Calculation of and NMR EPR Parameters..doc

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Martin Kaupp, Michael B4hl,
Vladimir G. Malkin
Calculation of NMR and EPR Parameters
Calculation of NMR and EPR Parameters. Theory and Applications.
Edited by Martin Kaupp, Michael B4hl, 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
4 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
9 Volumes
2002, ISBN 0-470-84784-0

Martin Kaupp, Michael B4hl, Vladimir G. Malkin
Calculation of NMR
and EPR Parameters
Theory and Applications

Editors
Prof. Dr. Martin Kaupp
Institute of Inorganic Chemistry
University of W4rzburg
Am Hubland
97074 W4rzburg
Germany
Priv. Doz. Dr. Michael B4hl Max-
Planck-Institute for Coal Research
Kaiser-Wilhelm-Platz 1 45470
M4lheim an der Ruhr
Germany
Dr. Vladimir G. Malkin, DrSc.
Slovak Academy of Sciences
Dubravska cesta 9
SK-84536 Bratislava
Slovak Republic
& This book was carefully produced. Nevertheless,
editors, authors and publisher do 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
<http://dnb.ddb.de>.
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 trans-
lated into machine language without written
permis-sion from the publishers. Registered
names, trade-marks, 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 K4hn & Weyh, Satz und Medien,
Freiburg
Printing betz-druck GmbH, Darmstadt Bookbinding
Buchbinderei J. Schäffer GmbH & Co. KG,
Gr4nstadt
ISBN 3-527-30779-6

V
Contents
Foreword XIII
List of Contributors XV
Part A Introductory Chapters
1 Introduction: The Quantum Chemical Calculation of NMR
and EPR Parameters 3
Martin Kaupp, Michael B4hl, and Vladimir G. Malkin
2 Theory of NMR parameters. From Ramsey to Relativity, 1953 to 1983 7
Pekka Pyykk.
2.1 Introduction 7
2.2 Spin–Spin Coupling 9
2.3 Chemical Shifts 11
2.4 General Aspects 13
2.5 From 1983 to 2003 15
3 Historical Aspects of EPR Parameter Calculations 21
Frank Neese and MarkØta L. MunzarovQ
4 The Effective Spin Hamiltonian Concept from a
Quantum Chemical Perspective 33
Gerald H. Lushington
5 Fundamentals of Nonrelativistic and Relativistic Theory of NMR
and EPR Parameters 43
Werner Kutzelnigg
5.1 Introduction 43
5.2 Classical Theory of the Interaction of a Charged Particle with an
Electromagnetic Field 44
5.3 Quantum Mechanical Hamiltonians in a Time-Independent
Electromagnetic Field 50
ISBN: 3-527-30779-6

VI Contents
5.4 Perturbation Theory of Magnetic Effects 58
5.5 Non-Relativistic Theory of EPR and NMR Parameters 62
5.6 Relativistic Theory of Magnetic Properties 69
5.7 The Leading Relativistic Corrections 72
5.8 Concluding Remarks 81
Part B NMR Parameters, Methodological Aspects
6 Chemical Shifts with Hartree–Fock and Density Functional Methods 85
Christoph van W4llen
6.1 Introduction 85
6.2 Linear Response and the Gauge Origin Problem 88
6.3 Determination of the First-Order Orbitals 90
6.4 Distributed Gauge Origins, IGLO and GIAO Approaches 92
6.5 Distributed Gauge Origins in Real Space, a “Continuous Set of
Gauge Transformations” 96
6.6 Beyond Pure Density Functional Theory 97
6.7 Conclusions 99
7 Spin–Spin Coupling Constants with HF and DFT Methods 101
Trygve Helgaker and Magdalena Pecul
7.1 Introduction 101
7.2 The Calculation of Indirect Nuclear Spin–Spin Coupling Constants 102
7.3 Examples of Applications 115
7.4 Conclusions 119
8 Electron-Correlated Methods for the Calculation of NMR Chemical Shifts 123
J4rgen Gauss and John F. Stanton
8.2 Theoretical Background 125
8.3 Electron-Correlated Treatment of NMR Chemical Shifts 132
8.4 Special developments 133
8.5 Numerical Results 134
8.6 Summary and Outlook 136
9 Semiempirical Methods for the Calculation of NMR Chemical Shifts 141
Thomas Heine and Gotthard Seifert
9.2 Methods 142
9.3 Representative Applications 147
9.4 Concluding Remarks: Limitations of Semiempirical Methods for the
Calculation of NMR Parameters 151

Contents
10 Ro-Vibrational Corrections to NMR Parameters 153
Torgeir A. Ruden and Kenneth Ruud
10.2 Perturbation Theory 154
10.3 Other Approaches for Calculating Vibrationally Averaged
NMR Properties 163
10.4 Examples of Vibrational Contributions to NMR Properties 164
10.5 Summary 171
11 Molecular Dynamics and NMR Parameter Calculations 175
Debra J. Searles and Hanspeter Huber
11.2 Methods 176
11.3 Examples 182
11.4 Summary and Conclusions 187
12 Use of Continuum Solvent Models in Magnetic Resonance
Parameter Calculations 191
Ilaria Ciofini
12.2 General Features of Continuum Models 192
12.3 Applications of Continuum Models to the Prediction of NMR
Parameters 197
12.4 Applications of Continuum Models to the Prediction of EPR
Parameters 201
12.5 Conclusions 205
13 Perturbational and ECP Calculation of Relativistic Effects
in NMR Shielding and Spin–Spin Coupling 209
Juha Vaara, Pekka Manninen, and Perttu Lantto
13.2 Nuclear Shielding and Spin–Spin Coupling 210
13.3 Electronic Hamiltonian 211
13.4 Non-Relativistic Contributions 212
13.5 Relativistic Kinematics and the Spin–Zeeman Effect 213
13.6 Spin–Orbit Coupling 216
13.7 Relativistic Corrections to Shielding and Coupling 217
14 Calculation of Heavy-Nucleus Chemical Shifts.
Relativistic All-Electron Methods 227
Jochen Autschbach
14.2 Methodological Aspects 229
VII

VIII Contents
14.3 Computational Results 234
14.4 Summary 244
15 Relativistic Calculations of Spin–Spin Coupling Constants of
Heavy Nuclei 249
Jochen Autschbach and Tom Ziegler
15.2 Methodological Aspects 251
15.3 Computational Results 253
15.4 Summary 262
16 Calculations of Magnetic Resonance Parameters in Solids
and Liquids Using Periodic Boundary Conditions 265
Chris J. Pickard and Francesco Mauri
16.2 Cluster Approaches to Extended Systems 265
16.3 The Limitations of the Cluster Approach 266
16.4 Infinite Crystals, Periodic Boundary Conditions 267
16.5 Magnetic Resonance Parameters within Periodic Boundary
Conditions 267
16.6 Applications of the Planewave-GIPAW Method 272
16.7 Work in Progress and Future Challenges 275
16.8 Conclusion 276
17 Calculation of Nuclear Quadrupole Coupling Constants 279
Peter Schwerdtfeger, Markus Pernpointner, and Witold Nazarewicz
17.2 Nuclear Quadrupole Moments 282
17.3 Field Gradients from Ab Initio Calculations 285
17.4 Field Gradients from Density Functional Calculations 288
18 Interpretation of NMR Chemical Shifts 293
Martin Kaupp
18.2 Nonrelativistic Case 295
18.3 Relativistic Effects 302
19 Interpretation of Indirect Nuclear Spin–Spin Coupling Constants 307
Olga L. Malkina
19.2 The Dirac Vector Model of Spin–Spin Coupling 309
19.3 Decomposition into Individual Contributions 310
19.4 Visualization of Coupling by Real-Space Functions 318

Contents
20 First-Principles Calculations of Paramagnetic NMR Shifts 325
Seongho Moon and Serguei Patchkovskii
20.2 Paramagnetic Shielding Tensor: The General Case Treatment 326
20.3 Paramagnetic Shielding for an Isolated Kramers Doublet State 330
20.4 Practical Applications 333
Part C NMR Parameters, Applications
21 NMR Parameters in Proteins and Nucleic Acids 341
David A. Case
21.2 Chemical Shifts, Classical Models 342
21.3 Chemical Shifts Calculations on Polypeptides and Proteins 345
21.4 Chemical Shifts in Nucleic Acids 346
21.5 Indirect Spin–Spin Couplings in Biomolecules 347
22 Characterizing Two-Bond NMR 13
C–15
N, 15
N–15
N, and 19
F–
15
N Spin–Spin Coupling Constants across Hydrogen Bonds
Using Ab Initio EOM-CCSD Calculations 353
Janet E. Del Bene
22.2 Methods 354
22.3 Discussion 355
23 Calculation of NMR Parameters in Carbocation Chemistry 371
Hans-Ullrich Siehl and Valerije Vrcˇek
23.2 Alkyl and Cycloalkyl Cations 372
23.3 Bicyclic and Polycyclic Carbocations 379
23.4 Vinyl Cations 382
23.5 P-Stabilized Carbocations 384
23.6 Heteroatom Stabilized Carbocations 388
24 Aromaticity Indices from Magnetic Shieldings 395
Zhongfang Chen, Thomas Heine, Paul v. R. Schleyer,
and Dage Sundholm
24.2 An Overview of Aromaticity Indices Based on Magnetic Shielding 395
24.3 Applications 401
24.4 Outlook 405
IX

X Contents
25 Fullerenes 409
Thomas Heine
25.2 Efficient Computation of NMR Parameters of Fullerenes
and Their Derivatives 410
25.3 Classical IPR Fullerenes 411
25.4
13
C NMR Spectra of Isomeric Fullerene Addition Compounds 413
25.5 Endohedral Fullerenes 414
25.6 Fullerene Dimers and Dimer-like Compounds 416
25.7 Solid State NMR of Fullerenes 418
25.8 Summary and Perspectives 418
26 NMR of Transition Metal Compounds 421
Michael B4hl
26.2 Ligand Chemical Shifts 422
26.3 Metal Chemical Shifts 424
26.4 Spin–Spin Coupling Constants 427
26.5 Miscellaneous 428
26.6 Conclusion and Outlook 429
27 Characterization of NMR Tensors via Experiment and Theory 433
Roderick E. Wasylishen
27.2 Magnetic Shielding and Chemical Shifts 434
27.3 Nuclear Spin–Spin Coupling 439
27.4 NMR Spectra of Quadrupolar Nuclei in Solids 443
28 Calculations of Nuclear Magnetic Resonance Parameters in Zeolites 449
Annick Goursot and DorothØe Berthomieu
28.2 Theoretical Methods 451
28.3 NMR of Framework Elements: Structure Characterization 453
28.4
1
H NMR: Acidity and Proton Transfer 455
28.5 NMR Studies of Guest Molecules in Zeolites: in situ NMR 457
Part D EPR Parameters, Methodological Aspects
29 DFT Calculations of EPR Hyperfine Coupling Tensors 463
MarkØta L. MunzarovQ
29.2 Theoretical Background 464

Contents
29.3 The Performance of the Model 467
30 Ab Initio Post-Hartree–Fock Calculations of Hyperfine Coupling Tensors
and Their Comparison with DFT Approaches 483
Bernd Engels
30.2 Problems Appearing in MR-CI Computations of Aiso 485
30.3 Error Cancellations in Computations of Aiso with DFT 489
31 Alternative Fermi Contact Operators for EPR and NMR 493
Vitaly A. Rassolov and Daniel M. Chipman
31.2 Derivation of New Alternative Operators 494
31.3 Formal Properties of Short-Range Alternative Operators 496
31.4 EPR Calculations 499
31.5 NMR Calculations 501
32 Calculation of EPR g-Tensors with Density Functional Theory 505
Serguei Patchkovskii and Georg Schreckenbach
32.2 The Physical Origin of the g-Tensor 506
32.3 DFT Expressions for g-Tensors of Isolated Molecules 508
32.4 Numerical Performance of the DFT Approaches 519
32.5 Summary and Outlook 530
33 Ab Initio Calculations of g-Tensors 533
Gerald H. Lushington
34 Zero-Field Splitting 541
Frank Neese
34.2 Zero-Field Splittings in EPR Spectroscopy 542
34.3 Theory of Zero-Field Splittings 552
34.4 Calculation of Zero-Field Splittings 557
Part E EPR Parameters, Applications
35 Computation of Hyperfine Coupling Tensors to
Complement EPR Experiments 567
Fuqiang Ban, James W. Gauld, and Russell J. Boyd
XI

XII
35.2 Insight Gained from a Conventional Ab Initio Approach 568
35.3 Benchmark Results Using Conventional Methods on Static Gas-phase
Structures 568
35.4 The Performance of Contracted Pople Basis Sets for Small Radicals
Consisting Only of First-Row Atoms 570
35.5 Density Functional Theory: An Alternative to a Conventional Ab Initio
Approach 571
35.6 Consideration of Environmental Effects 572
35.7 Illustration of the Applications of DFT Methods to Biological
Radicals 574
35.8 Summary 578
36 Applications to EPR in Bioinorganic Chemistry 581
Frank Neese
36.2 Biological Metal Sites 582
36.3 Concluding Remark 589
Index 593
Contents

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 interpreta-tions
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 struc-tures are often too close to
allow a unique identification of the stable isomer. Calcu-lated 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 wide-spread 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 develop-
ment 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 chemi-
cal 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
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 co-workers, 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 compu-tational efficiency.
The calculation of hyperfine coupling parameters suffers from two major
difficul-ties. 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; alterna-tive 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 theoreti-cal
work, and is well covered in several chapters. The calculation of electric field
gradients, necessary for predicting nuclear quadrupole coupling constants, comple-
ments 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 g-
tensors 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 introduc-tory chapters, written by distinguished scholars, will be
particularly useful for any-body 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
calcula-tion 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
Dalhousie University, Halifax
Nova Scotia
Canada B3H 4J3
Russell J. Boyd
& Biochemistry
University of Windsor
Windsor, Ontario
Canada N9B 3P4
DorothØe Berthomieu UMR
5618 CNRS, ENSCM 8 rue
de l’Ecole Normale 34296
Montpellier CØdex 5
France
Michael B4hl
Max-Planck-Institute
for Coal Research
Kaiser-Wilhelm-Platz 1
45470 M4lheim 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
Youngstown State University
Youngstown, Ohio 44555
USA
ISBN: 3-527-30779-6

XVI LIST OF CONTRIBUTORS
Bernd Engels
Institute of Organic Chemistry
Am Hubland
97074 W4rzburg
Germany
James W. Gauld
& Biochemistry
University of Windsor
Windsor, Ontario N9B
3P4 Canada
J4rgen Gauss
Institute of Physical Chemistry
University of Mainz
55099 Mainz
Germany
Annick Goursot
UMR 5618 CNRS,
ENSCM, 8 rue de l’Ecole
Normale 34296 Montpellier
CØdex 5 France
Thomas Heine
Institute of Physical Chemistry and
Electrochemistry
Technical University of Dresden
Mommsenstraße 13
01062 Dresden
Germany
Trygve Helgaker
University of Oslo
P.O. Box 1033 Blindern
0315 Oslo
Norway
Hanspeter Huber
The University of Basel
Klingelbergstr. 80
4056 Basel
Switzerland
Martin Kaupp
Am Hubland
97074 W4rzburg
Germany
Werner Kutzelnigg
Department of Theoretical Chemistry
Ruhr-University Bochum
44780 Bochum
Germany
Perttu Lantto
Department of Physical Sciences
P.O. Box 2000
90014 University of Oulu
Finland
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 9
SK-84536 Bratislava
Slovak Republic
Olga L. Malkina
Institute of Inorganic
Chemistry Slovak Academy of
Sciences Dubravska cesta 9
SK-84536 Bratislava
Slovak Republic
Pekka Manninen
P.O. Box 55 (A.I. Virtasen aukio
1) 00014 University of Helsinki
Finland

Francesco Mauri
Laboratoire de MinØralogie-
Cristallogr. de Paris
UniversitØ Pierre et Marie Curie
tour 16, case 115
4 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. MunzarovQ
National Centre
for Biomolecular Research
Faculty of Sciences
KotlQrskQ 2
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 M4lheim an der
Ruhr Germany
Serguei Patchkovskii
Steacie Institute for Molecular
Sciences National Research Council
of Canada, 100
Sussex Drive
Ottawa, Ontario K1A
0R6 Canada
LIST OF CONTRIBUTORS
Magdalena Pecul
University of Warsaw
Pasteura 1
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 Pyykk.
Finland
Vitaly A. Rassolov
Department of Chemistry and
Biochemistry
University of South Carolina
691 Sumter Street
Columbia, SC 29208
USA
Torgeir A. Ruden
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
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
Finland
Juha Vaara
Finland
Christoph van W4llen
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 1
10000 Zagreb
Croatia
Roderick E. Wasylishen
Gunning/Lemieux Chemistry
Centre University of Alberta
Edmonton, Alberta T6G 2G2
Canada
Tom Ziegler
University of Calgary
Calgary, Alberta T2N-1N4
Canada

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