Chapter 3.
MOLECULAR SHAPE AND STRUCTURE
THE VSEPR MODEL
3.1 The Basic VSEPR Model
3.2 Molecules with Lone Pairs on the Central Atom
3.3 Polar Molecules
VALENCE-BOND THEORY
3.4 Sigma and Pi Bonds
3.5 Electron Promotion and the Hybridization of Orbitals
3.6 Other Common Types of Hybridization
3.7 Characteristics of Multiple Bonds
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THE VSEPR MODEL (Sections 3.1-3.3)
3.1 The Basic VSEPR Model
– Lewis structure: showing the linkages between atoms and
the presence of lone pairs, but not the 3D arrangement of
atoms
 Valence-shell electron-pair repulsion model (VSEPR model, first
devized by Sidgwick and Powell, later modified by Gillespie and
Nyholm) is based on Lewis structures. Molecular shapes are predicted
by use of several rules that account for bond angles.
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Ideal Molecular Geometries According to VSEPR
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 Generic “VSEPR formula”, AXnEm
- A = central atom; Xn = n atoms bonded to central atom
Em = m lone pairs on central atom
E.g. BF3 (AX3), SO2 (AX2E), SO32- (AX3E), CH4 (AX4), PCl5 (AX5)
 Rule 1. Regions of high electron concentration
(bonds and lone pairs on the central atom) repel
one another and, to minimize their repulsions,
these regions move as far apart as possible while
maintaining the same distance from the central
atom.
This gives rise to the basic geometries, which are related
to the total number (Xn + En) of electron pairs around the
central atom (next slide).
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 Rule 2. There is no distinction between single and
multiple bonds: a multiple bond is treated as a single
region of high electron concentration.
E.g.
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Self-Test 3.1B
Predict the shape of a formaldehyde molecule, CH2O.
Solution
Although written, CH2O, carbon is the central atom in
a H2CO skeleton, hence Lewis structure is
O
H
C
H
C is bonded to 3 atoms, so the molecule is trigonal planar.
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3.2 Molecules with Lone Pairs on the
Central Atom
 Rule 3. All regions of high electron density, lone pairs and bonds,
are included in a description of the electronic arrangement, but
only the positions of atoms are considered when identifying the
shape of a molecule.
E.g.
Trigonal pyramidal
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Angular (bent or
V-shape)
8
-
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 Rule 4 The strength of repulsions are in the order
lone pair-lone pair > lone pair-atom > atom-atom.
trigonal
pyramidal
- AX3E type
more stable
- AX4E type
seesaw shaped
axial
equatorial
- AX3E2 type
- AX4E2 type
T-shaped
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square planar
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Self-Test 3.3B
(a) Give the VSEPR formula of the ClO2- ion. Predict (a)
its electron arrangement and (c) its shape.
Solution
The Lewis structure is
_
O
..
Cl
..
O , showing two
2 atoms and 2 lone pairs on the central Cl atom.
(a) Hence its VSEPR formula is AX2E2.
(b) The electron arrangement is tetrahedral.
(c) Its actual shape is angular (bent or V-shape).
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 Predicting the molecular shape of SF4
Step 1 Draw the Lewis structure.
Step 2 Assign the electron arrangement around
the central atom.
Step 3 Identify the molecular shape. AX4E.
Step 4 Allow for distortions.
(Bent) seesaw shape
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3.3 Polar Molecules
 Polar molecule: a molecule with a nonzero dipole moment.
A diatomic molecule is polar if its bond is polar (if the electronegativity
difference between the two atoms > 0.3) - see Chapter 2.12.
E.g. HCl is a polar molecule (dipole moment of 1.1 D).
H2 is a nonpolar molecule (zero dipole moment).
- A polyatomic molecule is polar if it has polar bonds arranged in
space in such a way that the dipole moments associated with
the bonds do not cancel.
See Table 3.1 for dipole moments of selected molecules.
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polar
nonpolar
polar
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nonpolar
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Molecular geometries giving non-polar or polar molecules:
AX2 – AX3E2 (Fig. 3.7)
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Molecular geometries giving non-polar or polar molecules:
AX4 – AX6 (Fig. 3.7)
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VALENCE-BOND (VB)THEORY
(Sections 3.4-3.7)
-The VB theory is based on the Lewis model: each
bonding electron pair is localized between two
bonded atoms.
It is a localized electron model, devized originally by
Heitler and London, and later modified by Pauling,
Slater and others.
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3.4 Sigma (s) and Pi (p) Bonds
 The s-bond is formed by ‘head-on’
overlap: there is no nodal surface
containing the interatomic (bond) axis.
- It is cylindrical or “sausage” shaped.
E.g. H2, s(1s, 1s)
HF, s(1s, 2pz)
N2, s(2pz, 2pz)
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See next slide
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 The p-bond is formed by ‘sideways’ overlap: there
is a nodal plane containing the interatomic (bond) axis.
-It is composed of two cylindrical shapes (lobes), one above
and the other below the nodal plane.
N2
one s-bond
with two
perpendicular
p-bonds
- In General, single bond (one s-bond),
double bond (one s- and one p-bond)
triple bond (one s- and two p-bonds)
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Self-Test 3.6A
How many s-bonds and how many p-bonds are there
in (a) CO2 and (b) CO?
p
Solution
Hs
O s C
(a) CO 2 is
and two p-bonds.
p
(b) CO is
C sO
p
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p
O
,with two s-bonds
with one s-bond and two p-bonds.
3.5 Electron Promotion and the Hybridization
of Orbitals
all C-H
bonds
equivalent
?
 Electron promotion: electron relocated to a higher-energy orbital
promotion
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hybridization
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 Hybrid orbitals: produced by hybridizing orbitals of a central atom
C [He]2s12px12py12pz1
4 sp3 hybrids
h1 = s + px + py + pz h2 = s - px - py + pz
h3 = s - px + py - pz h4 = s + px - py - pz
each
C-H
bond
sp3 hybrid orbital
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Examples of sp3 hybrid orbitals in bonding
- Ethane, C2H6
Each C atom uses sp3 hybrid orbitals.
The C-C bond is formed as s(C2sp3, C2sp3).
Each C-H bond is formed as s(C2sp3, H1s).
- Ammonia, NH3
Four sp3 hybrid orbitals; one occupied by a lone pair, and
the other three forming N-H s-bonds
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3.6 Other Common Types of Hybridization
 sp2 hybrid orbitals
in BF3
 sp hybrid orbitals in
CO2
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- sp3d
hybrid
orbitals
in PCl5
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- sp3d2
hybrid
orbitals
in SF6 and
XeF4
28
29
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Self-Test 3.8A
Describe (a) the electron arrangement, (b) the molecular
shape, and (c) the hybridization of the central atom in
chlorine trifluoride.
Solution
(a) The Lewis structure of ClF3 is
.. ..
F
Cl
F
F
The VSEPR formula of ClF3 is AX3E2, hence the electron
arrangement is trigonal bipyramidal.
(b) The molecular geometry is T-shaped.
(c) The hybridization on Cl is sp3d.
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3.7 Characteristics of Multiple Bonds
- Ethene, CH2=CH2
C-C s bond, s(C2sp2, C2sp2)
C-C p bond, p(C2p, C2p)
each C-H bond formed as s(C2sp2, H1s)
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- Benzene, C6H6
C-C s bond, s(C2sp2, C2sp2)
C-C p bond, p(C2p, C2p)
Each C-H bond formed as s(C2sp2, H1s)
- Ethyne (acetylene), C2H2
C-C s bond, s(C2sp, C2sp)
Two C-C p bond, p(C2px, C2px), p(C2py, C2py)
Each C-H bond formed as s(C2sp, H1s)
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Self-Test 3.9A
Describe the structure of the carbon suboxide molecule,
C3O2, in terms of hybrid orbitals, bond angles, and s- and
p -bonds. The atoms lie in the order OCCCO.
Solution
..
The Lewis structure is : O
C
C
C
..
O:
The VSEPR model predicts all three central C atoms to
be of the type AX2, and hence bonding to all three is linear.
All three C atoms are sp hybridized and oxygen is sp2 hybridized.
All bond angles are 180o.
Each carbon forms one s- and one p-bond, to each C or O
neighbor.
p
p
O s C s C s C s O
p
p
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Chapter 3.
MOLECULAR SHAPE AND
STRUCTURE
MOLECULAR ORBITAL THEORY
3.8 The Limitations of Lewis’s Theory
3.9 Molecular Orbitals
3.10 Electron Configurations of Diatomic Molecules
3.11 Bonding in Heteronuclear Diatomic Molecules
3.12 Orbitals in Polyatomic Molecules
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MOLECULAR ORBITAL THEORY
(Sections 3.8-3.12)
3.8 The Limitations of Lewis’s Theory
 Valence Bond (VB) theory deficiencies
- Cannot explain paramagnetism of O2 (existence of unpaired electrons)
- Difficulty treating electron-deficient compounds such as B2H6
- No simple explanation for spectroscopic properties of compounds
 Molecular Orbital (MO) theory advantages
- Addresses all of the above shortcomings of VB theory
- Provides a deeper understanding of electron-pair bonds
- Accounts for the structure and properties of metals and semiconductors
- Universally used in calculations of molecular structures
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3.9 Molecular Orbitals
 Molecular orbitals (MOs) contain the valence electrons in
molecules: they are delocalized over the whole molecule.
- In VB theory, bonding electrons are localized on atoms or
between pairs of atoms.
- n molecular orbitals must be constructed from n atomic orbitals:
 MOs are formed by linear combination of atomic orbitals
(LCAO-MO):
- Bonding orbital (constructive interference)
y = yA1s + yB1s
→ overall lowering of energy
- Antibonding orbital (destructive interference)
y = yA1s - yB1s
→ overall raising of energy
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Molecular orbital energy-level diagram
MO energy-level diagrams are an integral part of MO theory: they
give the following information.
1. Relative energies of original AOs and resulting MOs
2. Orbital location of electrons and electron spin (using arrows)
H2
- In H2, two 1s-orbitals
merge to form
the bonding orbital s1s
and the antibonding
orbital s1s*
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3.10 Electron Configurations of Diatomic
Molecules
Constructing MOs (by combining AOs) must follow a number of
rules,the first three of which are similar to those of the ‘Building-up
Principle’ for constructing atomic electron configuration:
1. Electrons are accommodated in the lowest-energy MO, then in
orbitals of increasingly higher energy.
2. According to the Pauli exclusion principle, each MO can
accommodate up to two electrons. If two electrons are present
in one orbital, they must be paired.
3. If more than one MO of the same energy is available, the
electrons enter them singly and adopt parallel spins (Hund’s rule).
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4. Only atomic orbitals of the same symmetry along the
bond axis can be combined.
+
+
s
(sideways)
+
p
p (head-on)
Not allowed:
+
p (head-on)
or
p
p
+
5. Atomic orbitals of the same or similar energy interact
more strongly than those with very different energies. Low
energy AOs contribute more to bonding MOs; high energy
AOs contribute more to antibonding MOs.
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Homonuclear diatomic molecules of Period 2
elements (Li2 – F2)
General Features
-Two 2s atomic orbitals (one on each atom) overlap to form
two s orbitals: one bonding (s2s-orbital) and the other antibonding
(s2s*-orbital).
- Six 2p atomic orbitals (three on each atom) overlap to
form six MOs: two 2pz orbitals to form s bonding and
antibonding (s2p, s2p*) MOs, and four 2px, 2py orbitals to
form two p2p and two p2p*MOs.
See next slide.
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For O2 and F2
Four 2px, 2py AOs
form two p2p and
two p2p* MOs
Two 2pz AOs form
bonding s2p and
antibonding s2p* MOs
Two 2s AOs form one
bonding (s2s) MO
and one antibonding
(s2s*) MO
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- For O2 and F2, the energy levels of 2s and 2p are well-separated.
from Shriver
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- From Li2 to N2, the energy levels of 2s and 2p are close, and thus
the 2s orbital also participates in forming s2p orbitals.
from Shriver
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MO theory account of bonding in N2
- In N2, each atom supplies five valence electrons.
A total of ten electrons fill the MOs.
LUMO
The ground configuration is,
b = ½(8-2) = 3
HOMO
 Bond order (b): net number of bonds
Bond order, b =
1
_
(Ne Ne*)
2
Ne = number of electrons in bonding MOs
Ne* = number of electrons in antibonding MOs
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MO theory account of bonding in O2
- In O2, each atom supplies six valence electrons.
A total of twelve electrons fill the MOs.
The ground configuration is,
LUMO
b = ½(8-4) = 2
accounts for paramagnetism of O2
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HOMO
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Self-Test 3.10A
s2p*
Deduce the electron configuration and bond order of
the ion C22-.
p 2p*
Solution
s2p
The ion C22- has the configuration of C2, but with two
extra electrons, which enter the s2p bonding MO.
p 2p
Configuration is s2s2s2s*2p2p 4s2p2
Bond order is 1/2(8
_
2) = 3
E
s2s*
s2s
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3.11 Bonding in Heteronuclear Diatomic
Molecules
 A diatomic molecule built from atoms of two different elements
is polar, with the electrons shared unequally by the two atoms.
- In a nonpolar covalent bond, cA2 = cB2
- In an ionic bond, the coefficient belonging to one ion is zero.
- In a polar covalent bond, the AO belonging to
the more electronegative atom has the lower
energy, and so it makes the larger
contribution to the lowest energy (bonding)
MO.
- Conversely, the contribution to the highestenergy (most antibonding) orbital is greater
for the higher-energy AO, which belongs to
the less electronegative atom.
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- For HF,
electronegativity of F (4.0), H (2.2)
- For EO (E = C or N),
mainly H1s-orbital
→ partial (+) charge
on H
mainly F2pz-orbital
→ partial (–) charge
on F
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Self-Test 3.11B
s2p*
Write the configuration of the ground state of the cyanide
ion, CN-, assuming that its molecular orbital energy diagram
is the same as that for CO.
p2p*
Solution
s2p
There are 4 + 5 + 1 = 10 electrons to accommodate into the
MOs of Fig. 3.35.
Hence the configuration is 1s22s* 21p43s2 (s2s2s2s*2p2p4s2p 2)
p2p
E
s2s*
s2s
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3.12 Orbitals in Polyatomic Molecules
- The MOs spread over all atoms in the molecule.
Experimentally studied by using ultraviolet and visible spectroscopy.
Water, H2O
- A water molecule with six atomic orbitals
(one O2s, three O2p, and two H1s)
antibonding orbitals
O2px
nonbonding orbitals
H1s-O2py-H1s
bonding orbitals
H1s-(O2s,2pz)-H1s
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 Benzene, C6H6
- All thirty C2s-, C2p-, and H1s-orbitals contribute to MOs.
- The orbitals in the ring plane:
C2s-, C2px, C2py, and six H1s-orbitals
→ delocalized s-orbitals for C-C and C-H
- six C2pz-orbitals perpendicular to the ring
→ delocalized p-orbitals spreading the ring
From VB, each C atom with sp2 hybrid
orbitals forming s-bonds and 120° angles.
From MO, the six C2pz-orbitals form six
delocalized p-orbitals.
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Great stability: the p-electrons occupy
only orbitals with a net bonding effect.
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 Hypervalent compounds (a central atom
forms more bonds than allowed by the octet rule)
- From VB, SF6 has S with sp3d2 hybridization
- From MO, four orbitals of S and six of F,
a total of 10 AOs → 10 MOs
12 electrons occupy bonding and nonbonding
Orbitals.
- Average bond order of each S-F is 2/3.
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 Colors of vegetation
- highest occupied molecular orbital (HOMO)
- lowest unoccupied molecular orbital (LUMO)
→ excited an electron from a HOMO to a LUMO,
by the photons with the energy of visible light
Beta-carotene and lycopene contain many conjugated C=C bonds.
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ULTRAVIOLET AND VISIBLE SPECTROSCOPY
 The Technique
- The electrons in the molecule can be excited to a higher energy state,
by electromagnetic radiation.
Bohr frequency condition, DE = hn
- UV-vis absorption gives us information about the electronic energy
levels of molecules.
i.e. Chlorophyll absorbs red and blue
light, leaving the green light present
in white light to be reflected.
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 Chromophores are characteristic groups of atoms in molecules
that absorb certain wavelengths of uv or visible light
– p-p* transition in nonconjugated double bonds ~ 160 nm, but for
molecules with many conjugated double bonds it is the visible region.
– n-p* transition in the carbonyl group ~ 280 nm
LUMO
HOMO
- d-to-d transition in d-metal complexes in visible ranges
- charge transfer transition in d-metal complexes electrons migrate
from the ligands to the metal atom or vice versa.
E.g. deep purple color of MnO42012 General Chemistry I
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