Chemical Bonding and Molecular Geometry. From Lewis to Electron Densities

307 Pages·2001·13.94 MB·English

by  Ronald J. Gillespie

CHEMICAL BONDING
AND
- .. .. -- - -- ~ ..- - ~ . - .
MOLECULAR GEOMETRY
• • •
From Lewis to Electron Densities
Ronald J. Gillespie
McMaster University
Paul L. A. Popelier
University ofManchester Institute ofScience and Technology
New York Oxford
OXFORD UNIVERSITY PRESS
2001
Oxford University Press
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Copyright © 2001 by Oxford University Press, Inc.
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LibraryofCongressCataloging-in-PublicationData
Gillespie, RonaldJ. (RonaldJames)
Chemicalbondingand moleculargeometryfrom Lewis toelectrondensities/ R.i.
Gillespie,P.L.A. Popelier.
p. cm.-(Topics in inorganicchemistry)
Includes bibliographicalreferences and index.
ISBN0-19-510496-X (ppk),0-19-510495-1 (cloth)
I. Chemical bonds-History. 2. Molecules-Models. I. Popelier,P.L.A. II.Title. III.
Series
QD461.G5372001
541.224-dc21 00-025404
CoverIllustration: Representations oftheSClz molecule. Center: Surfaces ofthe function
L = - V2pfor L =0au (blue) and L = 0.60au (orange).TheL = 0.60surface shows the
chargeconcentationscorrespondingto the lone pairson thesulfuratom and torodial charge
concentrations oneach chlorine atom (see also Figure 7.5). Topleft: TheLewis Struclure.
Top right: The VESPR model. Bottom left: Contourmap ofthe electron density. Bottom
right: ContourmapofL.
Printing(lastdigit): 98765432 I
Printedin the UnitedStatesofAmerica
on acid-freepaper
CONTENTS
Preface xi
Acknowledgments xiii
Chapter I The Chemical Bond: Classical Concepts and Theories
1.1 Introduction
1.2 Valence 1
1.3 The Periodic Table ofthe Elements 2
1.4 Structural Formulas 3
1.5 Stereochemistry 5
1.6 The Shell Model 6
1.7 The Ionic Model ofthe Chemical Bond 8
1.8 The Covalent Bond and Lewis Structures 9
1.9 Polar Bonds and Electronegativity 14
1.10 Polyatomic Anions and Formal Charges 17
1.11 Oxidation Number (Oxidation State) 18
1.12 Donor-Acceptor Bonds 19
1.13 Exceptions to the Octet Rule: Hypervalent and Hypovalent Molecules 20
1.14 Limitations ofthe Lewis Model 23
Chapter 2 Bond Properties 25
2.1 Introduction 25
2.2 Bond Lengths and Covalent Radii 27
2.3 Multiple Bonds and Bond Order 30
2.4 Ionic Radii 33
2.5 The Lengths ofPolar Bonds 37
2.6 Back-Bonding 38
2.7 Bond Dissociation Energies and Bond Enthalpies 39
2.8 Force Constants 42
2.9 Dipole Moments 43
vii
viii • Contents
Chapter 3 Some Basic Concepts of Quantum Mechanics 49
3.1 Introduction 49
3.2 Light, Quantization, and Probability 50
3.3 The Early Quantum Model ofthe Atom 51
3.4 The Wave Nature ofMatter and the Uncertainty Principle 53
3.5 The Schrbdinger equation and the Wave Function 53
3.6 The Meaning ofthe Wave Function: Probability and Electron Density 57
3.7 The Hydrogen Atom and Atomic Orbitals 58
3.8 Electron Spin 64
3.9 The Pauli Principle 64
3.10 Multielectron Atoms and Electron Configurations 69
3.11 Bonding Models 71
3.12 Ab Initio Calculations 79
3.13 Postscript 81
Chapter 4 Molecular Geometry and the VSEPR Model 84
4.1 Introduction 84
4.2 The Distribution ofElectrons in Valence Shells 85
4.3 Electron Pair Domains 88
4.4 Two, Three, Four, and Six Electron Pair Valence Shells 95
4.5 Multiple Bonds 99
4.6 Five Electron Pair Valence Shells 106
4.7 Limitations and Exceptions 110
Chapter 5 Ligand-Ligand Interactions and the Ligand Close-Packing (LCP) Model 113
5.1 Introduction 113
5.2 Ligand-Ligand Interactions 116
5.3 The Ligand Close-Packing (LCP) Model 119
5.4 Bond Lengths and Coordination Number 122
5.5 Molecules with Two or More Different Ligands 124
5.6 Bond Angles in Molecules with Lone Pairs 126
5.7 Weakly Electronegative Ligands 128
5.8 Ligand-Ligand Interactions in Molecules ofthe Elements in Periods 3-6 130
5.9 Polyatomic Ligands 130
5.10 Comparison ofthe LCP and VSEPR Models 132
Chapter 6 The AIM Theory and the Analysis of the Electron Density 134
6.1 Introduction 134
6.2 The Hellmann-Feynman Theorem 134
6.3 Representing the Electron Density 136
6.4 The Density Difference or Deformation Function 139
Contents • ix
6.5 The Electron Density from Experiment 143
6.6 The Topology ofthe Electron Density 144
6.7 Atomic Properties 153
6.8 Bond Properties 155
6.9 The Diatomic Hydrides ofPeriods 2 and 3 157
6.10 Summary 161
Chapter 7 The Laplacian of the Electron Density 163
7.1 Introduction 163
7.2 The Laplacian ofthe Electron Density 164
7.3 The Valence Shell Charge Concentration 165
7.4 The Laplacian and the VSEPR Model 170
7.5 Electron PairLocalization and the Lewis and VSEPR Models 178
7.6 Summary 179
Chapter 8 Molecules of the Elements of Period 2 180
8.1 Introduction 180
8.2 The Relationship Between Bond Properties and the AIM Theory 180
8.3 The Nature ofthe Bonding in the Fluorides, Chlorides, and Hydrides of
Li, Be, B, and C 184
8.4 The Geometry ofthe Molecules ofBe, B, and C 197
8.5 Hydroxo and Related Molecules ofBe, B, and C 198
8.6 The Nature ofthe CO and Other Polar Multiple Bonds 202
8.7 Bonding and Geometry ofthe Molecules ofNitrogen 209
8.8 The Geometry ofthe Molecules ofOxygen 216
8.9 The Geometry ofthe Molecules ofFluorine 220
Chapter 9 Molecules ofthe Elements of Periods 3-6 223
9.1 Introduction 223
9.2 Hypervalence 224
9.3 Bonding in the Fluorides, Chlorides, and Hydrides with an LLP Coordination
Number Up to Four 231
9.4 Geometry ofthe Fluorides, Chlorides, and Hydrides with an LLP Coordination
Number Up to Four 239
9.5 Molecules with an LLP Coordination Number ofFive 242
9.6 Molecules with an LLP Coordination Number ofSix 250
9.7 Molecules with an LLP Coordination NumberofSeven or Higher 251
9.8 Molecules ofthe Transition Metals 258
Index 259
Formula Index 265
PREFACE
The aim of this book is to provide undergraduate students with an introduction to models
andtheoriesofchemicalbondingand geometryas applied to the moleculesofthemain group
elements. We hope that it will give the student an understanding ofhow the concept ofthe
chemical bond has developed from its earliest days, through Lewis's brilliant conceptofthe
electron pair bond up to the present day, and ofthe relationships between the various mod
els and theories. We place particular emphasis on the valence shell electron pair (VSEPR)
and ligand close packing (LCP) models and the analysis ofelectron density distributions by
the atoms in molecules (AIM) theory.
Chapter I discusses classical models up to and including Lewis's covalent bond model
and Kossell's ionic bond model. It reviews ideas that are generally well known and are an
important background for understanding later models and theories. Some ofthese models,
particularly the Lewis model, are still in use today, and to appreciate later developments,
their limitations need to be clearly and fully understood.
Chapter 2 discusses the properties of bonds such as bond lengths and bond energies,
which provide much of the experimental information on which bonding concepts and ex
planations ofgeometry have been mainly based. Again this is a briefsummary at afairly el
ementarylevel, servingmainly as areview. Noattemptis made to deal with theexperimental
detailsofthe many differentexperimental methods used to obtain the information discussed.
In the 1920s it was found thatelectrons do notbehave like macroscopic objects thatare
governed by Newton's laws of motion; rather, they obey the laws of quantum mechanics.
The application ofthese laws to atoms and molecules gave rise to orbital-based models of
chemical bonding. In Chapter 3 we discuss some ofthe basic ideas ofquantum mechanics,
particularly thePauli principle, theHeisenberguncertainty principle, and theconceptofelec
tronic charge distribution, and we give a briefreview oforbital-based models and modem
ab initio calculations based on them.
Chapter4discussesthewell-known VSEPRmodel. Althoughthismodelcanberegarded
as an empirical model that does not directly use quantum mechanical ideas, its physical ba
sis is to be found in the Pauli principle. This dependence on aquantum mechanical concept
has notalways been clearly understood, so weemphasize this aspect ofthe model. We have
tried to give a rather complete and detailed review ofthe model, which has been somewhat
modified over the years since it was first proposed in 1957.
xi
xii • Preface
It has long been recognized that steric interactions between large atoms or groups in a
molecule may affect the geometry, and about 40 years ago it was suggested that repulsive
interactions between even relatively small atoms attached to a central atom often constitute
an important factor in determining molecular geometry. Nevertheless, the importance of
ligand-ligand repulsions in determining the geometry ofmany molecules, which led to the
development ofthe ligand close-packing model, was not clearly established until quite re
cently.Thismodel,whichprovidesanimportantandusefulcomplementtotheVSPERmodel,
is described in Chapter 5.
In recent years increasingly accurate information on the electron density distribution in
amolecule has becomeavailablefrom ab initiocalculations and X-ray crystallographicstud
ies. The atoms in molecules (AIM) theory developed by Bader and his coworkers from the
1970s on provides the basis for a method for analyzing the electron density distribution of
a molecule to obtain quantitative information about the properties ofatoms as they exist in
molecules and onthe bonds betweenthem. This theory isdiscussed in Chapters 6and 7. Un
fortunately, AIM has remained until now aratheresoteric mathematical theory whose great
relevance to the understanding ofbonding and molecular geometry has not been widely ap
preciated. Wegive apictorialand low-levelmathematical approach to thetheory suitablefor
undergraduates.
Chapters 8 and 9 are devoted to a discussion of applications of the VSEPR and LCP
models, the analysis ofelectrondensity distributions to the understandingofthebondingand
geometry ofmolecules ofthe main group elements, and on the relationship ofthese models
and theories to orbital models. Chapter 8 deals with molecules of the elements of period 2
and Chapter9 with the molecules ofthe main group elements ofperiod 3 and beyond.
We welcome comments and suggestions from readers. Please send comments via e-mailto
[email protected]@umist.ac.uk.Formoreinformationaboutourresearch,please
visit ourweb sites-Ronald Gillespie at http://www.chemistn..mcmaster.ca/faculty/gillespie and
Paul Popelier at http://www.ch.umist.ac.uk/popelier.htm.
ACKNOWLEDGMENTS
Wesincerelythankthefollowing friends, colleagues, andstudents,whokindly read and com
mented upon all or parts of the manuscript at various stages in its preparation: Dr. Peter
Robinson, ProfessorRichard Bader, ProfessorJack Passmore, Professor Steve Hartman, Dr.
George Heard, Dr. Alan Brisdon, Dr. Frank Mair, Ms. Maggie Austen, Mr. Paul Smith, and
Mr. Manuel Corral-Valero. We express our gratitude to Professors Wade, Hargittai, and
Wiberg, who critically reviewed the entire manuscript and made many useful suggestions
for its improvement. Wethank Dr. Stephane Noury, Dr. FernandoMartin,Dr. GeorgeHeard,
and Mr. David Bayles, who prepared many ofthe figures, and Dr. George Heard, Ms. Fiona
Aicken, and Mr. Sean O'Brien for their help in the generation ofdata. We thank the staffof
Oxford University Press for all their assistance and Karen Shapiro, Senior Production Edi
tor, in particular for guiding us so smoothly and competently through the deadlines and in
tricacies ofthe production process.
RJG thanks his wifeMadgefor herencouragement, support, and understandingthrough
out the whole project, and PLAP thanks his parents for their support.
xiii
CHEMICAL BONDING AND
MOLECULAR GEOMETRY
• • •