Orbital Interactions in Chemistry

Thomas A. Albright, Jeremy K. Burdett, Myung-Hwan Whangbo

• Publisher: Wiley-Interscience
• Year: 2013
• ISBN:
  9781118558256
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

Explains the underlying structure that unites all disciplinesin chemistry Now in its second edition, this book explores organic, organometallic, inorganic, solid state, and materials chemistry, demonstrating how common molecular orbital situations arisethroughout the whole chemical spectrum. The authors explore therelationships that enable readers to grasp the theory thatunderlies and connects traditional fields of study withinchemistry, thereby providing a conceptual framework with which tothink about chemical structure and reactivity problems. Orbital Interactions in Chemistry begins by developingmodels and reviewing molecular orbital theory. Next, the bookexplores orbitals in the organic-main group as well as in solids.Lastly, the book examines orbital interaction patterns that occurin inorganic-organometallic fields as well as clusterchemistry, surface chemistry, and magnetism in solids. This Second Edition has been thoroughly revised andupdated with new discoveries and computational tools since thepublication of the first edition more than twenty-five years ago.Among the new content, readers will find:
* Two new chapters dedicated to surface science and magneticproperties
* Additional examples of quantum calculations, focusing oninorganic and organometallic chemistry
* Expanded treatment of group theory
* New results from photoelectron spectroscopy Each section ends with a set of problems, enabling readers totest their grasp of new concepts as they progress through the text.Solutions are available on the book's ftp site. Orbital Interactions in Chemistry is written for bothresearchers and students in organic, inorganic, solid state, materials, and computational chemistry. All readers will discoverthe underlying structure that unites all disciplines inchemistry.

Chapter 1

Atomic and Molecular Orbitals

1.1 Introduction

The goal of this book is to show the reader how to work with and understand the electronic structures of molecules and solids. It is not our intention to present a formal discussion on the tenets of quantum mechanics or to discuss the methods and approximations used to solve the molecular Schrödinger equation. There are several excellent books [1–6], which do this, and many “canned” computer programs that are readily available to carry out the numerical calculations at different levels of sophistication with associated user manuals [7–9]. The real challenge, and the motivation behind this volume, is to be able to understand where the numbers generated by such computations actually come from. The first part of the book contains some mathematical material using which we have built a largely qualitative discussion of molecular orbital (MO) structure. Let us see how the molecular orbitals of complex molecules or solids may be constructed from smaller portions using concepts from perturbation theory and symmetry. Furthermore, we show how these orbitals change as a function of a geometrical perturbation, the substitution of one atom for another, or as a result of the presence of a second molecule as in a chemical reaction. Many concepts and results together form a common thread, which enables different fields of chemistry to be linked in a satisfying way. The emphasis of this book is on qualitative features and not on quantitative details. Our feeling is that just this perspective leads to predictive capabilities and insight.

1.2 Atomic Orbitals

The molecular orbitals of a molecule are usually expressed as a linear combination of the atomic orbitals (LCAOs) centered on its constituent atoms, which is discussed in Section 1.3. These atomic orbitals (AOs) using polar coordinates have the form shown in equation 1.1. This is a simple product of a function, R(r),

(1.1)

which only depends on the distance, r, of the electron from the nucleus, and a function Y(θ, ϕ), which contains all the angular information needed to describe the wavefunction. The Schrödinger wave equation may only be solved exactly for one-electron (hydrogenic) atoms (e.g., H, Li²⁺) where analytical expressions for R and Y are found. For many-electron atoms, the angular form of the atomic orbitals is the same as for the one-electron atom (Table 1.1), but now, the radial function R(r) is approximated in some way as shown later. The center column in Table 1.1 gives the form of Y in Cartesian coordinate space while that in the far right-hand side uses polar coordinates.

Table 1.1 Angular Components of Some Common Wavefunctions.

Orbital Type	Expression for Y
s	1	1
px	x/r	sin θ cos ϕ
py	y/r	sin θ sin ϕ
pz	z/r	cos θ
	(x^2 − y^2)/r^2	sin^2 θ cos 2ϕ
	(3z^2 − r^2)/r^2	3cos^2θ − 1
dxy	xy/r^2	sin^2 θ sin 2ϕ
dxz	xz/r^2	sin θ cos θ cos ϕ
dyz	yz/r^2	sin θ cos θ sin ϕ

Figure 1.1a shows a plot of the amplitude of the wavefunction χ for an electron in a ls orbital as a function of distance from the nucleus. This has been chosen to be the x-axis of an arbitrary coordinate system. With increasing x, the amplitude of χ sharply decreases in an exponential fashion and becomes negligible outside a certain region indicated by the dashed lines. The boundary surface of the s orbital, outside of which the wavefunction has some critical (small) value, is shown in Figure 1.1c. The corresponding diagrams for a 2p_x orbital are shown in Figure 1.1b, d. Note that the wavefunction for this p orbital changes sign when x → −x. It is often more convenient to represent the sign of the wavefunction by the presence or absence of shading of the orbital lobes as in 1.1 and 1.2. The c...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• About the Authors
• Chapter 1: Atomic and Molecular Orbitals
• Chapter 2: Concepts of Bonding and Orbital Interaction
• Chapter 3: Perturbational Molecular Orbital Theory
• Chapter 4: Symmetry
• Chapter 5: Molecular Orbital Construction from Fragment Orbitals
• Chapter 6: Molecular Orbitals of Diatomic Molecules and Electronegativity Perturbation
• Chapter 7: Molecular Orbitals and Geometrical Perturbation
• Chapter 8: State Wavefunctions and State Energies
• Chapter 9: Molecular Orbitals of Small Building Blocks
• Chapter 10: Molecules with Two Heavy Atoms
• Chapter 11: Orbital Interactions through Space and through Bonds
• Chapter 12: Polyenes and Conjugated Systems
• Chapter 13: Solids
• Chapter 14: Hypervalent Molecules
• Chapter 15: Transition Metal Complexes: A Starting Point at the Octahedron
• Chapter 16: Square Planar, Tetrahedral ML4 Complexes and Electron Counting
• Chapter 17: Five Coordination
• Chapter 18: The C2v ML3 Fragment
• Chapter 19: The ML2 and ML4 Fragments
• Chapter 20: Complexes of ML3, MCp and Cp2M
• Chapter 21: The Isolobal Analogy
• Chapter 22: Cluster Compounds
• Chapter 23: Chemistry on the Surface
• Chapter 24: Magnetic Properties
• Appendix I: Perturbational Molecular Orbital Theory
• Appendix II: Some Common Group Tables
• Appendix III: Normal Modes for Some Common Structural Types
• Index