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HYPERCARBON

HYPERCARBON CHEMISTRY

Second Edition

GEORGE A. OLAH G. K. SURYA PRAKASH KENNETH WADE ÁRPÁD MOLNÁR ROBERT E. WILLIAMS

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Library of Congress Cataloging-in-Publication Data: Hypercarbon chemistry / by George A. Olah . . . [et al.]. – 2nd ed. p. cm. Includes index. ISBN 978-0-470-93568-2 (cloth) 1. Carbonium . 2. Organometallic chemistry. I. Olah, George A. (George Andrew), 1927- QD305.C3H97 2011 547.01–dc22 2010044306

Printed in the United States of America ePDF ISBN 9781118016442 ePub ISBN 9781118016459 oBook ISBN 9781118016466

10 9 8 7 6 5 4 3 2 1 In Memory of the Late Professor William N. Lipscomb

CONTENTS

Foreword to the First Edition xiii Preface to the Second Edition xv Preface to the First Edition xvii

1. Introduction: General Aspects 1 1.1. Aims and Objectives 1 1.2. Some Defi nitions 2 1.3. Structures of Some Typical Hypercarbon Systems 5 1.4. The Three-Center Bond Concept: Types of Three-Center Bonds 10 1.5. The Bonding in More Highly Delocalized Systems 21 1.6. Reactions Involving Hypercarbon Intermediates 26 References 31

2. -Bridged (Associated) Alkyls 37 2.1. Introduction 37 2.2. Bridged Organoaluminum Compounds 41 2.3. Beryllium and Magnesium Compounds 50 2.4. Organolithium Compounds 53 2.5. Organocopper, , and Gold Compounds 58 2.6. Scandium, Yttrium, and Lanthanide Compounds 62 2.7. Titanium, Zirconium, and Hafnium Compounds 64 2.8. Manganese Compounds 66 2.9. Other Metal Compounds with Bridging Alkyl Groups 68 vii viii CONTENTS

2.10. Agostic Systems Containing Carbon––Metal 3c–2e Bonds 70 2.11. Conclusions 76 References 77

3. Carboranes and Metallacarboranes 85 3.1. Introduction 85 3.2. Carborane Structures and Skeletal Numbers 87 3.2.1. Closo Carboranes 88 3.2.2. Nido and Arachno Carboranes 89 3.2.3. Carbon Sites in Carboranes; Skeletal Connectivities k 97 3.2.4. Skeletal Bond Orders in Boranes and Carboranes 98 3.3. Localized Bond Schemes for Closo Boranes and Carboranes 98 3.3.1. Lipscomb’s Styx Rules and Williams’ Stx Rules 98 3.3.2. Bond Orders and Skeletal Connectivities 100 3.3.3. Bond Networks and Skeletal Connectivities 101 3.3.4. Calculated Charge Distributions and Edge Bond Orders 102 3.4. MO Treatments of Closo Boranes and Carboranes 104 3.5. The Bonding in Nido and Arachno Carboranes 107 3.5.1. Localized Bond Schemes 107 3.5.2. MO Treatments of Nido and Arachno Boranes and Carboranes 108 3.5.3. Some Boron-Free Nido and Arachno Systems 110 3.6. Methods of Synthesis and Interconversion Reactions 111 3.7. Some Carbon-Derivatized Carboranes 114 3.7.1. Carboranyl C–H---X Hydrogen-Bonded Systems 114 3.7.2. Carboranyl–Metal Systems 114 3.7.3. Some Aryl-Carboranes 116 3.8. Boron-Derivatized Carboranes: Weakly Basic Anions − [CB11H6X6] 122 3.9. Metallacarboranes 123 3.9.1. Structural Types, Electron Counts, and Isolobal Units 123 3.9.2. Predicting Structures from Formulae 126

3.9.3. Metal Complexes of CxBy Ring Systems 130 3.10. Supraicosahedral Carborane Systems 133 3.11. Conclusions 137 References 137

4. Mixed Metal–Carbon Clusters and Metal Carbides 149 4.1. Introduction 149

4.2. Complexes of CnHn Ring Systems with a Metal : Nido-Shaped MCn Clusters 150

4.3. Metal Complexes of Acyclic Unsaturated Ligands, CnHn+2 157 CONTENTS ix

4.4. Complexes of Unsaturated Organic Ligands with Two or More Metal : Mixed Metal–Carbon Clusters 160 4.5. Metal Clusters Incorporating Core Hypercarbon Atoms 162 4.6. Bulk Metal Carbides 173 4.7. Metallated Carbocations 176 4.8. Conclusions 176 References 177

5. Hypercoordinate Carbocations and Their Borane Analogs 185 5.1. General Concept of Carbocations: Carbenium Versus Carbonium Ions 185 5.1.1. Trivalent–Tricoordinate (Classical) Carbenium Ions 186 5.1.2. Hypercoordinate (Nonclassical) Carbonium Ions 187 5.2. Methods of Generating Hypercoordinate Carbocations 188 5.3. Methods Used to Study Hypercoordinate Carbocations 189 5.3.1. NMR in Solution 189 5.3.2. 13C NMR Additivity 192 5.3.3. Isotopic Perturbation Method 192 5.3.4. -State 13C NMR at Extremely Low Temperature 193 5.3.5. X-Ray Diffraction 193 5.3.6. Tool of Increasing Electron Demand 194 5.3.7. ESCA 194 5.3.8. Low Temperature Solution Calorimetry 195 5.3.9. Quantum Mechanical Calculations 195 + 5.4. Methonium (CH5 ) and Its Analogs 195 5.4.1. Alkonium Ions Incorporating Bridging + (Protonated Alkanes, CnH2n+3 ) 195 + 5.4.1.1. The Methonium Ion (CH5 ) 196 5.4.1.2. Multiply-Protonated Methane Ions and their Analogs 202 5.4.1.3. Varied Methane Cations 205 + 5.4.1.4. Ethonium Ion (C2H7 ) and Analogs 208 5.4.1.5. Proponium Ions and Analogs 210 5.4.1.6. Higher Alkonium Ions 211 5.4.1.7. Adamantonium Ions 217 5.4.1.8. Hydrogen-Bridged Cycloalkonium Ions 217 5.4.1.9. Hydrogen-Bridged Acyclic Ions 221 5.4.1.10. Five-Center, Four-Electron Bonding Structures 223 5.4.2. Hypercoordinate Carbocations Containing 3c–2e C---C---C Bonds 223 5.4.2.1. Cyclopropylmethyl and Cyclobutyl Cations 223 5.4.2.2. The 2-Norbornyl Cation 229 5.4.2.3. The 7-Norbornyl Cation 243 5.4.2.4. The 2-Bicyclo[2.1.1]hexyl Cation 243 5.4.2.5. The Polymethyl 2-Adamantyl Cations 245 x CONTENTS

5.5. Homoaromatic Cations 247 5.5.1. Monohomoaromatic Cations 247 5.5.2. Bishomoaromatic Cations 249 5.5.3. Trishomoaromatic Cations 256 5.5.4. Three-Dimensional 258 5.5.5. Möbius Homoaromaticity 259 5.6. Hypercoordinate (Nonclassical) Pyramidal Carbocations 260 + 5.6.1. (CH)5 -Type Cations 260 2+ 5.6.2. (CH)6 -Type Dications 264 5.7. Hypercoordinate Heterocations 266 5.7.1. Introduction 266 5.7.2. Hydrogen-Bridged Silyl Cations 266 5.7.3. Homoaromatic Heterocations 267 5.8. Carbocation–Borane Analogs 268 5.8.1. Introduction 268 5.8.2. Hypercoordinate Methonium and Boronium Ions 272 5.8.3. Cage Systems 272 5.8.4. Hypercoordinate Onium–Carbonium Dications and Isoelectronic Onium–Boronium Cations 274 5.9. Conclusions 276 References 277

6. Reactions Involving Hypercarbon Intermediates 295 6.1. Introduction 295 6.2. Reactions of Electrophiles with C–H and C–C Single Bonds 298 6.2.1. -Catalyzed Reactions and Rearrangements of Alkanes, Cycloalkanes, and Related Compounds 298 6.2.1.1. Carbon–Hydrogen and Carbon–Carbon Bond Protolysis 298 6.2.1.2. Isomerization and Rearrangement 307 6.2.1.3. Alkylation 320 6.2.2. Nitration and Nitrosation 325 6.2.3. Halogenation 328 6.2.4. Carbonylation 331 6.2.5. Oxyfunctionalization 332 6.2.5.1. Oxygenation with Hydrogen Peroxide 332 6.2.5.2. Oxygenation with Ozone 334 6.2.5.3. Oxygenation with Other Reagents 337 6.2.6. Sulfuration 339 6.2.7. Reactions of Coordinatively Unsaturated Metal Compounds and Fragments with C–H and C–C σ Bonds 340 CONTENTS xi

6.2.7.1. Carbon– Insertion 342 6.2.7.2. Carbon–Carbon Bond Insertion 362 6.2.8. Reactions of Singlet Carbenes, Nitrenes, and Heavy Carbene Analogs with C–H and C–C Bonds 371 6.2.9. Rearrangement to Electron-Defi cient Metal, Nitrogen, and Oxygen Centers 377 6.2.9.1. Isomerization, Rearrangement, and Redistribution of Alkylmetal Compounds 377 6.2.9.2. Rearrangements to Electron-Defi cient Nitrogen and Oxygen Centers 381 6.3. Electrophilic Reactions of π-Donor Systems 383 6.4. Bridging Hypercoordinate Species with Donor Atom Participation 388 6.4.1. Carbocations with 3c–2e Bond 388

6.4.2. Five-Coordinate SN2 Reaction Transition States and Claimed Intermediates 389 6.4.3. Six-Coordinate Hypervalent Compounds 393 6.5. Conclusions 394 References 394

Conclusions and Outlook 417 Index 419

FOREWORD TO THE FIRST EDITION

The periodic nature of the properties of atoms and the nature and chemistry of are based on the wave property of matter and the associated energetics. Concepts including the electron - pair bond between two atoms and the associated three- dimensional properties of molecules and reactions have served the chemist well, and will continue to do so in the future. The completely delocalized bonds of π - aromatic molecules, introduced by W. H ü ckel, also provided a basis for a rational description of molecular orbitals in these systems. An extended Hü ckel theory allowed a study of molecular orbitals throughout chemistry at a certain level of approximation. The localized multicenter orbital holds a certain intermediate ground, and is particularly useful when there are more valence orbitals then in a or transition state. First widely used in the boron and car- boranes, these three- center and multicenter orbitals provide a coherent and consistent description of much of the structure and chemistry of the upper left side of the , and of the interactions of metallic ions with other atoms or molecules. Skeletal electron counts (the sum of the styx numbers), fi rst proposed by Wade, Mingos, and Rudolph, have also provided a guide for synthesis, and have given a basis for fi lled bonding description of polyhedral species and their fragments. Together with the isolobal concept, diverse areas of chemistry have thereby been unifi ed. In this book, one sees the remarkable way in which these ideas bring together structure and reactivity in a great diversity of novel carbon chemistry and its relationship with that of boron, lithium, hydrogen, the , and others. The authors are to be congratulated. xiii xiv FOREWORD TO THE FIRST EDITION

Rather than ask why it has taken some 30 years for these concepts to become widely known, one can be amazed that the background for this fi ne book developed at all. It is due in no small part to the reluctance of chemists to adapt to the dynamic changes of chemistry. One can also hope that chem- istry will recover from the recent neglect of support of research in mechanistic organic chemistry and synthesis of compounds of the main group elements. In addition, much of the molecular structure determination that is so central to these arguments had to await the newer methods of X- ray diffraction and nuclear magnetic resonance, and the theory had to await the modern develop- ment in methods and computers. Thus, the emergence of the depth and breadth of these concepts in this book is a tribute to the dedication of the authors and to the vitality of the ideas themselves.

May 1986 W illiam N. L ipscomb

PREFACE TO THE SECOND EDITION

More than 20 years have passed since the publication of our book on hyper- carbon chemistry. The book became out of print and much progress has since been made in the fi eld. Hypercarbon chemistry has continued to grow, and indeed has become an integral part of the chemistry of carbon compounds usually referred to as high coordination compounds. Hence, it seems war- ranted to provide a comprehensively updated review and discussion of the fi eld with literature coverage until mid- 2009. Les Field was no longer available to help revise our book. However, our friend and colleague Á rp á d Molná r joined us as a coauthor during a sabbatical year in Los Angeles, and should be credited for his outstanding effort to make the new edition possible, which we hope will be of use to the chemical community. Our publisher is thanked for arranging the new updated edition.

G eorge A. O lah G. K. Surya P rakash K enneth W ade Á rp á d M oln á r November 2009 R obert E. W illiams

xv

PREFACE TO THE FIRST EDITION

Organic chemistry is concerned with carbon compounds. Over 6 million such compounds are now known, and their number is increasing rapidly. They range from the simplest compound methane, the major component of natural gas, to the marvelously intricate macromolecules that nature uses in life processes. Within such a rich and diverse subject, it is diffi cult for someone deeply familiar with one area to keep abreast of developments in others. This can hinder progress if discoveries in one fi eld that can have signifi cant impact on others are not recognized in a timely fashion. For example, developments in the chemistry of carbohydrates, proteins, or nucleotides are traditionally exploited by biochemists and biologists more than by organic chemists. Developments in organometallic chemistry, while increasingly attracting the attention of inorganic chemists, are not as well appreciated by mainstream organic chemists. In this book we have attempted to alleviate this problem by pooling our diverse experience and backgrounds but centering on a common interest in the fascinating topic of hypercarbon chemistry. The book centers on the theme that carbon, despite its fi rmly established tetravalency, can still bond simulta- neously to fi ve or more other atoms. We refer to such atoms as hypercarbon atoms (short for hypercoordinated atoms), since four valency [hence four coordination, using normal two - center, two - electron type bonds] is the upper limit for carbon (being a fi rst- row element, it can accommodate no more than eight electrons in its valence shell). Since their early detection in bridged metal alkyls, where they helped advance the concept of the three- center, two- electron bond (and later, the four - center, two - electron bond), hypercarbon atoms have now become a signifi cant feature of organometallics, carborane, xvii xviii PREFACE TO THE FIRST EDITION and cluster (carbide) chemistry, as well as acid- catalyzed hydrocarbon chem- istry and the diverse chemistry of carbocations. First, we survey the major types of compounds that contain hypercarbon. The relationships that link these apparently disparate species are demon- strated by showing how the bonding problems they pose can be solved by the use of three - or multicenter electron - pair bond descriptions or simple MO treatments. We also show the role played by hypercoordinated carbon inter- mediates in many familiar reactions (carbocationic or otherwise). Our aim here is to demonstrate that carbon atoms in general can increase their coor- dination numbers in a whole range in reactions. In our original plans for the book, we were privileged to have our friend and colleague Paul v. R. Schleyer participate, and we regret that other obliga- tions have made it impossible for him to continue. We gratefully acknowledge his many suggestions and thank him for his continued encouragement. We have mainly focused our attention on experimentally known hypercarbon systems and are not discussing only computationally studied ones (these are reviewed by Paul Schleyer elsewhere). Most chemists ’ familiarity with chemical bonding evolved in electron - suffi cient systems, where there are enough electrons not only for (2 c – 2 e ) bonds but also for nonbonded electron pairs. Hypercarbon atoms are generally found in electron - defi cient systems where electrons are in short supply and thus have to be spread relatively thinly to hold molecules or ions together. A relative defi ciency of electrons is not uncommon in chemistry, particularly in the chem- istry of the metallic elements. The (3c – 2 e ) and multicenter bonding concept of boranes and carboranes, pioneered by Lipscomb, further emphasizes this point. Thus, it is not surprising that the concept of hypercarbon bonding was accepted by inorganic and organometallic chemists earlier than by their organic colleagues. The well- publicized spirited debate over the classical– nonclassical nature of some carbocationic systems preceded their preparation and their spectroscopic study under long- lived stable ion conditions, which unequivocally established their structures. Debate, and even controversy, is frequently an essential part of the “ growing pains” of a maturing fi eld, and they should be welcomed as they help progress in fi nding answers. The impor- tance of hypercoordination in carbocations and related hydrocarbon is now fi rmly established. At the same time, hypercoordinate carbocations are but one aspect of the much wider fi eld of hypercarbon chemistry. It is signifi cant to note that almost all carbocations have known isoelec- tronic and isostructural neutral boron analogs. Boron compounds also provide useful models for many types of intermediates (transition states) of electro- philic organic reactions. The fi eld of hypercarbon chemistry is already so extensive that it is impos- sible to give an encyclopedic coverage of the topic. Instead, we have taken the liberty of organizing our discussion around selected topics with representative examples to emphasize major aspects. Our choices were arbitrary and we apologize for inevitably omitting much signifi cant work. PREFACE TO THE FIRST EDITION xix

Multiauthor books frequently lack the uniformity that a single - author book is able to convey. Our close cooperation, made possible by the Loker Hydrocarbon Research Institute, has helped us give a homogeneous presenta- tion that merges our individual viewpoints to refl ect our common goal. If we had succeeded in calling attention to the ubiquitous presence of hypercarbon compounds, breaching the conventional boundaries of chemistry, and arousing the interest of our readers, then we shall have achieved our purpose. We thank Ms. Cheri Gilmour for typing the manuscript and our editor, Dr. Theodore P. Hoffman, for helping along the project in his always friendly and effi cient way. Many friends and colleagues offered helpful comments and sug- gestions and we are grateful to them all.

G eorge A. O lah G.K. S urya P rakash R obert E. W illiams L eslie D. F ield October 1986 K enneth W ade

1 INTRODUCTION: GENERAL ASPECTS

1.1. AIMS AND OBJECTIVES

This book is concerned with an important area of organic (i.e., carbon) chem- istry that has developed enormously over the past half- century, yet is still neglected in many organic textbooks. This is the chemistry of compounds in which carbon atoms are covalently bonded to more neighboring atoms than can be explained in terms of classical two - center, electron - pair bonds. Such carbon atoms are referred to as hypercarbon atoms 1 (short for hypercoordi- nated carbon atoms) because when fi rst discovered, their coordination numbers seemed unexpectedly high .

Carbon contains four atomic orbitals (AOs) in its valence shell (the 2 s , 2p x , 2 py , and 2p z AOs) and thus can accommodate at most four electron pairs (the “ octet rule ” ).2 Commonly, these electron pairs are used to form four single bonds (as in alkanes), two single bonds and one (as in ), one and one (as in alkynes), or two double bonds (as in cumulenes). With only four bond pairs, carbon atoms cannot bond simultaneously to more than four neighboring atoms using only two- center electron - pair bonds. If attached to more than four neighboring atoms, they must resort to some form of multicenter σ bonding , in which the bonding power of a pair of electrons is spread over more than two atoms. All carbon atoms with coordination numbers greater than four are therefore necessarily hypercoordinated, and compounds containing such atoms (of which there are

Hypercarbon Chemistry, Second Edition. George A. Olah, G. K. Surya Prakash, Kenneth Wade, Árpád Molnár, Robert E. Williams. © 2011 John Wiley & Sons, Inc. Published by John Wiley & Sons, Inc.

1 2 INTRODUCTION: GENERAL ASPECTS now a very large number) will be the main concern of this book. However, there are circumstances in which carbon atoms with only three or four neigh- bors may participate in multicenter σ bonding to two or even three of these neighbors, and we shall include them in our discussion where appropriate. We have four main objectives:

1 . To illustrate the wide and developing scope of hypercarbon chemistry by illustrating the variety of compounds now known to contain hypercarbon atoms (carbocations,3 – 6 organometallics, 7 – 9 carboranes, 10 metal – carbon cluster compounds,11,12 and metal carbides 13). They include bridged metal 14 – 17 alkyls such as alkyl - lithium reagents (LiR)n in which the hypercoor- dinated nature of the metal- attached carbon atoms, and the roles that the metal atoms play in their chemistry, are often overlooked. 2 . To discuss the ways in which the bonding in such systems can be described , notably using three - center – two - electron (3c – 2 e ) bonds as well as classi- cal two - center – two - electron (2c – 2 e) bonds, but also by simple molecular orbital (MO) treatments that shed useful light on the more symmetrical systems. 3 . To show how hypercarbon compounds are closely related to many clas- sically bonded systems and aromatic systems, and are not exotic species remote from mainstream organic chemistry. 4 . To show how the study of hypercarbon compounds helps us to understand the mechanisms of many organic reactions, reactions in which carbon atoms become temporarily hypercoordinated in intermediates or transi- tion states even though the reagents and products contain only normally coordinated carbon atoms.

In introducing the subject in Section 1.2 , we defi ne some of the terms we shall be using. In Section 1.3 , we illustrate the various types of hypercarbon com- pounds now known. Since we shall rely heavily on the 3c – 2e bond concept in their bonding, and since its usefulness is perhaps less widely appreciated in organic chemistry than in inorganic or organometallic chemistry, we devote Section 1.4 of this introductory chapter to discussion of that concept and illus- trate its value for selected systems. We also demonstrate the relevance and value of some simple MO arguments applied to hypercarbon systems (Sections 1.4 and 1.5 ), and conclude this introductory chapter by indicating the types of reactions thought to involve hypercarbon systems. More detailed discussion of particular categories of hypercarbon compounds, including structural, bonding, thermochemical, and reactivity aspects, follow in subsequent chapters.

1.2. SOME DEFINITIONS

Throughout this book, we shall be concerned with the twin issues of coordina- tion and bonding. The terminology by which chemists refer to these issues SOME DEFINITIONS 3 varies considerably from area to area. It is important, therefore, to defi ne and to illustrate the sense in which certain terms will be used here. We defi ne the of an atom as the number of neighboring atoms by which that atom is directly surrounded, to each of which it is attached by the direct sharing of electronic charge. The coordinating atoms may not all be at the same distance (some may be bonded more strongly than others, and so may be closer to the atom under consideration), but all will be located in direc- tions and at distances that indicate sharing of electronic charge with the central atom, rather than linkage to the central atom via a second neighboring atom. On occasions, the term “ valence ” is used as if it were synonymous with “ coordination number.” We shall not use it in that sense here. We defi ne the valence of an atom as the number of bonding electron pairs used by that atom . Normally, carbon is tetravalent (i.e., the octet rule is obeyed), and hypercarbon compounds are no exception. (See also discussions about hypervalency by Akiba 18 and the octet rule and hypervalency by Gillespie and Silvi.19 ) A hyper- carbon atom uses four electron pairs to bond to whatever number of atoms there are in its coordination sphere. The carbon atom in methane is tetravalent and four coordinate, forming four 2c – 2 e bonds to its neighboring hydrogen atoms. It remains tetravalent but becomes pentacoordinate when methane is + protonated to form the methonium ion (CH5 ), an energetic, highly reactive species20 – 22 with a structure in which three hydrogen atoms remain at a normal, single - bond distance while the other two are at a greater distance. 20,23 – 26 + + However, the methyl cation CH 3 into which CH 5 decomposes contains a triply coordinated trivalent carbon atom [Eq. (1.1) : The lines from carbon in that equation represent links to the coordinating hydrogen atoms, not neces- sarily bonds in the classical electron - pair sense].

+ H H H H H+ + C H C C H (1.1) – H H2 H H H H H

+ The carbon atom in CH 3 is said to be coordinatively unsaturated, a term we shall use in connection with any atom that can readily expand its coordina- + tion number, either (as in the case of the carbon atom of CH3 ) by bonding to another ligand (a coordinating atom or group) , which supplies electrons for + − the purpose (e.g., CH 3 + X → C H3 X), or by using electrons that were previ- ously nonbonding , for example, as occurs when coordinatively unsaturated − carbon atoms in carbanions R3 C are protonated, that is, when nonbonding lone - pair electrons are converted into bond pairs [Eq. (1.2) ]:

R R _ C : + H+ C H (1.2)

R R R R 4 INTRODUCTION: GENERAL ASPECTS

H H H C + sp3 1s + H H H H or H C H H H H H C + H H Scheme 1.1

When discussing bonding, we shall fi nd it convenient to retain wherever practicable the concept of single, double, and triple bonds, that is, links between pairs of atoms that involve the sharing between those atoms of two, four, or six electrons, respectively. We shall refer to them as 2 c – 2 e , two - center – four - electron (2c – 4 e ), and two - center – six - electron (2c – 6 e) bonds. However, as already indicated, we shall fi nd it necessary, in discussing hypercarbon com- pounds, to use the concept of multicenter σ bonds, bonds in which the bonding power of a pair of electrons is considered to extend over three or occasionally + four atoms. In CH5 , for example, a 3c – 2e bond can account for the bonding between the carbon atom and the two hydrogen atoms furthest from the carbon atom, represented as in Scheme 1.1 . Such a 3c – 2 e bond is envisaged as resulting from the mutual overlap of a suitable AO from each of the atoms involved, a 1s AO from each hydrogen atom, and an sp 3 hybrid AO from carbon. The 3c – 2 e bond can be represented by broken lines from the atoms that meet at the center of that triangle, where the AOs of the three atoms will overlap (Scheme 1.1 ). It must be remembered, however, that there is no atom at the point at which the broken lines meet. It should be stressed that although such a 3 c – 2 e bond shares the bonding pair of electrons between three atoms instead of two as in classical bonds, and therefore is sometimes referred to as delocalized , the description of the + bonding in CH5 by three 2 c – 2 e bonds and one 3 c – 2 e bond is nevertheless a description in terms of localized bonds . It is a valence bond description of this cation that attempts to account for the distribution of the atoms and the inter- nuclear distances by allocating pairs of electrons to localized regions between pairs of atoms or within triangular arrays of three atoms. A delocalized descrip- tion of the bonding in this cation would allocate the four pairs of electrons to four MOs embracing all six atoms, each or most making some contribution to + all of the pairwise interactions, bonded or nonbonded, in CH 5 , but generating overall much the same electron density in particular regions as the localized bond model. Thus, electron density corresponding to essentially one pair of electrons would be found in each of the “ normal ” C – H bonds, but the electron STRUCTURES OF SOME TYPICAL HYPERCARBON SYSTEMS 5 density associated with each long C – H bond, and also in the H - - - H link between the two anomalous (hypercoordinated) hydrogen atoms, would approximate to two- thirds of an electron apiece (for electron bookkeeping purposes, the sharing of a pair of electrons between the three atoms linked by a 3 c – 2 e bond corresponds to the allocation of two- thirds of an electron to each edge of the triangle defi ned by those three atoms.). An additional term we may fi nd occasionally useful, though we shall restrict its use to avoid ambiguity, is electron defi cient . This term has at least three dif- ferent senses in which it has found use in connection with organic systems. It is often applied as meaning “ center for nucleophilic attack” to refer to carbon atoms bearing electron - withdrawing substituents. Second, it is also used in referring to compounds with coordinatively unsaturated carbon atoms like + those of carbenium ions, R3 C , which can accommodate an extra pair of elec- trons. The third usage,27,28 is as a label for molecules, or sections thereof, that contain too few electrons to allow their bonding to be described exclusively in terms of two- center, electron- pair bonds. In this book we prefer to restrict our discussion to compounds wherein molecules or sets of atoms are held together by multicenter bonding (i.e., by electron - defi cient bonding). Similarly, electron precise 28 is a term that can be used as a label for systems in which there are exactly the right number of electrons to give each pair a two - center -

bonding role, as in CH 4 . Electron - rich systems are those containing nonbonding − (lone - pair) electrons , as in CH3 , NH3 , or H2 O. A molecule or polyatomic ion containing n atoms can often be identifi ed as electron defi cient from its formula, if it contains fewer than ( n − 1) valence shell electron pairs. This is because at least ( n − 1) two - center covalent links will be needed to hold n atoms together, whatever the structure may be. Thus, + the methonium ion, CH5 , with six atoms held together by only four valence shell electron pairs, is clearly electron defi cient in this sense. The dication 2 + 29 CH6 , with seven atoms, is even more so.

1.3. STRUCTURES OF SOME TYPICAL HYPERCARBON SYSTEMS

Before exploring the various bonding situations that occur in hypercarbon systems, we illustrate the structures of some representative examples, grouped according to type in Figures 1.1 – 1.6 . Figure 1.1 shows the structures, determined in pioneering X- ray crystallo- graphic studies, of some bridged metal alkyls , aryls , alkenyls , and alkyn- yls . 9,14 – 17,27,30 – 36 Compounds of these types fi rst showed how the carbon atoms of typical monovalent organic groups could participate in multicenter σ bond- ing. Note that the hypercarbon atoms in all of these compounds bond to either two or three metal atoms, and that, although the coordination numbers of the 34 35 bridging carbon atoms in (AlPh3 )2 (isoBu2 AlCH = CH tert - Bu)2 , and (Me 36 BeC ≡ CMeNMe3 )2 are not unusual (4, 4, and 3, respectively) the (MC)2 rings 30 in these compounds (M represents the metal atom), like those in (AlMe 3 )2 6 INTRODUCTION: GENERAL ASPECTS

Me H CH2 3 H3 H3 C C C Li Li CH3 H C CH MeH2C CH2Me 3 Al Al 3 Mg Li Li Mg H3C Li H C CH3 3 C C C H Li Li H3C Li H3 3 H3 n MeH C CH Me 2 Li 2 Li CH3 C H2 Me

Al2Me 62 (MgMe )n (LiEt) 64 (LiMe)

Me tert-Bu-CH=CH C C Ph Ph isoBu isoBu Al Al Al Al Me N Me Ph Ph isoBu isoBu 3 Be Be Me NMe3 C HC=CH-tert-Bu C Me

Al2Ph 6 (isoBu2AlCH=CH-tert-Bu)2 [MeBe(Me3N)C CMe]2 Figure 1.1. Representative bridged metal alkyls, aryls, alkenyls, and alkynyls.

31 and (MgMe2 )n are held together by fewer electron pairs than two- center M – C links. n + Figure 1.2 shows the structures of various types of carbocations, Cx H y , + 20,23 including the highly reactive, unstable methonium cation (CH5 ), the + 37 hydrogen - bridged 1,6 - dimethylcyclodecyl cation (1,6 - Me2 C10 H17 ), the pyra- + 38,39 2 + 40 midal ions (1,2- Me 2 C5 H3 ) and (Me6 C6 ), the homoaromatic cation + 41 + 42 – 44 (C6 H9 ), and the 2 - norbornyl cation (C 7 H11 ) the structures of all of which were once the subjects of much debate. Although none of these structures has been determined by X - ray diffraction, good evidence for them was obtained from spectroscopic studies in solutions, 45,46 and the structures have subse- quently been supported by reliable calculations.47 – 49 (See further discussion in Chapter 5 , Sections 5.4 , 5.5 , and 5.6 ) There was never any doubt about the structures of the two metalla - carbocations also shown in Figure 1.2 , + 50,51 2 + 51,52 [C(AuPPh3 ) 5 ] and [C(AuPPh3 ) 6 ] , which may be regarded as per- + 2 + metallated derivatives of the elusive cations CH 5 and CH 6 , in which the hydrogen atoms have been replaced by AuPPh3 units. Also shown in Figure 1.2 (b) are the structures of the carbocationic transition states through which + + the classically bonded carbocations isoPrCMe2 and tert - BuCMe2 can undergo degenerate rearrangement, that is, rearrangement in which migration of an atom or group from one atom to another generates a product equivalent but not identical to the original. Figure 1.3 shows the structures of some deltahedral (i.e., triangular- faced polyhedral) carboranes , 8 – 10,53 – 61 mixed clusters of boron and carbon with BBB, BBC, or BCC faces. Each carbon atom in these cluster compounds has a hydrogen atom attached to it by a bond pointing away from the center of the cluster, but otherwise uses its three remaining valences to bond to the STRUCTURES OF SOME TYPICAL HYPERCARBON SYSTEMS 7

H2 (a) H3C C H H H H CC * + * * + C* H + H C H * 2 C CH2 H H H3C * H + + + CH5 1,6-Me2C10H17 C6H9

2+ Me + Me * C * C Me CCMe HC CH MeC CMe + HC CMe C * * Me + + 2+ C7H11 1,2-Me2C5H3 Me6C6

L + L Au Au 2+ C LAu AuL * C* LAu AuL LAu AuL Au LAu AuL L + 2+ [C(AuPPh3)5] [C(AuPPh3)6]

(b) H H H + Me + Me + C C Me CCMe CC Me Me Me Me Me Me Me * * Me + Me4C2H

Me Me Me + Me + Me + C C Me CCMe CC Me Me Me Me Me Me Me * * Me + Me5C2 Figure 1.2. Carbocations containing hypercarbon atoms. (a) Carbocations; (b) carbocationic intermediates or transition states (* denotes hypercarbons). four or fi ve neighboring boron or carbon atoms. The examples chosen include some with fi ve - or six - coordinate carbon atoms (C 2 B4 H 6 , C2 B5 H7 , C2 B10 H 12 ) and others (C 2 B3 H5 , C2 B5 H7 ) where the environment (and bonding) of the carbon atoms is similar, although they are only four coordinate. Despite the generally high coordination numbers of their carbon atoms, many carboranes are now known that are highly thermally and oxidatively stable substances, with a vast derivative chemistry and potential for a variety of applications in pure and applied chemistry and in materials and biological sciences. 8 INTRODUCTION: GENERAL ASPECTS

H H H C C B H H H H H B B B B B H B H B H B H B H B B H C C H C H H H

1,5-C2B3H5 1,6-C2B4H6 CB5H7 H H H H C H H H C H B H H B B C H B B B B B H Me H B C B H B H H C C H B B H C H C B B B B H B Me H B H B H H H H B B H H H H H – 1,2-C2B3H 7 2,3-Me2C2B4H 5 2,4-C2B5H 7 1,2-C2B10H12 Figure 1.3. Some carboranes.

Figure 1.4 shows the structures of some mixed metal – carbon clust- ers .8,9,11,12,14,27 Their shapes closely resemble those of the carboranes just men- tioned, a resemblance we shall fi nd of considerable signifi cance. It is also apparent that the polyhedral (generally deltahedral) examples chosen [Fe 3 62 63 64 (CO)9 C2 Ph2 , Co 4 (CO) 10 C2 Et2 , and Fe3 (CO)8 C4 Ph4 ] have many features in common with the cyclopentadienyl- , cyclobutadiene- , and butadiene- metal complexes (C5 H5 )Mn(CO)3 , (C 4 H4 )Fe(CO)3 , and (C 4 H6 )Fe(CO)3 also shown. The family relationship that extends from carboranes through mixed metal – carbon clusters to metal complexes of aromatic ring systems like the cyclopen- − 10,65 tadienide anion (C5 H5 ) also extends to aromatic ring systems themselves. In Figure 1.5 , we show the structures of some metal carbide clusters , 11,12 compounds in which hypercarbon atoms are embedded in polyhedra (such as square pyramids,66 octahedra, 67 trigonal prisms, 68 or square antiprisms 69 ) of metal atoms. Although these carbon clusters may appear to be remote from typical organic systems, they illustrate clearly the capacity of carbon atoms to bond simultaneously to fi ve, six, or, even eight neighboring atoms, and provide useful models for what may be the key species in Fischer– Tropsch and related chemistry at metal surfaces. The carbon atoms of carbon monoxide may undergo conversion at metal surfaces into carbide environments such as these, through which loss of carbon to the bulk metal or ultimate conversion into hydrocarbons may take place.

The carbon atoms of most binary metal carbides M x Cy have hypercoordi- nated environments like those shown in Figure 1.5 . In particular, octahedral carbon coordination is common in the interstitial carbides formed by many transition metals, materials of variable composition in which carbon atoms STRUCTURES OF SOME TYPICAL HYPERCARBON SYSTEMS 9

H Ph

C C* Ph M Ph OC C* *C M C* H M C* Ph M M C C Ph M Ph * M' * M M CO M

Fe3(CO)9C2Ph2 Co4(CO)10C2Et23 Fe (CO)8C4Ph4 [M = Fe(CO)3] [M = Co(CO)23] [M = Fe(CO) ] [M' = Fe(CO)2]

R Me M Me H * M * H C C* *C C C R C M C C C OH H C H HO M C* M * * * H * 5 Co2(CO)6C2R2 Fe2(CO)6(CMe)2(COH)2 (η -C5H5)Mn(CO)3 [M = Co(CO)3] [M = Fe(CO)3] [M = Mn(CO)3]

M M H H H C H H CC H C C H C * * * * C * C * * * H H H 4 4 Fe(CO)3(η -C4H4) Fe(CO)3(η -CH2=CH-CH=CH2) [M = Fe(CO)3] [M = Fe(CO)3] Figure 1.4. Mixed metal – carbon cluster compounds (metal – hydrocarbon π complexes) ( * denotes hypercarbons).

occupy interstices in the metal lattice that may suffer little distortion, even though the carbon valence shell electrons enter the metal valence band and so modify (and commonly strengthen) the .13 Both octahedral and distorted trigonal prismatic arrangements of atoms about carbon atoms are believed to feature in the various iron carbide phases that are so important in iron and steel production. Mankind has been exploiting the ben- efi cial aspects of carbon hypercoordination, albeit unrecognized as such, since the dawn of the Iron Age. To conclude this brief survey of the various types of compound known to contain hypercarbon atoms, Figure 1.6 shows examples of compounds in which coordinatively unsaturated metal atoms (metal atoms with fewer electrons in the valence shell than can be accommodated in a low - energy vacant AO) form strong agostic bonding interactions with neighboring C – H groups, effectively forming 3 c – 2 e CHM bonds (where M is the metal). The term “ agostic ” was adopted for these systems (from the Greek “ to hold or clasp to oneself, as of 10 INTRODUCTION: GENERAL ASPECTS

M M M M C M' M M M *C * M M CO M'

Ru6(CO)17C Fe5(CO)15C [M = Ru(CO)3] [M = Fe(CO)3] [M' = Ru(CO)2]

M M M M * M M M C C* M M M M M M M 2– 2– Rh6(CO)15C Co8(CO)18C (metal carbide core only) [M = RhCO] (all edges CO bridged) Figure 1.5. Metal carbides ( * denotes hypercarbons). a shield ” ) 70 because the metal atoms distort the coordination spheres of the carbon atoms involved, drawing their CH units toward the metal, converting normal classically bonded carbon atoms into hypercarbon atoms. Such agostic systems attracted much interest because they showed how coordinatively unsaturated metal atoms could activate C– H bonds, not only in ligands already attached to the metal atom by another bond (generally a metal – carbon bond) but indeed by coordination to the σ - bonding electrons of otherwise uncoordi- nated alkanes. There is now a growing literature on what are referred to as σ complexes , complexes in which an H – E bond, where E = H, C, B, or Si, acts as a two - electron donor to a metal center. Such complexes are increasingly being seen as facilitating a variety of metathetical reactions at metal centers, as in σ - complex - assisted metathesis (sigma - CAM) reactions ,71 without the signifi cant changes in metal oxidation states that accompany more traditional explana- tions invoking successive oxidative addition and reductive elimination reactions.

1.4. THE THREE - CENTER BOND CONCEPT: TYPES OF THREE - CENTER BONDS

+ In Section 1.2 we noted that the bonding in CH 5 could be described in terms of three 2 c – 2 e C– H bonds and one 3 c – 2 e C - - - H - - - H bond. In Section 1.3 we noted that 3c – 2 e C - - - H - - - M bonds could account for agostic interactions between coordinatively unsaturated metal atoms and substituent alkyl groups, and indeed for metal – alkane σ complexes. Similarly, 3c – 2 e M - - - C - - - M bonds THE THREE-CENTER BOND CONCEPT: TYPES OF THREE-CENTER BONDS 11

M Os (CO) Cl H 4 Me 2 H2 P C M (CO)3 Os Os(CO)3 H C*H C M Me2P Ti 2 * H M * C Cl H H H H Cl Fe4H(CO)12CH Os3H(CO)10CH3 TiCl3(Me2PCH2)2Et [M = Fe(CO)3]

t-Bu Me2 C H C* C + 2 H Cl H N PPh PPh NC(t-Bu) 3 3 H Li Al 2 Ru Rh NC(t-Bu) * * H N 2 PPh3 PPh3 P P H C Ph Cl Ph 2 C C 2 2 Me * 2 t-Bu

+ RuCl2(PPh3)3 Rh(PPh3)3 LiAl[NC(tert-Bu)2]4

CMe Me C Me2 Cl * P * H PPh3 CMe CH2 P Ti Pd C H Me Me2 Br Cl P Ph3 Cl

Pd(CMe)4H(PPh3)2Br TiCl3[(Me2PCH2)2]CH3 Figure 1.6. Agostic systems containing carbon – hydrogen – metal 3c – 2 e bonds ( * denotes hypercarbons). can be used to account for the bridged structures of metal alkyls, alkenyls, and aryls (Fig. 1.1 ). The hydrogen bridge across the middle of the cyclodecyl ring + 37 in 1,6 - Me2 C 10 H17 (Fig. 1.2 ) can be explained by a 3c – 2 e C – H – C bond. Such bond schemes, illustrated in Figure 1.7 , show that 3 c – 2 e C - - - C - - - C, C - - - C - - - B, or C - - - B - - - B bonds may help us describe the bonding in pyramidal carbocations or carboranes, though resonance between several canonical forms (delocalization) may need to be invoked for the more symmetrical species. That section of the molecule over which delocalization of two- and three- center bonds occurs is represented by broken lines in Figure 1.7 . Details of such bonding schemes are discussed in later chapters dealing with specifi c categories of compound. Here, however, it is appropriate to attempt to put such systems in perspective by noting their relationship to other examples of 3 c – 2 e bonding, and by noting the characteristic features of such systems. The simplest known example of a 3 c – 2 e bond is that in the trihydrogen + cation (H3 ), the existence of which, in the gas , was fi rst demonstrated 12 INTRODUCTION: GENERAL ASPECTS

CH3 CH3 CH3 H C 3 Al CH3 Ph Ph Al Mg Mg Al Al H3C CH3 Ph Ph CH n CH3 3 CH3

Al2Me6 (MgMe2)n Al2Ph6

H2 H C H C 3 H H H CC C + + * + H H H C CH * H H 2 C 2 H3C H + + + CH5 C6H9 1,6-Me2C10H17

Me Me HC CMe C C + + CMe H C C H H C C H C C C C HC CH H Me H Me

+ 1,2-Me2C5H3 Me Me

+ C + C

H C C H H C C H C C C C H Me H Me

H H

B – – B Me H Me H C B CB Me C B H Me C B H B B H H H H – 2,3-Me2C2B4H5

t-Bu Me2 Cl C C Os(CO)4 H + Me2 H H2C P 2 PPh C N NC(t-Bu)2 (CO)3Os Os(CO) 3 H H 3 P Ti NC(t-Bu) Rh CH2 H Li Al 2 C Me2 N PPh3 Cl H P Cl H H2C C H H Ph2 C Me2 t-Bu

+ Os3H(CO)10CH3 Rh(PPh3) 3 TiCl3(Me2PCH2)2Et LiAl[NC(tert-Bu)2]4 Figure 1.7. Two - and three - center – two - electron bonding schemes for representative compounds from Figures 1.1 to 1.6 .

by J. J. Thompson 72 in 1911 (even before G. N. Lewis formulated his electron- pair theory73 of chemical bonding). Later, much additional evidence was + 74 75 + obtained for H 3 even in solution chemistry (superacids). The H3 cation is the most abundant ion present when hydrogen gas is subjected to an electrical + + discharge. Its formation by the reaction H 2 + H2 → H 3 + H is some THE THREE-CENTER BOND CONCEPT: TYPES OF THREE-CENTER BONDS 13

Hydrogen Linear Bent Triangular AOs H H H HH H H H H

MO (iii)

MO (ii)

E

MO (i)

+ Figure 1.8. The H3 cation; possible geometries and MO energies.

40 kcal mol − 1 (170 kJ mol − 1 ) exothermic, 76 and this illustrates the power of two electrons to hold together three atomic nuclei at the corners of an equilateral triangle calculated to have an edge length of 0.87 Å ,76,77 some 0.12 Å longer than the single, 2 c – 2 e (0.75 Å ) in the dihydrogen molecule, H 2 . + 78 The 2c – 1 e bond in H 2 is 1.08 Å in length. These lengths refl ect the lower + + electron density in the H - - - H linkages in H2 and H3 compared with H2 . In three- center bonded systems in general, interatomic distances typically exceed those in related 2c – 2 e - bonded systems by about 0.15 – 0.25 Å . 27 + The three hydrogen nuclei in H3 are effectively held together by the elec- tronic charge that accumulates when the three hydrogen 1 s AOs mutually overlap (Fig. 1.8 ). A linear arrangement of the three nuclei would allow less effective overlap of the AOs involved, as the MO correlation diagram in Figure 1.8 indicates. Note how the energy of the occupied bonding MO (that which corresponds to the 3c – 2 e bond) decreases as the shape changes from linear to bent to equilateral triangular, strengthening the bonding interaction between what were originally the terminal hydrogen atoms. Vibrational spectroscopic and calculational studies have substantiated the equilateral triangular structure.74 Similar orbital correlation diagrams can be constructed for other sets of three atoms contributing comparable AOs, in particular for XHX systems where the atom X, a carbon, boron, or metal atom, for example, contributes a p or sp hybrid AO (Fig. 1.9 ), although the antibonding orbitals MO (ii) and MO (iii) would not then become equal in energy for the triangular structure. Provided that the triatomic system needs to accommodate only one pair of electrons, a triangular arrangement is again preferred because this strengthens the 3c – 2 e X - - - H - - - X bond [stabilizing orbital MO (i)] by increasing X - - - X bonding at no expense to X- - - H bonding interactions. However, if two electron pairs have to be accommodated, as in the case of classical hydrogen bonds79,80 14 INTRODUCTION: GENERAL ASPECTS

Atomic Linear Bent Triangular orbitals H H XXH X X XX MO (iii)

H 1s MO (ii) X hybrids E

MO (i)

Figure 1.9. Triatomic XHX systems in which X uses a hybrid AO; possible geom- etries and MO energies. with N – H - - - N, O – H - - - O, F – H - - - F, or similar units, then both MO (i) and MO (ii) will be occupied, and there is no incentive for the XHX system to bend, since any stabilization of MO (i) is offset by a greater destabilization of MO (ii), which is exclusively X- - - X antibonding. In classical hydrogen - bonded systems , where four electrons are involved, the unit X - - - H - - - X is linear, in contrast to the triangular shape preferred by the 3c – 2 e systems. (Many further examples of the way electron numbers infl uence molecular shape will be found in later chapters of this book, notably Chapters 3 and 4 ). A different triatomic system with which it is instructive to contrast these systems is the XCY linear triatomic unit that features in the transition state in an SN 2 reaction [Eq. (1.3) ]:

– 1 R1 R R1 X– Y X Y X (1.3) –Y– R3 R3 2 R2 R R3 R2

The carbon atom in the transition state is fi ve- coordinate, and might at fi rst sight appear to be pentavalent by apparently accommodating fi ve pairs of electrons in its valence shell. However, this is not the case. First - row elements like carbon have no suitable low - energy AOs available to allow a total of 10 valence shell electrons.81,82 In the transition state, the carbon atom can be assumed to use three sp 2 hybrid AOs to form classical 2c – 2 e bonds to the substituents R1 , R2 , and R3 , and we can treat it as a carbenium ion, R1 R 2 R 3 C + , sandwiched between the incoming nucleophile, X −, and the leaving group, Y − , THE THREE-CENTER BOND CONCEPT: TYPES OF THREE-CENTER BONDS 15

R1 MO (iii) X Y (antibonding)

2 R R3

R1 (nonbonding; MO (ii) X Y no contribution 2 from carbon AO) R R3

R1 MO (i) X Y (bonding)

2 R R3 Figure 1.10. MOs involving the fi ve - coordinate carbon atom in the transition state in an SN 2 reaction. with which it can interact using its vacant 2 p AO. The MO diagram for this system is shown in Figure 1.10 . Once again, there is one strongly bonding MO, MO (i), formed from the carbon 2p AO and an out - of - phase combination of X − and Y − AOs, corresponding to a linear 3c – 2 e bond. The next MO, MO (ii), has no contribution from the carbon 2 p AO, because it consists of an in- phase combination of the orbitals on X and Y, a combination of the wrong symmetry to combine with the carbon p AO. It is this MO, sharing a pair of electrons between X and Y but not involving the carbon atom, that accommodates the second pair of electrons in the triatomic system (X − and Y − contribute a pair apiece). These electrons therefore do not add to the four pairs already associ- ated with the carbon atom’ s valence shell. The (XCR 1 R 2 R 3 Y) − system just discussed, and the classical hydrogen bonds mentioned earlier, are examples of triatomic systems that have to accommo- date two pairs of electrons, each atom contributing one AO (see also Reference 83 ). There are many other systems in which two pairs of electrons fulfi ll a bonding role between three atomic nuclei, but in which one or more of the atoms contributes more than one AO with which to bond to its two neighbors. The various possibilities for hydrocarbon systems are shown in Figure 1.11 , together with some classically bonded systems. The numbers of electrons and AOs listed are those available to link the three atoms concerned, the other AOs being used for σ bonds to hydrogen or carbon atoms. From Figure 1.11 (a), (i) – (iii), it is evident that 3c – 2 e σ bonding can occur between three carbon atoms, or between two carbon atoms and a hydrogen atom, in circumstances where (1) there is no other bonding between the three atoms concerned, (2) two of the atoms are linked by a single (2 c – 2 e) bond as well, or (3) two of the atoms are linked by a double (2 c – 4 e ) bond as well. The requirements for 3c – 2e bonding are thus: Either all three atoms concerned con- tribute one AO apiece, or one of the atoms concerned contributes only one AO, 16 INTRODUCTION: GENERAL ASPECTS

(a)

H H H + (i) (3c–2e) systems using three AOs +

+ + + alkonium ions such as CH5 ; + C2H7 or cyclodecyl, C10H19 , HHC 3c–2e bond type of cation; CHC 3c–2e bond

+ trishomocyclopropenium, C3H9 , type of cation; CCC 3c–2e bond

H (ii) + + (3c–2e) systems using five AOs

protonated ; 2-norbornyl type or alkylated alkene; CHC 3c–2e bond CCC 3c–2e bond

H + (iii) + (3c–2e) systems using seven AOs protonated alkyne; alkylated alkyne; CHC 3c–2e bond CCC 3c–2e bond

(b) H H H + H H + H H H + + allyl cation, C3H5 ; cyclopropenium cation, C3H3 ; a (3c–6e) system using seven AOs a (3c–8e) system using nine AOs

(c)

H H H H H H H H H H H H H H H H H H

propane, C3H8; cyclopropane, C3H6; , C3H4; a (3c–4e) system a (3c–6e) system a (3c–8e) system using four AOs using six AOs using eight AOs Figure 1.11. Three - center bonding possibilities for some cationic and neutral hydrocarbon systems. (a) Some σ delocalized systems; (b) some π delocalized systems; (c) some related electron - precise hydrocarbons. THE THREE-CENTER BOND CONCEPT: TYPES OF THREE-CENTER BONDS 17 and the total number of electrons available for bonding between the three atoms is one fewer than the number of AOs available. If each of the three atoms involved uses more than one AO, and if the number of electrons available is one fewer than the number of AOs, then 3c – 2 e π bonding can occur, as shown by the examples of the allyl and cycloprope- nium cations [Fig. 1.11 (b)]. The difference arises because the establishment of a framework of 2c – 2 e σ bonds between two or all three of the carbon atoms limits the three- center bonding to that arising from p AOs oriented perpen- dicular to the plane in which the carbon atoms lie. Also shown in Figure 1.11 (c), for purposes of comparison, are three neutral classically bonded hydrocarbons, propane, cyclopropane, and cyclopropene. For these systems, and for electron- precise systems in general, the number of electrons available for bonding (n ) is equal to the number of AOs available (and so precisely the right number to fi ll the n /2 bonding MOs). Note that the systems in Figure 1.11 that have 3c – 2 e bonds, whether σ [Fig. 1.11 (a)] or π [Fig. 1.11 (b)], are cationic , as is necessary if the number of AOs is to exceed the numbers of electrons available. Noting this allows us to envis- age carbocations and their neutral hydrocarbon precursors or products of their possible decomposition (Fig. 1.12 ), points that will prove relevant to a consid- eration of the mechanisms of reactions involving hypercarbon intermediates or transition states. Thus, protonation of a 2 c – 2 e C– H bond can be envisaged as a means of generating a 3 c – 2 e CHH bond, while protonation of a 2c – 2 e C – C bond can in principle to a 3 c – 2 e CHC bond. Similar protonation of a carbon – carbon multiple bond, whether double or triple, converts a pair of carbon – carbon π - bonding electrons into a pair of 3c – 2 e C - - - H - - - C σ - bonding electrons. Figure 1.12 also serves as a reminder that carbocationic species requiring a 3c – 2 e C - - - H - - - C or C - - - C - - - C bond may revert to, or indeed be less stable than, a classically bonded carbenium ion structure in which one of the available AOs remains unused (as a 2p AO on the carbocationic center, ori- ented perpendicular to the plane of the σ bonds to that center). Before turning from a consideration of three- center bond systems to ones in which the bonding is more delocalized, it is worth noting briefl y what other types of systems exhibit 3c – 2 e σ bonding, to set these carbon systems in a more general context. We have already noted that bridged metal alkyls and aryls exhibit 3c – 2 e M - - - C - - - M bonding (where M is an electropositive metal atom, Figure 1.1 ) and that coordinatively unsaturated metal atoms can convert 2 c – 2 e C– H bonds into 3 c – 2 e C - - - H - - - M bonds (Fig. 1.6 ). These and the various other three- center bonding possibilities open to organometallic systems are sum- marized in Figure 1.13 , which shows the relationship between the systems already mentioned and metal – alkene or metal – alkyne complexes, and - ated metal– carbenes and metal– carbynes. It should be mentioned, however, that although the metal– alkene and metal – alkyne interactions shown in Figure 1.13 indicate the type of weak bonding that the coordinatively unsaturated metal atoms of monomeric aluminum trialkyls AlR3 can participate in with alkenes or alkynes, they show only part of the metal– carbon bonding that (a)

H H + H + H + H H H H -H H H H H 2 H + + CH4 CH5 CH3

H H H H H H H H+ H H H + + -CH3 H H H H H H H + C2H6 C2H7 CH4

H H H H + H H H H H CH3 + H + H H -CH3 H H H H H H H H H + C2H6 C3H9 C2H6

(b) H + H H H H+ H H + H

H H H H H H H + + C2H4 C2H5 C2H5

H H H H H H H H CH + 3 + + H H H H H H H H H H + + C2H4 C3H7 C3H7

(c) H H+ + H + H H H H H H + + C2H2 C2H3 C2H3

H H + H H + CH3 H H H H + H H H H + + C2H2 C3H5 C3H5 (will rearrange to an allyl cation) Figure 1.12. Different types of hypercoordinated carbocations; formation from hydrocarbon precursors by protonation or alkylation and cleavage products. (a) Three - center – two electron (3c – 2 e ) systems; (b) three - center – four electron (3c – 4 e ) systems; (c) three - center – six electron (3 c – 6 e ) systems.

18