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Chapter 24
Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
Thomas Engel, Philip Reid
Objectives
• Discussion of both localized and delocalized bonding
models.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Outline
1. Lewis Structures and the VSEPR Model
2. Describing Localized Bonds Using Hybridization
for Methane, Ethene, and Ethyne
3. Constructing Hybrid Orbitals for Nonequivalent
Ligands
4. Using Hybridization to Describe Chemical
Bonding
5. Predicting Molecular Structure Using Molecular
Orbital Theory
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Outline
6. How Different Are Localized and Delocalized
Bonding Models?
7. Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel
Model
8. From Molecules to Solids
9. Making Semiconductors Conductive at Room
Temperature
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.1 Lewis Structures and the VSEPR Model
•
•
•
Lewis structure is a description of molecule in
terms of localized bonds and lone pairs.
Lewis structures are useful in understanding the
stoichiometry of a molecule and nonbonding
electron pairs (lone pairs).
It is less useful in predicting the geometrical
structure of molecules.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.1 Lewis Structures and the VSEPR Model
•
Valence shell electron pair repulsion
(VSEPR) model provides a qualitative
theoretical understanding of molecular
structures using Lewis concepts of localized
bonds and lone pairs.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 24.1
Using the VSEPR model, predict the shape of
NO3- and OCl2
Solution:
Lewis structure shows one of the three resonance
structures of the nitrate ion:
The Lewis structure for OCl2 is
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.2 Describing Localized Bonds Using Hybridization for
Methane, Ethene, and Ethyne
•
•
•
In VB model, AOs on the same atom are
combined to generate a set of directed orbitals
in a process called hybridization.
The combined orbitals are referred to as
hybrid orbitals.
Molecules in carbon in is characterized by the
sp3, sp2, and sp hybridizations, respectively
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.2 Describing Localized Bonds Using Hybridization for
Methane, Ethene, and Ethyne
•
The appropriate linear combination of carbon
AOs is
•
It can be simplified to
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 24.2
Determine the three unknown coefficients in the
following equation by normalizing and orthogonalizing
the hybrid orbitals.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
We first normalize  a . Terms such  2*p 2 p d and  2*s2 p d
as do not appear in the following equations because
all of the AOs are orthogonal to one another.
Evaluation of the integrals is simplified because the
individual AOs are normalized.
y
2
z
 1 
*




d


c


d






1 
2 pz
2 s2 s d  1
 a

3

1
2
 c1    1
3
where c1  2 3
*
a
2
*
2 pz
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
y
Solution
Orthogonalizing  a and  b , we obtain
2
*

 a b d  c4
2 *
 1 
*


d






2 pz 2 pz
2 p z 2 p z d  0


3
3

 c4
c4  
2 1
  0 and
3 3
1
6
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
Normalizing  b , we obtain
2

1
 1 
*
*
*
*






d





d





d



c



6  2 p x 2 p x
 a b  6   2 pz 2 pz  3   2 pz 2 pz


1 1
2
 c6     1 and
3 6
1
c6  
2
2
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
We have chosen the positive root so that the
coefficient of 2 p in  b is negative. Using these
results, the normalized and orthogonal set of
hybrid orbitals is
x
2
1
 a  2 p z  2 s
3
3
1
1
1
 b   2 p z  2 s  2 p x
6
2
3
1
1
1
 c   2 p z  2 s   2 p x
6
2
3
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.2 Describing Localized Bonds Using Hybridization for
Methane, Ethene, and Ethyne
•
The properties of C-C single bonds depend on
the hybridization of the carbon atoms,
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.3 Constructing Hybrid Orbitals for Nonequivalent
Ligands
• Henry Bent formulated the following guidelines:
 Central atoms that obey the octet rule can be
classified into three structural types:
a) tetrahedral geometry and sp3 hybridization
b) trigonal geometry and sp2 hybridization
c) linear geometry and sp hybridization
 different ligands is assigned a different
hybridization to all nonequivalent ligands and
lone pairs
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 24.4
a. Use Bent’s rule to estimate the change in the XC-X bond angle in
when going from H2CO to F2CO.
b. Use Bent’s rule to estimate the deviation of the
H-C-H bond angle in FCH3 and ClCH3 from 109.4°.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
a. To first order, the carbon atom should exhibit sp2
hybridization. Because F is more electronegative
than H, the hybridization of the C-F ligand contains
more p character than does the C-H ligand.
Therefore, the F-C-F bond angle will be smaller
than the H-C-H bond angle.
b. Using the same argument as in part (a), the H-C-H
bond angles in both compounds will be smaller
than 109.4°. The angle will be larger in FCH3 than
in ClCH3.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.4 Constructing Hybrid Orbitals for Nonequivalent
Ligands
•
•
Using hybridization model to create local
bonding orbitals, Lewis structures concept can
be used.
To make a connection to Lewis structures in a
BeH2 bond, the bonding electron pair is placed
in the overlap region between the Be and H
orbitals.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.4 Constructing Hybrid Orbitals for Nonequivalent
Ligands
•
In the bonding of ethene (left) and ethane
(right) using hybrid bonding orbitals, the
maximal overlap between the p orbitals to
create a π bond in ethene occurs when all
atoms lie in the same plane.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.4 Constructing Hybrid Orbitals for Nonequivalent
Ligands
•
a)
b)
c)
Advantages of hybridization are:
Retains the main features of Lewis structures
Provides a theoretical basis for the VSEPR rules
understanding bond angles in molecules
• Disadvantages of hybridization are:
a) Semiempirical prescriptions must be used to estimate
the s and p character
b) Assumed electron density is highly concentrated
c) Assumed formalism used in creating hybrid orbitals is
high
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.5 Predicting Molecular Structure Using Molecular
Orbital Theory
•
•
Using a variational method, the total energy of
the molecule is minimized with respect to all
parameters of the occupied MOs.
The approach here is to focus on a more
qualitative approach rather than extensive
mathematics.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 24.6

Predict the equilibrium shape of H 3 , LiH2, and NH2
using qualitative MO theory.
Solution:
H 3 has two valence electrons and is bent as predicted
by the variation of the 1a1 MO energy. LiH2 or any
molecule of the type H2A with four electrons is
predicted to be linear. NH2 has one electron fewer
than H2O, and using the same reasoning as for water,
is bent.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
a. To first order, the carbon atom should exhibit sp2
hybridization. Because F is more electronegative
than H, the hybridization of the C-F ligand contains
more p character than does the C-H ligand.
Therefore, the F-C-F bond angle will be smaller
than the H-C-H bond angle.
b. Using the same argument as in part (a), the H-C-H
bond angles in both compounds will be smaller
than 109.4°. The angle will be larger in FCH3 than
in ClCH3.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.5 Predicting Molecular Structure Using
Molecular Orbital Theory
•
The difference in energies between the HOMO
and LUMO orbitals on A and B will determine
the direction of charge transfer.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.6 How Different Are Localized and Delocalized
Bonding Models?
•
•
Molecular orbital theory and hybridization-based
valence bond theory have been developed sing
delocalized and localized bonding, respectively.
On the basis of the symmetry requirements the
two lowest energy MOs for BeH2 are
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.6 How Different Are Localized and
Delocalized Bonding Models?
•
The many-electron determinantal wave function that
satisfies the Pauli requirement is
•
Use a property of a determinant
•
Where one can add a column of the determinant
multiplied by an arbitrary constant to another column
without changing the value of the determinant.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.7 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel Model
•
•
•
Conjugated molecules has a a delocalized π
network which has more strongly bonded
molecule with shorter single bonds.
Aromatic molecules are based on ring
structures that are particularly stable in
chemical reactions.
Hückel model is used to calculate energy
levels of the delocalized π electrons in
conjugated and aromatic molecules.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.7 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel Model
•
The secular determinant that is used to
obtain the MO energies and the coefficients of
the AOs for ethene is
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.7 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel Model
•
Consider 1,3-butadiene for which the secular
determinant is
•
Assumptions that all elements are more than
one position removed from the diagonal are
zero, we have
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.7 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel Model
•
Hückel rules for a monocyclic conjugated
system with N electrons is:
a) N=4n+2, molecule is stabilized
b) N=4n+1, molecule is free radical.
c) N=4n, molecule has two unpaired
electrons and very reactive.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.7 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The Hückel Model
•
Resonance stabilization energy arises in
aromatic compounds through the presence of
closed circuits of mobile electrons.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 24.7
Use the inscribed polygon method to calculate the
Hückel MO energy levels for benzene.
Solution:
The geometrical construction shows that the energy
levels are   2 ,    ,    and   2
The sum of the orbital energies
for the six Π electrons is
6  8
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.8 From Molecules to Solids
•
•
Hückel model is use to understand how energy
spectrum is generated.
As N becomes very large, the energy spectrum
becomes continuous. The energy range of the
MOs is shown in units of β.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
24.9 Making Semiconductors Conductive at Room
Temperature
•
We can change the properties of Si by adding
other atoms (dopant) that occupy Si sites in the
silicon crystal structure, called doping.
Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd