shape and Chemical Bonding
63
3.3. Molecular Shape
The molecular shape is determined experimentally:
By electron diffraction in gas phase
By X-ray diffraction in crystalline phase
The molecular shape can be predicted from the Lewis structure of the molecule, using the
VSEPR theory (Valence Shell Electron Pair Repulsion). Valence electron pairs form groups
and are arranged around the central atom and repel each other. Therefore the shape of the
molecule depends primarily on the number of groups.
Example: the molecular shapes of boron trichloride and nitrogen trichloride .
lp
Cl
Cl
N
N
B
B
Cl
Cl
Cl
BCl3: planar shape
Cl
Cl
Cl
Cl
Cl
Cl
Cl
NCl3: non-planar shape
The shape of a molecule is determined by the three-dimensional arrangement of the valence
electrons; whether in bonding pairs, in lone pairs or unpaired.
3.3.1. Geometry and shape
The shape of a molecule is the disposition of all the molecule’s atoms. It is determined by
the arrangement of the bond pairs (bp) around central atoms.
The geometry of a molecule is the three-dimensional arrangement of the molecule’s valence
electrons (bond pairs, lone pairs and unpaired electrons). The molecular geometry
determines many of the substance’s properties such as chemical reactivity, polarity, colour
or magnetism.
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TOPIC 3. Molecular Shape and Chemical Bonding
64
Examples: sulfur hexafluoride (SF6), chlorine pentafluoride (ClF5), xenon tetrafluoride
(XeF4).
ClF 5
SF6
XeF4
F
F
F
F
F
F
F
Cl
S
F
F
F
F
Xe
F
F
F
Shape
F
square pyramidal
octahedral
square planar
F
F
F
F
F
F
F
F
Xe
Cl
S
F
F
F
F
F
F
F
Geometry
octahedral
octahedral
octahedral
3.3.2. VSEPR
The Valence Shell Electron Pair Repulsion (VSEPR) theory is used to predict the shape of
molecules and is based on electron-pair electrostatic repulsion. The model is based on a
central atom A and a number of valence electron group (electron-pairs) which can be
bonding (X) to a substituent or non-bonding (lone pair) (E). All valence electrons groups
repel each other and dictate the shape of the molecule.
The basic geometry.
For simple molecules, made of a central atom A and where all electron-pairs X are bonding
to substituent(s) we describe five basic geometries depending on the number of valence
electron group X (from 2 to 6X).
Example:
2X
3X
X
X
o
A
108
4X
A
X
X
X
linear
X
o
120
trigonal planar
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o
109
A
X
6X
5X
X
X
tetrahedral
X
X
A
X
o
X
90
X
X
120o
X
X
trigonal bipyramidal
A
X
90o
X
X
octahedral
TOPIC 3. Molecular Shape and Chemical Bonding
65
Predicting molecular shape with VSEPR theory.
Determine the basic geometry from the Lewis structure.
Lone pairs have greater electrostatic repulsion than bonding pairs, therefore they
require more space than bonding pairs. When they are present; refine the geometry
and determine the molecular shape.
Examples: with one lone pair AXnE.
1 lp
1 lp
1 lp
AX2E
AX3E
AX4E
X
<120o
A
A
X
X
X
X
o
<109
1 lp
AX5E
<90o X
X
<120o A
X
X
bent or angular trigonal pyramid
X
X
A
X
X
X <90o
see-saw
square pyramidal
Example: with two lone pairs AXnE2.
2 lp
2 lp
AX2E2
AX3E2
X
A
<<109o X
bent or angular
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o
<90 X
X
A
2 lp
AX4E2
X
A
X
X
o
90
X
X
T-shape
square planar
TOPIC 3. Molecular Shape and Chemical Bonding
66
Example: with three lone pairs AXnE3.
3 lp
3 lp
AX2E3
AX3E3
X
180o
X
A
A
X
o
<90
X
X
linear
T-shape
The VSEPR theory in four simple rules:
rule 1. The distances between valence electron groups X are maximized
rule 2. Lone pairs (lp) require more space than bonding pairs (bp).
rule 3. Multiple bonds require more space than single bonds
rule 4. The space required by bp decreases with increasing of peripheral atom.
The rules 1 and 2 give the basic shape of the molecule and rules 3 and 4 refine the shape.
Rule 1: The distances between valence electron groups X are maximized
- Two groups (AX2): linear geometry.
Note: a multiple bond counts as one group.
o
180
F
Be
F
2 bp, 2 single bonds
AX 2
F
Be
F
Linear shape
o
180
O
C
O
4 bp, 2 double bonds
AX2
O
C
O
Linear shape
o
180
H C
N
4 bp, 1 triple bond
and 1 single bond
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AX2
H
C
N
Linear shape
TOPIC 3. Molecular Shape and Chemical Bonding
67
- Three groups (AX3): trigonal geometry.
Note: a lone pair E counts as one group.
F
F
F
o
120
F
B
3 bp, 3 single bonds
B
AX3
trigonal planar
geometry
(trigonal planar shape)
F
F
O
O
S
5 bp, 2 double bonds
and 1 lone pair
AX 2E
S
trigonal planar
geometry
(angular shape)
O
O
- Four groups (AX4): tetrahedral geometry.
H
H
H
H
C
4 bp, 4 single bonds
H
C
H
H
H
H
N
4 bp, 3 single bonds
o
109.5
AX 4
AX 3E
H
H
tetrahedral geometry
N
H
H
tetrahedral
H
(trigonal pyramidal shape)
H
O
4 bp, 2 single bonds
AX 2E2
H
tetrahedral geometry
O
H
H
(bent or angular shape)
-Five groups (AX5): trigonal bipyramidal (tbp) geometry.
F
F
F
F
P
5 bp, 5 single bonds
AX 5
o
90
P
F
trigonal bipyramidal
F
F
F
F
F
F
F
F
S
F
5 bp, 4 single bonds
and 1 lone pair
F
AX 4E
F
S
F
F
(see-saw shape)
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trigonal bipyramidal
TOPIC 3. Molecular Shape and Chemical Bonding
68
-Six groups (AX6): octahedral geometry.
F
F
F
F
F
F
F
F
F
F
F
P
F
octahedral geometry
F
F
F
I
F
AX 6
6 bp, 6 single bonds
P
F
AX 5E
6 bp, 5 single bonds
and 1 lone pair
F
F
I
F
octahedral geometry
F
F
(square pyramidal shape)
O
F
Xe
F
F
F
AX 5E
7 bp, 4 single bonds,
1 double bond, and
1 lone pair
F
F
Xe
F
octahedral geometry
F
O
(square pyramidal shape)
Rule 2: Lone pairs (E) require more space than bonding pairs (X).
The electrostatic repulsion caused by lone pairs is greater than the repulsion caused by
bonding pairs.
This has an effect on the molecule’s angles (the lone pair(s) push the bonding pairs away).
H
H
C
H
H
H
o
109.5
O
N
H
H
H
H
o
o
105
107
And has an effect on molecular shape (lone pairs have more space in equatorial position
than in axial):
F
F
F
S
S
F
F
F
F
(see-saw shape)
prefered isomer: lp equatorial
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X
F
(trigonal pyramidal shape)
lp axial is not favourable
TOPIC 3. Molecular Shape and Chemical Bonding
F
equatorial to
equatorial angle
F
o
102
F
S
69
F
F
Cl
Xe
F
F
F
F
o
173
axial to axial angle
lone pairs in equatorial position
Rule 3: Multiple bonds require more space than single bonds.
A double bond is made of four valence electrons, a triple bond of six; they have a greater
electrostatic repulsion than a bond pair.
H
H
F
O
C
B
C
C
F
F
H
o
120
H
H
o
H
o
116
117
Rule 4: The space required by bp decreases with increasing of peripheral atom.
The bonding pairs are attracted by the more electronegative atom. The more electronegative
the peripheral atom the greater the attraction toward the periphery and less space is
required by the bonding pair around the central atom.
O
O
+
H
H
electronic density is between C and H
-
F
F
-
electronic density attracted by F
more space available around the central atom
O
O
H
H
o
116
F
F
108
o
The rules 1 and 2 give the basic shape of the molecule and rules 3 and 4 refine the shape.
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TOPIC 3. Molecular Shape and Chemical Bonding
70
When the peripheral atoms are different the refined shapes is inevitably a distorted basic
shapes.
Example of sulfur hexafluoride (SF6) and sulfur monochloride pentafluoride (SClF 5).
Chloride is less electronegative than fluoride, therefore requires more space .
o
90
F
F
o
F
90
S
F
F
Cl >90o
F
F
S
F
each angle is 90o
F
F
F
Cl is less than F
Cl requires more space than F
no distorsion
o
each angle is 90
octahedral
distorsion
octahedral
distorted octahedral
3.3.3. Further examples of Lewis structure / VSEPR
Chlorine dioxide (ClO2+)
First; write the Lewis structure.
6 e per O plus 7 e on Cl
O
each O needs 8 valence electrons
remove one electron to make positive charge
Lewis structure
O
Cl
Cl
O
O
Cl
O
O
Then apply the VSEPR rules; count the number of groups and apply rules 1 to 4 to
determine and refine the molecular shape.
3 groups of valence electron-pairs gives a basic trigonal planar geometry. 2 groups
are double bond Cl=O and 1 is a lone pair. AX2E
Cl
O
O
bent shape
trigonal planar geometry
The molecule has a bent or angular shape and a trigonal planar geometry.
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TOPIC 3. Molecular Shape and Chemical Bonding
71
Azide ion (N3-)
First; write the Lewis structure.
one lone pair from central N is used to make a co-ordinate covalent bond
lp
5 e per N
N
N
N
each N needs 8 valence electrons
N
N
N
add one electron to make negative charge
Lewis structure
N
N
N
Then apply the VSEPR rules; count the number of groups and apply rules 1 to 4 to
determine and refine the molecular shape.
2 groups of valence electron-pairs, Linear geometry. AX2.
N
N
N
The molecule has a linear shape and a linear geometry.
Note: the charges on the nitrogens; the central atom forms a co-ordinate covalent bond with
one peripheral nitrogen atom and therefore gets a positive charge (for the same reason the
peripheral nitrogen gets a negative charge). The electron is added to the second peripheral
nitrogen which comes with a negative charge .
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TOPIC 3. Molecular Shape and Chemical Bonding
72
Nitric acid (HNO3)
First; write the Lewis structure.
H
5 valence electrons on N, 1 on H and 6 per O
lone pair of N forms a co-ordinate bond with one O
H
H
Lewis structures:
O
O
N
O
O
N
O
O
N
O
O
O
Then apply the VSEPR rules; count the number of groups and apply rules 1 to 4 to
determine and refine the molecular shape.
3 groups of valence electron-pairs, Trigonal planar geometry. AX3.
1 group is a single bonding pair (N-O) and 2 groups are partial double bond (the
structure is delocalized). These two groups require more space than the first one:
therefore the molecule has a distorted trigonal planar shape.
O
HO
-1/2
N
O -1/2
3.3.4. Inert pair effects
The inert pair effect is a tendency of the s valence electrons to remain as a lone pair in
compounds of post-transition metals.
Selenium hexachloride (SeCl6 2-)
s
p
d
s
p
d
s
p
d
Se [Ar] 4s2 4p4
Ground state Se2- [Ar] 4s2 4p6
2-
2
3
3
Excited state Se [Ar] 4s 4p 4d
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TOPIC 3. Molecular Shape and Chemical Bonding
73
We expect the 8 valence electrons to form seven valence electron groups: six bonding pairs
with Cl and one lone pair; a AX6E geometry (pentagonal bipyramidal geometry).
pentagonal bipyramidal
We do not obverse a AX6E geometry but a AX6 octahedral geometry.
2
Cl
Cl
Cl
Se
Cl
Cl
Cl
octahedral geometry
The valence electrons of the 4s-orbital are inert, they do not affect the shape of the
molecule: they are stereochemically inactive.
For post-transition elements, such as Se, the valence s-electrons are relatively deeply buried
and are not really valence. So if s-electrons are not part of the valence, only 12 valence
electrons are involved in forming six groups and we observe a AX6 octahedral geometry.
Note. This is related to the tendency of post-transition elements to form two oxidation states:
a normal oxidation state (using all valence s- and p-electrons and a lower oxidation state
(leaving the s-electrons).
This phenomenon is known as the thermodynamic inert pair effect.
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TOPIC 3. Molecular Shape and Chemical Bonding
74
Example:
Sn (IV)
Tin Sn
10
[Kr] 4d
2
[Kr] 4d10
2
5s 5p
Lead Pb
[Xe] 4f
14
10
5d
10
2
2
6s 6p
14
2
10
14
10
5d
[Xe] 4f
2
[Kr] 4d
Tl (III)
1
[Xe] 4f
14
14
10
5d
10
[Kr] 4d
6s 6p
2
6s
2
In (I)
10
1
5s 5p
5d
[Xe] 4f
5s
Pb (II)
In (III)
Thallium Tl
[Xe] 4f
10
[Kr] 4d
Pb (IV)
Indium In
[Kr] 4d
Sn (II)
5s
2
Tl (I)
10
[Xe] 4f14 5d10 6s2
5d
3.3.5. Shape and Molecular Dipoles
The shape of molecule has an effect on the molecular magnetism. When two bonded atoms
have different electronegativity the bond is polarized. In molecules where there is more
than one polarized bond; the dipoles resulting from polar bonds can either cancel each other
(and the molecule is not polar) or contribute to create a molecular dipole and the molecule is
polar, depending on the shape of the molecule.
Bond dipole moment (expressed in Debye) is used to measure the polarity of a chemical
bond, where d is the bond length and the value of the partial charge .
=
d
It is a vector, parallel to the bond axis.
It is pointing from negative to positive charge.
In polyatomic molecules the total molecular dipole moment is the vector sum of
individual bond dipole moment and is depending on the molecular shape.
The measure of the molecular dipole gives information on molecular shape.
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TOPIC 3. Molecular Shape and Chemical Bonding
75
Example: The molecular dipole moment of water H2O is 1.85 Debye, of carbon dioxide is 0
Debye.
O
H
+
net dipole = 1.85 D
+
C
- O
molecule is bent
H
+
O -
net dipole = 0 D
molecule is linear
Example 2 : Two isomers of 1,2-Dichloroethylene are isolated, one (a) is polar with a
molecular dipole moment of 1.90 D and the second (b) is non-polar with a molecular dipole
moment of 0 D. Determine which is the cis and trans-isomers from the value of the
molecular dipole moment.
Cl
Cl
+
C
+
C
H
(a) is cis-isomer
net dipole = 0 D
(b) is trans-isomer
H
Cl
H
+
C
H
net dipole = 1.90 D
+
C
Cl
-
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TOPIC 3. Molecular Shape and Chemical Bonding
76
3.4. Valence Bond (VB) Theory
The valence bond (VB) theory is a complement to the molecular orbital (MO) theory and was
developed to explain chemical bonding.
It focuses on localized bonding (when MO theory describes orbitals covering the
whole molecule).
Is not suited to describing delocalization.
Is a good qualitative model
3.4.1. Basis
According to the theory, a covalent bond is formed between two atoms by the overlap of two
atomic orbitals of the same phase. Each atomic orbital containing one unpaired electron.
Example. Two s-orbitals of the same phase form the single bond in H 2.
AO
AO
H (1s)
H (1s)
orbital overlap
H2 (Sigma s)
Example. One s-orbital from H and one p-orbital from Cl form HCl single bond.
AO
AO
orbital overlap
H (1s)
Cl (3p)
HCl (Sigma sp)
Note. The electrons have opposite spin in the overlapped orbital.
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TOPIC 3. Molecular Shape and Chemical Bonding
77
3.4.2. Hybrid Orbitals
Atomic hybrid orbitals are the result of mixing atomic orbitals (s, p, d, etc) from the same
atom and have their own shape and energy. Hybrid orbitals are very useful in explaining
molecular geometry and bonding properties.
Example. Methane CH4 is a tetrahedral molecule in which each bond is similar and identical
in energy.
Looking at the atomic orbital of carbon:
Ground state of C [He] 2s
2
2
2p
Energy
2p
2p
2s
2s
In order to create four bonding pairs, one electron from the 2s-orbital is promoted to an
empty 2p orbital. The result is an excited state where all four valence electrons (upe) from C
are available for bonding with the upe of the four hydrogen atom .
1
3
Energy
Excited state of C [He] 2s 2p
2p
2p
2s
2s
In the excited state, four upe are available for bonding, but are from two different energy
levels. To reflect the fact that all bonds formed are of identical energy one s-orbital is mixed
with all three p-orbitals resulting in four hybrid sp 3 orbitals (of identical energy level).
sp3 hybridisation
Energy
3
sp
sp3
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TOPIC 3. Molecular Shape and Chemical Bonding
78
The shape of the hybrid sp3 atomic orbitals
One s-AO is mixed with three p-AO
Each of the four hybrid sp 3 orbitals retains 25% of the s-AO character and 75 % of
the p-AO.
The energy level of the new hybrid orbitals is intermediate, between the s and p AO’s
energy levels.
25%
75%
s
p
sp3
Bonding hybrid orbital:
Four covalent bonds are formed between the four sp 3 hybrid orbitals of carbon and by the
overlap of four s-atomic orbitals of the four hydrogen atoms making four sigma ( ) bonds.
CH4
C+4H
3
The hybridization reflects the geometry; sp hybridisation of the central carbon is consistent
with the observed tetrahedral geometry on CH 4.
For other geometries, other hybridisation schemes are used .
Example:
H
sp
H
C
C
C
H
H
H
H
trigonal
3
dsp
P
F
F
trigonal bipyramidal
sp
H
F
F
F
d2sp3
S
F
F
C
tetrahedral
F
F
3
2
C sp
H
linear
H
H
F
F
octahedral
Valence bond theory allows a simple view of chemical bonding once the geometry is known.
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TOPIC 3. Molecular Shape and Chemical Bonding
79
3.4.3. VB construction
To construct the valence bonds, first the Lewis structure and then the geometry (using
VSEPR) must be determined.
Example. BF3
2
1
sp2 hybridised B
B [He] 2s 2p
F
2p
F
2p
F
2
sp
2s
two p-orbitals are mixed with s-orbitals, making three sp2 hybrids
one p-orbital is not hybridised and is perpendicular to the molecular plane
Example. H2O
AO
O [He] 2s2 2p4
sp3 hybridised O
lp
2p
3
sp
lp
H
H
2s
three p-orbitals are mixed with s-orbital, making four sp3 hybrids.
two sp3 orbitals overlap a H (1s) orbital and two are lone pairs.
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TOPIC 3. Molecular Shape and Chemical Bonding
80
Example. SF6
F
AO
2
4
2
S [Ne] 3s 3p
3
F
F
F
F
d sp hybridised S
3d
F
3d
3p
d2sp3
3s
six d2sp3 orbitals result from mixing two d threep and one s AO.
Example : C2H4. Representation of multiple-bonds with VB theory
Three sp2 orbitals result from mixing one s and two p-orbitals. These three new orbitals
overlap with two hydrogen (1s) orbital and one (sp 2) orbital from the second carbon; forming
three single bonds (sigma bonds).
2
2
2
ground state of C [He] 2s 2p
hybridisation sp
p
p
C
C
Energy
H
H
p
2p
H
H
2
sp
2s
The sp2 hybridisation leaves one p-orbital unchanged on each carbon. Each p-orbitals are
perpendicular to the molecular plan and parallels to each other: they overlap and form a
bond.
2
hybridisation sp + p
bond
H
C
C
H
H
H
p
sp2
A double bond is made of one sigma ( ) bond and one pi (
Note. The
bond.
bond has two opposite phases, one above and one bellow the molecular plan.
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81
3.5. Molecular Orbital (MO) Theory- a brief introduction
The molecular orbital theory is a method for determining molecular structures in which
electrons are not assigned to individual bonds between atoms, but are delocalised on the
whole molecule.
Atomic orbitals have phase (+ or -).
Bonding molecular orbitals (BMO) are formed when two AO of the same phase
combine, they are more stable than the two AO.
Antibonding molecular orbitals (ABMO) are formed when two AO of opposite phase
combine, they are less stable than the two AO.
In AMO, the electronic density between the two atoms is zero.
Molecule of H 2, constructed from two H, called H
A
and HB
Energy
ABMO
A
-
B
B
A
BMO
A
+
B
The bond order of a pi orbital is:
Bo = (number of electron pairs in BMO) – (number of ep in ABMO) = 1
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