Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 24 Molecular Structure and Energy Levels for Polyatomic Molecules

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Objectives Discussion of both localized and delocalized bonding models.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Example 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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 sp 3, sp 2, and sp hybridizations, respectively

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Example 24.2 Determine the three unknown coefficients in the following equation by normalizing and orthogonalizing the hybrid orbitals.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution Orthogonalizing, we obtain

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution Normalizing, we obtain

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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,

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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 sp 3 hybridization b)trigonal geometry and sp 2 hybridization c)linear geometry and sp hybridization  different ligands is assigned a different hybridization to all nonequivalent ligands and lone pairs

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Example 24.4 a. Use Bent’s rule to estimate the change in the X- C-X bond angle in when going from H 2 CO to F 2 CO. b. Use Bent’s rule to estimate the deviation of the H-C-H bond angle in FCH 3 and ClCH 3 from 109.4°.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution a.To first order, the carbon atom should exhibit sp 2 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 FCH 3 than in ClCH 3.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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 BeH 2 bond, the bonding electron pair is placed in the overlap region between the Be and H orbitals.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 24.4 Constructing Hybrid Orbitals for Nonequivalent Ligands Advantages of hybridization are: a)Retains the main features of Lewis structures b)Provides a theoretical basis for the VSEPR rules c)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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Example 24.6 Predict the equilibrium shape of, LiH 2, and NH 2 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 fewer than H2O, and using the same reasoning as for water, is bent.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules Solution a.To first order, the carbon atom should exhibit sp 2 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 FCH 3 than in ClCH 3.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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 BeH 2 are

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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 The sum of the orbital energies for the six Π electrons is

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.

© 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 24: Molecular Structure and Energy Levels for Polyatomic Molecules 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.