Perspectives in Theoretical Stereochemistry PDF
Preview Perspectives in Theoretical Stereochemistry
Editors Prof. Dr. Gaston Berthier Prof. Dr. JOrgen Hinze Universite de Paris Fakultat fOr Chemie Institut de Biologie Universitat Bielefeld Physico-Chimique Postfach 8640 Fondation Edmond de Rothschild 0-4800 Bielefeld 13, rue Pierre et Marie Curie F-75005 Paris Prof. Dr. Hans H. Jaffe Department of Chemistry Prof. Dr. Michael J. S. Dewar University of Cincinnati Department of Chemistry Cincinnati, Ohio 45221/USA The University of Texas Austin, Texas 78712/USA Prof. Joshua Jortner Prof. Dr. Hanns Fischer Institute of Chemistry Physikalisch-Chemisches Institut Tel-Aviv University der Universitat ZOrich 61390 Ramat-Aviv Ramistr.76 Tel-Aviv/lsi\el CH-8001 ZOrich Prof. Kenichi Fukui Prof. Dr. Werner Kutzelnigg Kyoto University Lehrstuhl fOr Theoretische Chemie Dept. of Hydrocarbon Chemistry der Universitat Bochum KyotolJ apan Postfach 102148 0-4630 Bochum 1 Prof. Dr. George G. Hall Department of Mathematics The University of Nottingham Prof. Dr. Klaus Ruedenberg University Park Department of Chemistry Nottingham NG7 2RO/Great Britain Iowa State University Ames, Iowa 50010/USA Prof. Dr. Hermann Hartmann Akademie der Wissenschaften und der Literatur zu Mainz Prof. Dr. Eolo Scrocco Geschwister-Scholl-StraBe 2 Via Garibaldi 88 0-6500 Mainz 1-00153 Roma Lecture Notes in Chemistry Edited by G. Berthier M. J. S. Dewar H. Fischer K. Fukui G. G. Hall H. Hartmann J. Hinze H. H. Jaffe J. Jortner W. Kutzelnigg K. Ruedenberg E. Scrocco 36 I. Ugi J. Dugundij R.Kopp D. Marquarding Perspectives in Theoretical Stereochem istry Springer-Verlag Berlin Heidelberg New York Tokyo 1984 Authors J.Dugundij Department of Mathematics, University of Southern California Los Angeles, CA 90089-1113, USA R. Kopp D. Marquarding t I. Ugi Organisch-Ghemisches Institut der Technischen Universit:at MOnchen 0-8046 Garching ISBN-13:978-3-540-13391-9 e-ISBN-13:978-3-642-93266-3 001: 10.1007/978-3-642-93266-3 Library of Congress Cataloging in Publication Data. Main entry under title: Perspectives in theoretical stereochemistry. (Lecture notes in chemistry; 36) Includes bibliographies and index. 1. Stereochemistry. I. Ugi,lvar, 1930-.11. Series. Q0481.P37 1984 541.2'23 84-14190 ISBN-13:978-3-540-10273-1 (U.S.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the Gennan Copyright Law where copies are made for other thamnnvate use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1984 2152/3140-543210 We dedicate this monogpaph to the memopy of ppofessop Dietep Mapquapding, ~ho died on 9 July 1982 at the age of 47. The theopy ppesented hepe owes much to his effopt: his extensive and deep insight into the natupe kno~ledge of stepeochemical ppocesses was dipectZy instpumentaZ in isolating and fopmulating many of oup concepts. The purpose of the mathematical physicists is not to calculate phenomena quantitatively but to understand them qualitatively. Their aim is to clarify with mathematical precision the meaning of the concepts upon which physical theories are built. Freeman J. Dyson "Unfashionable Pursuits" A. v. H. Stiftung Mitteilungen 41, 12 (1983) Where is mathematical chemistry? PRE F ACE This treatment of stereochemistry was developed in numerous joint discussions at the Technische Universit!t Munchen over the period 1976-1982. It is applicable to all molecules, flexible or rigid, and can be regardeo as a complement to the known algebraic treat ment of constitutional chemistry in terms of BE- and R-matrices. We extend our gratitude to Dr. John Showell, who helped us formulate and clarify some concepts; to Prof. Daniel S. Kemp, who critically analyzed the manuscript and proposed numerous changes and additions that improved the readability of this book; and to Profs. R. Bau, M. Gielen, K. Mislow, F. Ramirez, K. Sch!fer, Drs. J. Brandt, J. Gasteiger, W. Schubert and Mr. T. Damhus for their helpful comments. We wish to thank the Mss. Eva Nuytten, Sigrid Rossel, Herta SchOn mann, Inge Schwarz, Marina Thoma, Maria Ulkan, and Mr. Michael Capone for their patience and cheerful cooperation in the prepara tion, illustrations, revision, and proofreadings of the text, so well as Dr. J. Bauer, Mr. E. Fontain and Mr. K. Stadler for the development of computer software that was used in the production of this manuscript. The development of this book has gone througij many stages and versions over the years. We are very much indebted to Doz. Dr. Josef B£andt and Ms. Sigrid Minker who went alon9 all the way with us. This monograph would never have reached the present form without their creative contribution, diligence and patience in organizing, computer-editing, improving and preparing in final form the manus cript, despite a variety of adverse conditions, including the repeated breakdown of aged computer hardware. We gratefully acknowledge the generous financial support given to the project by the A. v. Humboldt Foundation, the Stiftung Volkswagenwerk e.V., and the Fonds der Chemischen Industrie. June, 1982 The Authors INTRODUCTION Stereochemistry is the part of chemistry that relates observable prop erties of chemical compounds to the structure of their molecules, i. e. the relative spatial arrangement of their constituent atoms. In classical stereochemistry, the spatial arrangements relevant for interpreting and predicting a given chemical property are customarily described by geometric features/ symmetries in some suitably chosen rigid model of the molecule The solution of stereochemical problems involving single molecular species is the danain of the geometry based approaches, such as the methods of classical stereochemistry, molecular mechanics and quantum chemistry. The molecules of a pure chemical compound form generally an ensemble of molecular individuals that differ in geometry and energy. Thus it is generally impossible to represent a chemical compund adequately by the geo metry of a rigid molecular model. In modern stereochemistry it is often necessary to analyze molecular relation within ensembles and families of stereoisomers and permutation isomers, including molecules whose geometric features are changing with time. Accordingly, there is definitely a need for new types of ideas, concepts, theories and techniques that are usable beyond the scope of customary methodology. This is why the present text was written. The majority of organic molecules studied in modern stereochemistry are flexible; depending on the observation conditions, they undergo a variety of internal motions which are mown to playa significant role in determining their chemical behavior. There may be no chemically meaningful VII rigid model that expresses the essential spatial features of such a molecule: for example, the fluxional motions of bullvalene [2] pass through arrangements that differ in chemical constitution, so that bull- valene cannot be meaningfully represented by any single, rigid model. elc. Moreover, even in cases where a flexible molecule can be described by a reasonable geometric model, the classical geometric considerations may not correctly predict the observed behaviour, as is illustrated by the mixed ester of (+) and (-)-menthol with 2,2',6,6'-tetra-nitro-4,4'-diphenic acid which was observed by Mislow [3] to be achiral, despite the fact that it has no conceivable achiral conformation (see I,2). Though various modifications and extensions of the classical geometry based stereochemical principles have been devised for treating individual flexible molecules [4], ~o single approach relying solely on geometry has been found to be universally applicable for describing the stereochemistry of such molecules which correspond to ensembles of interconverting con- formations. Indeed, the proliferation of ad hoc treatments for individual molecules has generated anbiguities and misunderstandings (see I). VIII Thus, there is a growing insight [5,6J that new ideas beyond geometry are needed to cope with the great variety of rigid and nonrigid stereo chemical systems. The purpose of this book is to provide a solid founda tion for a completely general and rigorous unified treatment of stereo chemistry. Though in special cases, our theory may be more ctmlbersome to use than the more familiar and less rigorous geometric, or energetic-geo- metrical methods, our theory is nevertheless applicable in all cases and can be used to dete:nnine the validity of conclusions reached by using either other models or simply ad hoc procedures. In our view, stereochemistry cannot be treated adequately by con sidering the molecular structure and the molecular chemistry separately. Rather, it is an interaction of these two features that is fundamental, and the basic concepts of stereochemistry should therefore reflect this inter action. To develop this viewpoint, we first need a precise way, applicable to all molecules, for describing the molecular structure relevant to a stereochemical question, and the rearrangements of this structure that will be considered and/or allowed. We accomplish this by considering a given molecule to consist of a set of n sites (called the molecular skeleton) and a set of n ligands, and defining a structure to be a placement of the ligands on the sites. In this representation of molecular struc ture, the skeleton need not be rigid, nor even contiguous; the placement of a spec ified ligand on a specified site is a well-defined operation, requiring only that the site be identifiable and not that it always be located at the same place in space. By pe:nnuting the ligands, we can then uniquely de scribe all the possible rearrangements of the molecular structure, even for flexible molecules. The pe:nnutation isomers of a given molecule are IX obtained by placing the ligands on the sites in all the possible different J. ways [7 Our fundamental notion is that of the chemical identity group. This is defined for molecules in which the ligands are all chemically distinguish able, and consists of all the ligand permutations that preserve the chemi cal identity of the given molecule. To describe its construction in heuris tic terms, let us assume that we have made a film of a (possibly flexible) molecule, and that we have selected a "snapShot" as a reference. A per mutation of the ligands on that reference is said to preserve the chemical identi ty of the molecule if the resulting molecule is geometrically identi cal to some frame in the film. The set of all such ligand permutations will form a group S, which we call the chemical identity group of the molecule. Note that we do not deal only with symmetries and geometries, as do the customary permutational approaches to stereochemistry: we use permu tations simply to express rearrangements of the ligands, and not a symmetry of some geometric system. Our chemical identity group expresses the geo metry/ chemistry interac tion in a given molecule; its construction for a given molecule requires knowledge of a momentary spatial arrangement, the manner in which that arrangement changes under the given observation con ditions, and the chemistry of the molecule. Al though S is obtained by con sidering the "least symmetric" molecule of a skeletal class, it can be used to obtain the stereochemistry of molecules in that skeletal class having sets of chemically indistinguishable ligands. The notions of chemical identity group and permutational isomerism provide the foundation for our formalization of stereochemistry. With this formalism, we can unambiguously express concepts relevant for stereo-
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