physical chemistry 2 nd edition thomas engel, philip reid chapter 24 molecular structure and energy...

Physical Chemistry 2Physical Chemistry 2ndnd Edition EditionThomas Engel, Philip Reid

Chapter 24 Chapter 24 Molecular Structure and Energy Levels for Polyatomic

Molecules

© 2010 Pearson Education South Asia Pte Ltd

Physical Chemistry 2nd EditionChapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules

ObjectivesObjectives

• Discussion of both localized and delocalized bonding models.



OutlineOutline

1. Lewis Structures and the VSEPR Model2. 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



OutlineOutline

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 Solids9.Making Semiconductors Conductive at

Room Temperature



24.1 Lewis Structures and the VSEPR Model24.1 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.



24.1 Lewis Structures and the VSEPR 24.1 Lewis Structures and the VSEPR ModelModel

• Valence shell electron pair repulsion (VSEPR) model provides a qualitative theoretical understanding of molecular structures using Lewis concepts of localized bonds and lone pairs.



Example 24.1Example 24.1

Using the VSEPR model, predict the shape of

Solution:Lewis structure shows one of the three resonance structures of the nitrate ion:

The Lewis structure for OCl2 is

2-3 OCl and NO



24.2 Describing Localized Bonds Using 24.2 Describing Localized Bonds Using Hybridization for Hybridization for Methane, Ethene, and Ethyne 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




• The appropriate linear combination of carbon AOs is

• It can be simplified to




Determine the three unknown coefficients in the following equation by normalizing and orthogonalizing the hybrid orbitals.



SolutionSolution

We first normalize . Terms such 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.

32c where

13

1c

13

1c

1

21

2*2

2

2*2

21

*

ddd ssppaa zz

a ddyzy pspp 2

*22

*2 and



SolutionSolution

Orthogonalizing , we obtainba and

6

1c

and 03

1

3

2

03

1

3

2

4

4

2*2

2

2*24

*

c

ddcdzzzz ppppba



SolutionSolution

Normalizing , we obtainb

2

1c

and 16

1

3

1

3

1

6

1

6

26

2*262

*2

2

2*2

2

*

c

cdddxxzzzz ppppppba



SolutionSolution

We have chosen the positive root so that the coefficient of is negative. Using these results, the normalized and orthogonal set of hybrid orbitals is

bpx in 2

xz

xz

z

pspc

pspb

spa

222

222

22

2

1

3

1

6

1

2

1

3

1

6

1

3

1

3

2




• The properties of C-C single bonds depend on the hybridization of the carbon atoms,



24.3 Constructing Hybrid Orbitals for 24.3 Constructing Hybrid Orbitals for Nonequivalent Nonequivalent Ligands 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 hybridizationb) trigonal geometry and sp2 hybridizationc) linear geometry and sp hybridization different ligands is assigned a different

hybridization to all nonequivalent ligands and lone pairs




a. Use Bent’s rule to estimate the change in the X-C-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°.



SolutionSolution

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.




• 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.




• 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.




• Advantages of hybridization are:a) Retains the main features of Lewis structuresb) Provides a theoretical basis for the VSEPR rulesc) understanding bond angles in molecules

• Disadvantages of hybridization are:a) Semiempirical prescriptions must be used to

estimate the s and p characterb) Assumed electron density is highly

concentratedc) Assumed formalism used in creating hybrid

orbitals is high



24.5 Predicting Molecular Structure Using 24.5 Predicting Molecular Structure Using Molecular Orbital TheoryMolecular 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.




Predict the equilibrium shape of , LiH2, and NH2 using qualitative MO theory.

Solution: 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 fewerthan H2O, and using the same reasoning as for water, is bent.

3H

3H



SolutionSolution

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.



24.5 Predicting Molecular Structure Using 24.5 Predicting Molecular Structure Using Molecular Orbital TheoryMolecular Orbital Theory

• The difference in energies between the HOMO and LUMO orbitals on A and B will determine the direction of charge transfer.



24.6 How Different Are Localized and 24.6 How Different Are Localized and Delocalized Bonding Models?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



24.6 How Different Are Localized and 24.6 How Different Are Localized and Delocalized Bonding Models?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.



24.7 Qualitative Molecular Orbital Theory for 24.7 Qualitative Molecular Orbital Theory for Conjugated and Aromatic Molecules: The Hückel Conjugated and Aromatic Molecules: The Hückel ModelModel

• 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.




• The secular determinant that is used to obtain the MO energies and the coefficients of the AOs for ethene is




• 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




• 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.




• Resonance stabilization energy arises in aromatic compounds through the presence of closed circuits of mobile electrons.




Use the inscribed polygon method to calculate the Hückel MO energy levels for benzene.

Solution:The geometrical construction shows that the energy levels areThe sum of the orbital energies for the six Π electrons is

86

2 and , ,2



24.8 From Molecules to Solids24.8 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.



24.9 Making Semiconductors Conductive at 24.9 Making Semiconductors Conductive at Room Room Temperature Temperature

• We can change the properties of Si by adding other atoms (dopant) that occupy Si sites in the silicon crystal structure, called doping.

physical chemistry 2 nd edition thomas engel, philip reid chapter 24 molecular structure and energy...

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