CalculationOfNMRAndEPRParameters TV pdf Martin Kaupp, Michael Bühl, Vladimir G Malkin Calculation of NMR and EPR Parameters Calculation of NMR and EPR Parameters Theory and Applications Edited by Mart[.]
Martin Kaupp, Michael Bühl, Vladimir G Malkin Calculation of NMR and EPR Parameters Calculation of NMR and EPR Parameters Theory and Applications Edited by Martin Kaupp, Michael Bühl, Vladimir G Malkin Copyright 2004 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 3-527-30779-6 Further Titles of Interest: J Gasteiger (Ed.) Handbook of Chemoinformatics From Data to Knowledge Volumes 2003, ISBN 3-527-30680-3 Ch Schorn NMR Spectroscopy: Data Acquisition 2nd Edition 2004, ISBN 3-527-31070-3 F Gerson, W Huber Electron Spin Resonance Spectroscopy of Organic Radicals 2003, ISBN 3-527-30275-1 O Zerbe (Ed.) BioNMR in Drug Research 2003, ISBN 3-527-30465-7 P Carloni, F Alber (Eds.) Quantum Medicinal Chemistry 2003, ISBN 3-527-30456-8 D M Grant, R K Harris (Eds.) Encyclopedia of Nuclear Magnetic Resonance Volumes 2002, ISBN 0-470-84784-0 Martin Kaupp, Michael Bühl, Vladimir G Malkin Calculation of NMR and EPR Parameters Theory and Applications Editors Prof Dr Martin Kaupp Institute of Inorganic Chemistry University of Würzburg Am Hubland 97074 Würzburg Germany Priv Doz Dr Michael Bühl Max-Planck-Institute for Coal Research Kaiser-Wilhelm-Platz 45470 Mülheim an der Ruhr Germany Dr Vladimir G Malkin, DrSc Institute of Inorganic Chemistry Slovak Academy of Sciences Dubravska cesta SK-84536 Bratislava Slovak Republic & This book was carefully produced Nevertheless, editors, authors and publisher not warrant the information contained therein to be free of errors Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate Library of Congress Card No applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at 2004 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form – nor transmitted or translated into machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law Printed in the Federal Republic of Germany Printed on acid-free paper Typesetting Kühn & Weyh, Satz und Medien, Freiburg Printing betz-druck GmbH, Darmstadt Bookbinding Buchbinderei J Schäffer GmbH & Co KG, Grünstadt ISBN 3-527-30779-6 V Contents Foreword XIII List of Contributors XV Part A Introductory Chapters Introduction: The Quantum Chemical Calculation of NMR and EPR Parameters Martin Kaupp, Michael Bühl, and Vladimir G Malkin Theory of NMR parameters From Ramsey to Relativity, 1953 to 1983 Pekka Pyykkö Introduction Spin–Spin Coupling Chemical Shifts 11 General Aspects 13 From 1983 to 2003 15 2.1 2.2 2.3 2.4 2.5 Historical Aspects of EPR Parameter Calculations Frank Neese and MarkØta L Munzarovµ The Effective Spin Hamiltonian Concept from a Quantum Chemical Perspective 33 Gerald H Lushington Fundamentals of Nonrelativistic and Relativistic Theory of NMR and EPR Parameters 43 Werner Kutzelnigg Introduction 43 5.1 5.2 5.3 21 Classical Theory of the Interaction of a Charged Particle with an Electromagnetic Field 44 Quantum Mechanical Hamiltonians in a Time-Independent Electromagnetic Field 50 Calculation of NMR and EPR Parameters Theory and Applications Edited by Martin Kaupp, Michael Bühl, Vladimir G Malkin Copyright 2004 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 3-527-30779-6 VI Contents 5.4 5.5 5.6 5.7 5.8 Perturbation Theory of Magnetic Effects 58 Non-Relativistic Theory of EPR and NMR Parameters Relativistic Theory of Magnetic Properties 69 The Leading Relativistic Corrections 72 Concluding Remarks 81 62 Part B NMR Parameters, Methodological Aspects 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7.1 7.2 7.3 7.4 8.1 8.2 8.3 8.4 8.5 8.6 9.1 9.2 9.3 9.4 Chemical Shifts with Hartree–Fock and Density Functional Methods Christoph van Wüllen Introduction 85 Linear Response and the Gauge Origin Problem 88 Determination of the First-Order Orbitals 90 Distributed Gauge Origins, IGLO and GIAO Approaches 92 85 Distributed Gauge Origins in Real Space, a “Continuous Set of Gauge Transformations” 96 Beyond Pure Density Functional Theory 97 Conclusions 99 Spin–Spin Coupling Constants with HF and DFT Methods Trygve Helgaker and Magdalena Pecul Introduction 101 101 The Calculation of Indirect Nuclear Spin–Spin Coupling Constants Examples of Applications 115 Conclusions 119 102 Electron-Correlated Methods for the Calculation of NMR Chemical Shifts Jürgen Gauss and John F Stanton Introduction 123 Theoretical Background 125 Electron-Correlated Treatment of NMR Chemical Shifts 132 Special developments 133 Numerical Results 134 Summary and Outlook 136 123 Semiempirical Methods for the Calculation of NMR Chemical Shifts Thomas Heine and Gotthard Seifert Introduction 141 Methods 142 Representative Applications 147 141 Concluding Remarks: Limitations of Semiempirical Methods for the Calculation of NMR Parameters 151 Contents 10 10.1 10.2 10.3 10.4 10.5 11 11.1 11.2 11.3 11.4 12 12.1 12.2 12.3 12.4 12.5 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 14 14.1 14.2 Ro-Vibrational Corrections to NMR Parameters Torgeir A Ruden and Kenneth Ruud Introduction 153 Perturbation Theory 154 153 Other Approaches for Calculating Vibrationally Averaged NMR Properties 163 Examples of Vibrational Contributions to NMR Properties 164 Summary 171 Molecular Dynamics and NMR Parameter Calculations Debra J Searles and Hanspeter Huber Introduction 175 Methods 176 Examples 182 Summary and Conclusions 187 175 Use of Continuum Solvent Models in Magnetic Resonance Parameter Calculations 191 Ilaria Ciofini Introduction 191 General Features of Continuum Models 192 Applications of Continuum Models to the Prediction of NMR Parameters 197 Applications of Continuum Models to the Prediction of EPR Parameters 201 Conclusions 205 Perturbational and ECP Calculation of Relativistic Effects in NMR Shielding and Spin–Spin Coupling 209 Juha Vaara, Pekka Manninen, and Perttu Lantto Introduction 209 Nuclear Shielding and Spin–Spin Coupling 210 Electronic Hamiltonian 211 Non-Relativistic Contributions 212 Relativistic Kinematics and the Spin–Zeeman Effect 213 Spin–Orbit Coupling 216 Relativistic Corrections to Shielding and Coupling 217 Conclusions 223 Calculation of Heavy-Nucleus Chemical Shifts Relativistic All-Electron Methods 227 Jochen Autschbach Introduction 227 Methodological Aspects 229 VII VIII Contents 14.3 14.4 Computational Results Summary 244 15 Relativistic Calculations of Spin–Spin Coupling Constants of Heavy Nuclei 249 Jochen Autschbach and Tom Ziegler Introduction 249 Methodological Aspects 251 Computational Results 253 Summary 262 15.1 15.2 15.3 15.4 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 17 17.1 17.2 17.3 17.4 18 18.1 18.2 18.3 18.4 19 19.1 19.2 19.3 19.4 19.5 234 Calculations of Magnetic Resonance Parameters in Solids and Liquids Using Periodic Boundary Conditions 265 Chris J Pickard and Francesco Mauri Introduction 265 Cluster Approaches to Extended Systems 265 The Limitations of the Cluster Approach 266 Infinite Crystals, Periodic Boundary Conditions 267 Magnetic Resonance Parameters within Periodic Boundary Conditions 267 Applications of the Planewave-GIPAW Method 272 Work in Progress and Future Challenges 275 Conclusion 276 Calculation of Nuclear Quadrupole Coupling Constants 279 Peter Schwerdtfeger, Markus Pernpointner, and Witold Nazarewicz Introduction 279 Nuclear Quadrupole Moments 282 Field Gradients from Ab Initio Calculations 285 Field Gradients from Density Functional Calculations 288 Interpretation of NMR Chemical Shifts Martin Kaupp Introduction 293 Nonrelativistic Case 295 Relativistic Effects 302 Concluding Remarks 305 293 Interpretation of Indirect Nuclear Spin–Spin Coupling Constants Olga L Malkina Introduction 307 The Dirac Vector Model of Spin–Spin Coupling 309 Decomposition into Individual Contributions 310 Visualization of Coupling by Real-Space Functions 318 Conclusions 323 307 Contents 20 20.1 20.2 20.3 20.4 20.5 First-Principles Calculations of Paramagnetic NMR Shifts Seongho Moon and Serguei Patchkovskii Introduction 325 325 Paramagnetic Shielding Tensor: The General Case Treatment 326 Paramagnetic Shielding for an Isolated Kramers Doublet State 330 Practical Applications 333 Conclusions 337 Part C NMR Parameters, Applications 21 21.1 21.2 21.3 21.4 21.5 21.6 22 22.1 22.2 22.3 22.4 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 24 24.1 24.2 24.3 24.4 NMR Parameters in Proteins and Nucleic Acids David A Case Introduction 341 Chemical Shifts, Classical Models 342 341 Chemical Shifts Calculations on Polypeptides and Proteins Chemical Shifts in Nucleic Acids 346 Indirect Spin–Spin Couplings in Biomolecules 347 Conclusions 349 345 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants across Hydrogen Bonds Using Ab Initio EOM-CCSD Calculations 353 Janet E Del Bene Introduction 353 Methods 354 Discussion 355 Concluding Remarks 369 Calculation of NMR Parameters in Carbocation Chemistry Hans-Ullrich Siehl and Valerije Vrcˇek Introduction 371 Alkyl and Cycloalkyl Cations 372 Bicyclic and Polycyclic Carbocations 379 Vinyl Cations 382 p-Stabilized Carbocations 384 Heteroatom Stabilized Carbocations 388 Conclusions 391 371 Aromaticity Indices from Magnetic Shieldings 395 Zhongfang Chen, Thomas Heine, Paul v R Schleyer, and Dage Sundholm Introduction 395 An Overview of Aromaticity Indices Based on Magnetic Shielding 395 Applications 401 Outlook 405 IX X Contents 25 Fullerenes 409 Thomas Heine 25.1 25.2 Introduction 409 Efficient Computation of NMR Parameters of Fullerenes and Their Derivatives 410 Classical IPR Fullerenes 411 13 C NMR Spectra of Isomeric Fullerene Addition Compounds Endohedral Fullerenes 414 Fullerene Dimers and Dimer-like Compounds 416 Solid State NMR of Fullerenes 418 Summary and Perspectives 418 25.3 25.4 25.5 25.6 25.7 25.8 26 26.1 26.2 26.3 26.4 26.5 26.6 27 27.1 27.2 27.3 27.4 27.5 28 28.1 28.2 28.3 28.4 28.5 28.6 NMR of Transition Metal Compounds 421 Michael Bühl Introduction 421 Ligand Chemical Shifts 422 Metal Chemical Shifts 424 Spin–Spin Coupling Constants 427 Miscellaneous 428 Conclusion and Outlook 429 Characterization of NMR Tensors via Experiment and Theory Roderick E Wasylishen Introduction 433 Magnetic Shielding and Chemical Shifts 434 Nuclear Spin–Spin Coupling 439 NMR Spectra of Quadrupolar Nuclei in Solids 443 Conclusions 444 29.1 29.2 433 Calculations of Nuclear Magnetic Resonance Parameters in Zeolites 449 Annick Goursot and DorothØe Berthomieu Introduction 449 Theoretical Methods 451 NMR of Framework Elements: Structure Characterization 453 H NMR: Acidity and Proton Transfer 455 NMR Studies of Guest Molecules in Zeolites: in situ NMR 457 Conclusions 459 Part D EPR Parameters, Methodological Aspects 29 413 DFT Calculations of EPR Hyperfine Coupling Tensors MarkØta L Munzarovµ Introduction 463 Theoretical Background 464 463 Contents 29.3 29.4 The Performance of the Model Concluding Remarks 479 30 Ab Initio Post-Hartree–Fock Calculations of Hyperfine Coupling Tensors and Their Comparison with DFT Approaches 483 Bernd Engels Introduction 483 Problems Appearing in MR-CI Computations of Aiso 485 Error Cancellations in Computations of Aiso with DFT 489 Concluding Remarks 491 30.1 30.2 30.3 30.4 31 31.1 31.2 31.3 31.4 31.5 31.6 32 32.1 32.2 32.3 32.4 32.5 Alternative Fermi Contact Operators for EPR and NMR Vitaly A Rassolov and Daniel M Chipman Introduction 493 Derivation of New Alternative Operators 494 493 Formal Properties of Short-Range Alternative Operators EPR Calculations 499 NMR Calculations 501 Conclusions 503 Ab Initio Calculations of g-Tensors Gerald H Lushington 34 Zero-Field Splitting 541 Frank Neese Introduction 541 533 Zero-Field Splittings in EPR Spectroscopy Theory of Zero-Field Splittings 552 Calculation of Zero-Field Splittings 557 Conclusions 561 542 Part E EPR Parameters, Applications 35 35.1 496 Calculation of EPR g-Tensors with Density Functional Theory 505 Serguei Patchkovskii and Georg Schreckenbach Introduction 505 The Physical Origin of the g-Tensor 506 DFT Expressions for g-Tensors of Isolated Molecules 508 Numerical Performance of the DFT Approaches 519 Summary and Outlook 530 33 34.1 34.2 34.3 34.4 34.5 467 Computation of Hyperfine Coupling Tensors to Complement EPR Experiments 567 Fuqiang Ban, James W Gauld, and Russell J Boyd Introduction 567 XI XII Contents Insight Gained from a Conventional Ab Initio Approach 568 Benchmark Results Using Conventional Methods on Static Gas-phase Structures 568 The Performance of Contracted Pople Basis Sets for Small Radicals Consisting Only of First-Row Atoms 570 Density Functional Theory: An Alternative to a Conventional Ab Initio Approach 571 Consideration of Environmental Effects 572 Illustration of the Applications of DFT Methods to Biological Radicals 574 Summary 578 35.2 35.3 35.4 35.5 35.6 35.7 35.8 36 Applications to EPR in Bioinorganic Chemistry Frank Neese Introduction 581 Biological Metal Sites 582 Concluding Remark 589 36.1 36.2 36.3 Index 593 581 XIII Foreword It is difficult to overemphasize the importance of magnetic resonance techniques in chemistry Experimental spectra can usually be successfully interpreted empirically, but more difficult cases require a prediction based on the electronic structure In the last 25 years the calculation of magnetic resonance parameters from first principles has become a powerful research tool that can significantly enhance the utility of magnetic resonance techniques when empirical interpretations are insufficient This can be crucial even for NMR spectra of organic molecules, where the interpretations are the simplest and where empirical material has been collected for half a century Examples can be found in such diverse fields as the identification of new fullerenes, the use of calculated chemical shifts as probes of peptide conformation, and the study of hydrogen bonding Calculations play an even more important role in the inorganic and organometallic fields, where empirical interpretations are far more difficult The ability to calculate NMR and EPR parameters also increases the efficacy of electronic structure calculations Computed energies of different structures are often too close to allow a unique identification of the stable isomer Calculated NMR spectra, however, are often significantly different, so that even simple calculations can lead to unambiguous identification in such cases The unprecedented improvement in the cost-effectiveness ratio of computers (about six orders of magnitude over the last 20 years), and the continuing fast pace of development, together with improved computational techniques, will certainly make the calculation of NMR and EPR parameters more routine and more widespread in the future This book, then, is particularly timely, edited as it is by three researchers of the younger generation who have themselves played an important role in the development and application of theoretical techniques The author list includes many of the original developers of improved theoretical methods, as well as a number of leaders in chemical applications, offering a comprehensive coverage of the field The calculation of NMR and EPR parameters is less straightforward than the calculation of most other molecular properties Understanding the source of these difficulties led ultimately to their successful solution In the theory of NMR chemical shifts, for instance, Hameka has clarified many of the concepts, paving the way to Ditchfield’s seminal work on Gauge-Independent (later Gauge-Including) Atomic Orbitals (GIAOs) However, computers and programs in the early seventies were Calculation of NMR and EPR Parameters Theory and Applications Edited by Martin Kaupp, Michael Bühl, Vladimir G Malkin Copyright 2004 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 3-527-30779-6 XIV Foreword not yet ready for calculations on chemically relevant larger molecules A renaissance in NMR chemical shift calculations began around a decade later, with the Individual Gauge for Localized Orbitals (IGLO) method developed by Kutzelnigg and coworkers, with a parallel development by Hansen and Bouman It took a few more years to show that the currently preferred GIAO method can achieve similar computational efficiency The calculation of hyperfine coupling parameters suffers from two major difficulties Firstly, electron correlation is important, particularly when the direct effect – due to the spin density of the unpaired orbital – vanishes for reasons of symmetry Much of our understanding of this problem is due to Davidson’s analysis The other problem is high basis set sensitivity, due to the local nature of the interaction A possible solution for Gaussian basis sets was calculated early on by Meyer; alternative methods are discussed in the present volume The calculation of spin-spin coupling constants has a long history but until very recently has received less attention than NMR shieldings, and therefore a summary of recent progress in the field is particularly welcome Another timely topic, both for chemical shifts and for spin-spin couplings, is the effect of relativity Because of its importance in inorganic chemistry, this has been in the forefront of recent theoretical work, and is well covered in several chapters The calculation of electric field gradients, necessary for predicting nuclear quadrupole coupling constants, complements the calculation of NMR parameters Some other recent topics of high interest include the theory of NMR in paramagnetic systems, and the calculation of EPR gtensors and zero-field splittings The interpretation of resonance parameters in terms of chemical concepts, although necessarily a somewhat arbitrary procedure, is important for the chemical community; its inclusion here fills a void The book covers a wide range of methods, from semi-empirical through density functional to highly accurate correlated wave functions where vibrational corrections become important The chapter on extended systems will no doubt help bridge the gap between the chemistry and the physics communities in this area The introductory chapters, written by distinguished scholars, will be particularly useful for anybody entering the field Finally, the application chapters provide broad coverage, and will be a valuable guide to future work In summary, this book promises to become the standard reference for the calculation of NMR and EPR parameters, and will undoubtedly stimulate research in this fascinating and important field Peter Pulay Jan 2004 Department of Chemistry and Biochemistry Fulbright College of Arts and Sciences University of Arkansas, Fayetteville, Arkansas XV List of Contributors Jochen Autschbach Department of Chemistry University of Buffalo State University of New York 312 Natural Sciences Complex Buffalo, NY 14260-3000 USA Fuqiang Ban Department of Chemistry Dalhousie University, Halifax Nova Scotia Canada B3H 4J3 Russell J Boyd Department of Chemistry & Biochemistry University of Windsor Windsor, Ontario Canada N9B 3P4 DorothØe Berthomieu UMR 5618 CNRS, ENSCM rue de l’Ecole Normale 34296 Montpellier CØdex France Michael Bühl Max-Planck-Institute for Coal Research Kaiser-Wilhelm-Platz 45470 Mülheim an der Ruhr Germany David A Case Department of Molecular Biology The Scripps Research Institute La Jolla, CA 92037 USA Zhongfang Chen Computational Chemistry Annex The University of Georgia Athens, GA 30602-2525 USA Daniel M Chipman Radiation Laboratory University of Notre Dame Notre Dame, IN 46556 USA Ilaria Ciofini Laboratoire d’Electrochimie et Chimie Analytique CNRS-UMR7575 Ecole Nationale SupØrieure de Chimie de Paris 11, Rue P et M Curie 75231 Paris France Janet E Del Bene Department of Chemistry Youngstown State University Youngstown, Ohio 44555 USA Calculation of NMR and EPR Parameters Theory and Applications Edited by Martin Kaupp, Michael Bühl, Vladimir G Malkin Copyright 2004 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 3-527-30779-6 XVI List of Contributors Bernd Engels Institute of Organic Chemistry University of Würzburg Am Hubland 97074 Würzburg Germany Martin Kaupp Institute of Inorganic Chemistry University of Würzburg Am Hubland 97074 Würzburg Germany James W Gauld Department of Chemistry & Biochemistry University of Windsor Windsor, Ontario N9B 3P4 Canada Werner Kutzelnigg Department of Theoretical Chemistry Ruhr-University Bochum 44780 Bochum Germany Jürgen Gauss Institute of Physical Chemistry University of Mainz 55099 Mainz Germany Perttu Lantto Department of Physical Sciences P.O Box 2000 90014 University of Oulu Finland Annick Goursot UMR 5618 CNRS, ENSCM, rue de l’Ecole Normale 34296 Montpellier CØdex France Thomas Heine Institute of Physical Chemistry and Electrochemistry Technical University of Dresden Mommsenstraße 13 01062 Dresden Germany Trygve Helgaker Department of Chemistry University of Oslo P.O Box 1033 Blindern 0315 Oslo Norway Hanspeter Huber Department of Chemistry The University of Basel Klingelbergstr 80 4056 Basel Switzerland Gerald H Lushington University of Kansas Molecular Graphics and Modeling Laboratory 1251 Wescoe Hall Dr Lawrence, KS 66045 USA Vladimir G Malkin Institute of Inorganic Chemistry Slovak Academy of Sciences Dubravska cesta SK-84536 Bratislava Slovak Republic Olga L Malkina Institute of Inorganic Chemistry Slovak Academy of Sciences Dubravska cesta SK-84536 Bratislava Slovak Republic Pekka Manninen Department of Chemistry P.O Box 55 (A.I Virtasen aukio 1) 00014 University of Helsinki Finland List of Contributors Francesco Mauri Laboratoire de MinØralogieCristallogr de Paris UniversitØ Pierre et Marie Curie tour 16, case 115 Place Jussieu 75252 Paris, Cedex 05 France Seongho Moon Department of Molecular Biology The Scripps Research Institute 10550 North Torrey Pines Road La Jolla, California 92037 USA MarkØta L Munzarovµ National Centre for Biomolecular Research Faculty of Sciences Kotlµrskµ 61137 Brno Czech Republic Witold Nazarewicz Department of Physics and Astronomy University of Tennessee 401 Nielsen Physics Building Knoxville, Tennessee 37996-1200 USA Frank Neese Max-Planck-Institute of Bioinorganic Chemistry Postfach 10 13 65 45470 Mülheim an der Ruhr Germany Serguei Patchkovskii Steacie Institute for Molecular Sciences National Research Council of Canada, 100 Sussex Drive Ottawa, Ontario K1A 0R6 Canada Magdalena Pecul Department of Chemistry University of Warsaw Pasteura 02-093 Warsaw Poland Markus Pernpointner Faculty of Chemistry Institute of Physical Chemistry Ruprecht-Karls-University of Heidelberg Im Neuenheimer Feld 229 69120 Heidelberg Germany Chris J Pickard University of Cambridge Cavendish Laboratory, TCM Group Madingley Rd Cambridge, CB3 OHE Great Britain Pekka Pyykkö Department of Chemistry P.O Box 55 (A.I Virtasen aukio 1) 00014 University of Helsinki Finland Vitaly A Rassolov Department of Chemistry and Biochemistry University of South Carolina 691 Sumter Street Columbia, SC 29208 USA Torgeir A Ruden Department of Chemistry University of Oslo P.O Box 1033 Blindern 0315 Oslo Norway XVII XVIII List of Contributors Kenneth Ruud Department of Chemistry University of Tromsø 9037 Tromsø Norway Paul von Rague Schleyer University of Georgia Department of Chemistry Athens, GA 30602-2556 USA Georg Schreckenbach University of Manitoba Winnipeg, Manitoba, R3T 2N2 Canada Peter Schwerdtfeger Department of Chemistry The University of Auckland Private Bag 92109, Auckland New Zealand Debra J Searles School of Science Griffith University Brisbane, Qld 4111 Australia Gotthard Seifert Institute of Physical Chemistry and Electrochemistry Technical University of Dresden Mommsenstr 13 01062 Dresden Germany Hans-Ullrich Siehl Department of Organic Chemistry I University of Ulm 89069 Ulm Germany John F Stanton Institute for Theoretical Chemistry Departments of Chemistry and Biochemistry The University of Texas at Austin Austin, TX 78712 USA Dage Sundholm Department of Chemistry P.O Box 55 (A.I Virtasen aukio 1) 00014 University of Helsinki Finland Juha Vaara Department of Chemistry P.O Box 55 (A.I Virtasen aukio 1) 00014 University of Helsinki Finland Christoph van Wüllen Technical University Berlin, Sekr C3 Straße des 17 Juni 135 10623 Berlin Germany Valerije Vrcek Faculty of Pharmacy and Biochemistry University of Zagreb A Kovacica 10000 Zagreb Croatia Roderick E Wasylishen Department of Chemistry Gunning/Lemieux Chemistry Centre University of Alberta Edmonton, Alberta T6G 2G2 Canada Tom Ziegler Department of Chemistry University of Calgary Calgary, Alberta T2N-1N4 Canada