n 0

Keviews in Computational Chemistry 8

Edited by

Kenny B. Lipkowitz and Donald B. Boyd

8 WILEYVCH New York Chichester Weinheim Brisbane Singapore Toronto

Reviews in Computational Chemistry Volume 8

n

Keviews in Computational Chemistry 8

Edited by

Kenny B. Lipkowitz and Donald B. Boyd

@ WILEYmVCH New York Chichester Weinheim Brisbane Singapore Toronto

Kenny B. Lipkowitz Department of Chemistry Indiana University-Purdue University at Indianapolis I125 East 38"' Street Indianapolis, Indiana 46205, USA boyd-donald-b@lilly.com Ipjzl OO@indyvax.iupui.edu

Donald B. Boyd Lilly Research Laboratories Eli Lilly and Company Lilly Corporate Center Indianapolis, Indiana 46285, USA

This book has been electronically reproduced from digital information stored at John Wiley & Sons, Inc. We are pleased that the use of this new technology will enable us to keep works of enduring scholarly value in print as long as there is reasonable demand for them. The content of this

Copyright 0 1996 by John Wiley & Sons, Inc. All rights reserved.

Originally published as ISBN 1-5608 1-929-4

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A NOTE TO THE READER This book has been electronically reproduced from digital information stored at John Wiley & Sons, Inc. We are pleased that the use of this new technology will enable us to keep works of enduring scholarly value in print as long as there is reasonable demand for them. The content of this book i s identical to wevious erintings.

Preface

Computational chemistry is broadly applicable to the study of molecules and provides information to buttress, clarify, extend, and stimulate experimenta- tion. Thus it has gained wide acceptance in a variety of disciplines. This leads to an interesting question: How widely used is computational chemistry? Compu- tational chemistry per se has been around for more than 15 years. If it is truly useful, one should expect to see it being applied in many areas of research. How true is this? What would you guess is the percentage of papers incorporating some aspect of computational chemistry in some of the well-respected organic, inorganic, or medicinal chemistry journals?

To address this question of the prevalence of computational chemistry in the fabric of modern research, one could poll scientists doing research, but a more practical approach is to look at the number of publications mentioning the use of computational chemistry techniques and programs. Thus, the scien- tific literature can be examined to determine what percentage of the published papers relies, either partly or fully, on computational chemistry.

One way to accomplish this task is by computer searching of original literature databases, as was first done in a chapter entitled “Molecular Modeling in Use: Publication Trends” in Volume 6.“ The databases used contained complete articles, so all the text, tables, references, and so on were accessible for searching, The task can also be approached manually by examining individual, hard copy issues of some important journals, such as the Journal of the American Chemical Society, Angewandte Chemie International Edition English, Journal of Organic Chemistry, Inorganic Chemistry, and Journal of Medicinal Chemistry.

The database survey,“ which was done by searching for key words, clearly indicated a large and growing use of computational chemistry. Computer searching of databases has both advantages and limitations, as pointed out in that chapter. Among the limitations is the failure of many authors to uniformly cite software tools used. Sometimes one finds results of calculations given, but neither the program used nor the source of that program is specified, so a key

“D. B. Boyd, in Reviews in Computational Chemistry, Vol. 6 , K . B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1995, pp. 317-354. Molecular Modeling in Use: Publication Trends.

V

vi Preface

word search might miss them. Furthermore, there exist many programs for computational chemistry in addition to the major ones, and, unless these are individually searched, papers based on them will be missed. Thus, one might expect that a computerized search would underestimate to some unknown degree the prevalence of the use of computational chemistry.

On the other hand, however, there is also a tendency to overestimate the percentage of papers actually using computational chemistry. For example, there are cases of key words like “AM1” and “MM2” appearing in statements such as “Full details of the AM1 and MM2 calculations will be presented in a forthcoming paper.” Other false hits arise when authors cite prior calculations but do not report new calculations.

To bypass these potential problems, we manually browsed a small subset of the literature for papers that actually use computational tools. Rather than read through all the papers in the selected journals, a random subset of papers was examined to see which used computational chemistry techniques. To test the accuracy of this approach, the results obtained from one-quarter of the total number of issues in a given year was compared with the results found by browsing all issues in that volume. The test case was the 1994 volume of Journal of Organic Chemistry. The random selection yielded 14%, whereas inspection of all 1376 papers also yielded 14%. Thus browsing a fraction of the issues of a journal should suffice for our purposes. At least one-fourth of the total number of issues of the journals listed in Table 1 were read, but one-third to one-half were evaluated for the smaller journals.

Before discussing the results in Table 1, we point out that not all computer applications found in the published papers were included in this

Table 1 Percentage of Papers Using Computational Chemistry Published in lournals During 1994

Percent Breakdown by Type Journal Overall of Manuscript

~ ~~ ~~~

Journal of the American Chemical Society

lournal of Medicinal Chemistry

Angewandte Chemie lnter- national Edition EnglishR

lnorganic Chemistry

Journal of Organic Chemistry

26.6 Papers, 22.2

25.3 Articles, 21.5 Communications, 4.4

Notes, 2.5 Communications, 1.3

20.7 Communications, 18.3 Reviews, 2.4

16.3 Articles, 13.7 Communications, 2.1 Notes, 0.5

Communications, 1.3 Notes, 1.3

13.9 Articles, 1 1.3

~~~~ ~~~ ~

”In this journal, the articles are called “communications.”

Preface vii

survey. Arbitrarily omitted were papers in which computers were used only for data analysis, molecular graphics involving only superpositioning of molecules (although this is a very valid and useful function of molecular modeling), EXAFS studies, magnetic susceptibility calculations, NMR and EPR fitting (line shape analysis and the like), kinetic modeling, X-ray crystallography, normal coordinate calculations for IR spectroscopy, and routine searches of the Protein Data Bank and Cambridge Structural Database (although here again this is a very valid and useful function of molecular modeling). Included though were papers using statistics to develop QSAR regression models, principal components analysis for QSAR, CLOGP calculations, 3D structural database searches, and related techniques, where it seemed that computational chemis- try was an important part of the research. The results of the manual survey thus represents an approximate lower bound to the actual use of computational chemistry in the selected journals for the selected years.

While our formulation of what to exclude or include in this survey is admittedly subjective, the findings are nonetheless indicative. The results in the table are listed in descending order of percentage of papers using computa- tional chemistry. The tabulations are further partitioned into full papers and articles, notes, communications, and reviews depending on the journal format. Clearly, in most journals, most of the computational work appears in the full papers and articles rather than in the notes and communications. This might lead one to speculate that computational chemistry is used to explain science after the fact (not a bad idea) or that computational chemists are less likely than experimentalists to dash out little communications. Many papers use computational tools in a predictive mode, but this practice is not addressed in our evaluation.

Of the journals covered in this survey, the one publishing the greatest percentage of papers using computational tools is, as expected, the Journal of the American Chemical Society, followed closely by Journal of Medicinal Chemistry. Scientists publishing in Inorganic Chemistry used quantum-based tools primarily, whereas chemists publishing in Journal of Organic Chemistry used both molecular mechanics and quantum mechanics. Articles in Journal of Medicinal Chemistry used a wide range of computational methods related directly or indirectly to the goal of drug discovery.

We now come back to our original question: How prevalent is computa- tional chemistry in chemical research as we near the end of this millennium? The answer is about 15-30%, depending on the discipline of chemistry. Is this what you expected? It impresses us as being very substantive. And, equally important, we know from the earlier survey" that the prevalence is on a steady upward trend.

Is the range of percentages found consistent with the results of the earlier computer searching? In the computerized survey of 19 journals published by the American Chemical Society, 13% of the papers published in 1994 men- tioned well-known computational chemistry software. Thus, manual searching

viii Preface

turned up a larger percentage of papers. The percentages should be compared in the light of three conditions: (1) the computer searches were done on a broader range of chemistry disciplines and included some journals in which almost no computational chemistry appears, (2) the Journal of the American Chemical Society has long been heavily weighted with theoretical papers, and the other journals in Table 1 are also known for publishing a great deal of computational chemistry work, and (3) the search criteria differ in the two surveys. Nevertheless, we are comfortable with the degree of agreement. Clearly, computational chemistry is playing a large role in chemical science,

It should be kept in mind that as time passes, and the abilities of theories and models to simulate nature in computero improve, the percentages will grow even higher. We believe it is inevitable, even in disciplines of molecular science where computational chemistry has not yet made many inroads, that the average bench chemist will more frequently use computational tools to aid research, both a priori to decide what compounds to make or properties to measure, as well as a posteriori to help interpret experimental results.

This volume, the eighth, of Reviews in Computational Chemistry, repre- sents our ongoing effort to provide tutorials and reviews for both novice and experienced computational chemists. These chapters are written for new- comers learning about molecular modeling techniques as well as for seasoned professionals who need to quickly acquire expertise in areas outside their own.

This eighth volume in the series covers some “heavy” material. We mean this in the sense that three of the chapters deal with the heavier elements of the periodic table, and one of the chapters deals with high molecular weight assem- blages of carbon atoms. All the chapters in this volume have a quantum me- chanical theme.

In Chapter 1 Professors Zdenek Slanina, Shyi-Long Lee, and Chin-hui Yu discuss the timely topic of fullerenes and carbon aggregates. They show how ubiquitous semiempirical molecular orbital techniques need to be adjusted to correctly determine the three-dimensional geometries, energies, and properties of these species. Modern approximate methods prove useful for species too large for exploratory or routine ab initio work. Ab initio and mathematical studies of carbon clusters are also covered in the chapter.

Chapters 2 and 3 elucidate the so-called effective core potential o r pseu- dopotential methods that have proved invaluable for handling transition metals and other heavy elements. ECPs allow the field of the core electrons to be modeled, thereby reducing the dimensionality of the problem so that only the valence and outer core electrons have to be treated explicitly. The group at Marburg of Professor Dr. Gernot Frenking and his co-workers, Drs. Iris Antes, Marlis Bohme, Stefan Dapprich, Andreas W. Ehlers, Volker Jonas, Arndt Neu- haus, Michael Otto, Ralf Stegmann, Achim Veldkamp, and Sergei F. Vyboish- chikov, give one perspective in Chapter 2. The University of Memphis group of Professor Thomas R. Cundari and his students, Michael T. Benson, M. Leigh Lutz, and Shaun 0. Sommerer, gives a complementary treatment in Chapter 3.

Preface ix

In Chapter 4 Professors Jan Almloft and Odd Gropen present the quan- tum theory for describing relativistic effects, which are particularly important for heavier elements. Such treatments are necessary to be able to predict bond distances and other properties accurately. Along with Chapters 2 and 3 , this chapter illustrates the opening of more of the periodic table to the purview of computational chemistry.

Finally in Chapter 5, Professor Donald B. Chesnut reviews NMR chemi- cal shifts, an area of research in which he has been active for many years. The methodology is explained, and among the examples presented in this tutorial are buckminsterfullerenes, heterocycles, proteins, and other large molecules.

Prior volumes of Reviews in Computational Chemistry have had a com- pendium of software for computational chemistry. An extensive, 55-page com- pendium appeared in Volume 7. No appendix is included with the present volume, to allow more room for chapters. However, periodically in future volumes we will provide an updated compendium. In the meantime, the com- pendium of Volume 7 should serve as a handy reference for the reader.

We express our deep gratitude to the authors who contributed the excel- lent chapters in this volume. We hope that you too will find them helpful and enlightening. We acknowledge Joanne Hequembourg Boyd for invaluable assis- tance with the editorial processing of this book. We thank the readers of this series who have found the books useful and have given us encouragement.

Finally, we would like to point out that information about Reviews in Com~utational Chemistry is now available on the World Wide Web. Back- ground information about the scope and style are provided for potential readers and authors. In addition, the home page contains the tables of contents of all volumes, colorful details related to the book series, and the international addresses of VCH Publishers. The Reviews in Computational Chemistry home page is also used to present color graphics and supplementary material as ad- juncts to the chapters. You may find us at http://chem.iupui.edu/

Kenny B. Lipkowitz and Donald B. Boyd Indianapolis

February 1996

tNote added in proofs: Sadly we note the passing of Professor Jan Erik Almlof while this volume was in production. We join the scientific community in extending our sympathy to his family and colleagues. An innovator in the applications of high performance computers to chemistry, he developed the now widely used direct SCF approach [ J. Almlof, K. Faegri, Jr., and K. Korsell,]. Comput. Chem., 3, 385 (1982). Principles for a Direct SCF Approach to LCAO-MO Ab-Initio Calculations]. I t allows ab initio calculations of electronic wave- functions and energies of molecules to take advantage of the speed at 'which modern computers can recalculate two-electron integrals, rather than having to store and retrieve them. His scientific productivity and brilliance will be missed.

Contents

1.

2.

Computations in Treating Fullerenes and Carbon Aggregates Zdene'k Slanina, Shyi-Long Lee, and Chin-hui Yu

Introduction Relevant Methodology

Hypersurface Stationary Points Semiempirical Methods Ab Initio Computations Algebraic Enumerations Absolute and Relative Stabilities of Fullerenes

Illustrative Applications Small Carbon Clusters Higher Fullerenes Functionalized Fullerenes

Acknowledgment References

1

1 2 2 7

17 23 27 33 33 36 41 44 45

Pseudopotential Calculations of Transition Metal Compounds: Scope and Limitations 63 Gernot Frenking, lris Antes, Marlis Bohme, Stefan Dapprich, Andreas W. Ehlers, Volker Jonas, Arndt Neuhaus, Michael Otto, Ralf Stegmann, Achim Veldkamp, and Sergei F. Vyboishchikov

Introduction Scope Application of Quantum Mechanical Methods Heavy-Atom Molecules Pseudopotential Methods: An Overview Technical Aspects of Pseudopotential Calculations

General Rules for Calculating Transition Metal Complexes with ECP Methods

63 63 64 65 67 69

72

X i

xii Contents

Some Remarks About Calculating Transition Metal Compounds and Molecules of Main Group Elements

Results and Discussion of Selected Examples Carbonyl Complexes Methyl and Phenyl Compounds of Late Transition

Carbene and Carbyne Complexes 0 x 0 and Nitrido Complexes Alkyne and Vinylidene Complexes in High

Chelate Complexes of TiCl, and CH3TiC13

Metals

Oxidation States

Conclusion and Outlook Acknowledgment References

3. Effective Core Potential Approaches to the Chemistry of the Heavier Elements Thomas R. Cundari, Michael T. Benson, M . Leigh Lutz, and S h a m 0. Sommerer

Introduction 0 b jective The Challenges of Computational Chemistry of the Heavier

Elements Increasing Numbers of Electrons and Orbitals The Electron Correlation Problem Relativistic Effects

The Promise of Computational Chemistry Across

Effective Core Potential Methods Derivation of Effective Core Potentials and Valence Basis Sets

Selecting a Generator State Nodeless Pseudo-orbitals Relativistic Effective Potentials (REPs)

and Averaged REPs Analytical Representation for the Pseudo-orbitals Analytical Forms for the Potentials Optimized Valence Basis Sets

the Periodic Table

Computational Methods Representative Examples: Main Group Chemistry

Alkali and Alkaline Earth Metals Triels Tetrels Pnictogens

74 75 75

93 99

106

116 122 129 130 130

145

145 146

147 147 147 149

150 151 153 153 155

158 159 160 161 163 163 164 165 167 171

Contents xiii

Representative Examples: Transition Metal and Lanthanide Chemistry

Core Size Valence Basis Sets Energetics Metal-0x0 Complexes Multiply Bonded Transition Metal Complexes

Bonding in Heavily w l o a d e d Complexes Methane Activation

Summary and Prospectus Acknowledgments References

of Heavier Main Group Elements

Relativistic Effects in Chemistry Jan Almlof and Odd Gropen

Introduction Nonrelativistic Quantum Mechanics

General Theory The LCAO Expansion Electron Correlation

Relativistic Quantum Mechanics General Principles The Klein-Gordon Equation The Dirac Equation Transformation to Two- and One-Component Theory The Foldy-Wouthuysen Transformation The “Douglas-Kroll” Transformation

Four-Component Methods Comparison of Methods

Applications

Conclusions References

The Ab Initio Computation of Nuclear Magnetic Resonance Chemical Shielding Donald B. Chesnut

Introduction The General Problem Theory

The Basic Quantum Mechanics The Gauge Problem

173 173 174 175 176

178 181

191 192 193

203

183

203 205 205 209 209 212 212 216 217 222 223 229 23 1 23 1 235 239 240

245

245 246 249 249 256

xiv Contents

What Is Observed? Shift and Shielding Scales

How Well Can We Do? A Sample Calculation Examples

A Calculation on a Large Molecule Deshielding in the Phospholide Ion Some Approaches to Treating Large Systems An Ab Initio Approach to Secondary and Tertiary

A Molecular Dynamics and Quantum Mechanical

Effects of Correlation

Effects in Proteins

Study of Water

Concluding Remarks References

25 9 260 261 267 272 272 275 282

282

284 286 29 1 292

Author Index 299

Subject Index 315

Contributors

Iris Antes, Organisch-Chemisches Institut, Universitat Zurich, Winterthurer Strasse 190, CH-8057 Zurich, Switzerland (Electronic mail: antes@ ocisgl6.unizh.ch)

Michael T. Benson, Department of Chemistry, University of Memphis, Mem- phis, Tennessee 38152, U.S.A. (Electronic mail: mtbenson@cc.memphis.edu)

Marlis Bohme, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany

Donald B. Chesnut, Department of Chemistry, Duke University, Durham, North Carolina 27708, U.S.A. (Electronic mail: dbc@dbc.chem.duke.edu)

Thomas R. Cundari, Computational Inorganic Chemistry Laboratory, Depart- ment of Chemistry, University of Memphis, Memphis, Tennessee 38 152, U.S.A. (Electronic mail: cundarit@cc.memphis.edu)

Stefan Dapprich, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany

Andreas W. Ehlers, Afdeling Theoretische Chemie, Faculteit Scheikunde, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands (Electronic mail: ehlers@iodine.chem.vu.nl)

Gernot Frenking, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany (Electronic mail: frenking @ p s l 5 1S.chemie.uni-marburg.de)

Volker Jonas, MD-IM-FA Bayer AG, Gebaude 4 1 8 , D-51368 Leverkusen, Ger- many (Electronic mail: debaymt9@ibmmail.com)

Shyi-Long Lee, Department of Chemistry, National Chung-Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan

xv

xvi Contributors

M. Leigh Lutz, 938 Delaware Avenue, Erie, Pennsylvania 16505, U.S.A.

Arndt Neuhaus, McKinsey Company, Taunusanlage 21, 60325 Frank- furt/Main, Germany

Michael Otto, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany

Zdenek Slanina, Department of Chemistry, National Chung-Cheng Univer- sity, Ming-Hsiung, Chia-Yi 621, Taiwan

Shaun 0. Somrnerer, Department of Physical Sciences, Barry University, 11300 NE Second Avenue, Miami Shores, Florida 33161, U.S.A. (Electronic mail: sommerer@buaxpl.barry.edu)

Ralf Stegrnann, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany

Chin-hui Yu, Department of Chemistry, National Tsing-Hua University, Hsinchu 30043, Taiwan

Achim Veldkamp, Fachbereich Chemie, Philipps-Universitat Marburg, Hans- Meerwein-Strasse, D-35032 Marburg, Germany

Sergei F. Vyboishchikov, Fachbereich Chemie, Philipps-Universitat Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

Contributors to Previous Volumes'

VOLUME 1

David Feller and Ernest R. Davidson, Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions.

James J. P. Stewart,t Semiempirical Molecular Orbital Methods.

Clifford E. Dykstra,+ Joseph D. Augspurger, Bernard Kirtman, and David J. Malik, Properties of Molecules by Direct Calculation.

Ernest L. Plummer, The Application of Quantitative Design Strategies in Pesti- cide Design.

Peter C . Jurs, Chemometrics and Multivariate Analysis in Analytical Chemis- try.

Yvonne C. Martin, Mark G. Bures, and Peter Willett, Searching Databases of Three-Dimensional Structures.

Paul G . Mezey, Molecular Surfaces.

Terry P. Lybrand,§ Computer Simulation of Biomolecular Systems Using Mo- lecular Dynamics and Free Energy Perturbation Methods.

*For chapters where no author can be reached at the address given in the original volume, the current affiliation of the senior author is given here in footnotes. tCurrent address: 15210 Paddington Circle, Colorado Springs, C O 80921. (Electronic mail: jstewart@fai.com) *Current address: Indiana University-Purdue University at Indianapolis, Indianapolis, IN 46202. (Electronic mail: dykstra@chem,iupui.edu) §Current address: University of Washington, Seattle, WA 98195. (Electronic mail: lybrand@proteus.bioeng.washington.edu)

xvii

xuiii Contributors to Previous Volumes

Donald B. Boyd, Aspects of Molecular Modeling.

Donald B. Boyd, Successes of Computer-Assisted Molecular Design.

Ernest R. Davidson, Perspectives on Ab Initio Calculations.

VOLUME 2

Andrew R. Leach," A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules.

John M. Troyer and Fred E. Cohen, Simplified Models for Understanding and Predicting Protein Structure.

J. Phillip Bowen and Norman L. Allinger, Molecular Mechanics: The Art and Science of Parameterization.

Uri Dinur and Arnold T. Hagler, New Approaches to Empirical Force Fields.

Steve Scheiner, Calculating the Properties of Hydrogen Bonds by Ab Initio Methods.

Donald E. Williams, Net Atomic Charge and Multipole Models for the Ab Initio Molecular Electric Potential.

Peter Politzer and Jane S. Murray, Molecular Electrostatic Potentials and Chemical Reactivity.

Michael C. Zerner, Semiempirical Molecular Orbital Methods.

Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling.

I. B. Bersukert and A. S. Dimoglo, The Electron-Topological Approach to the QSAR Problem.

Donald B. Boyd, The Computational Chemistry Literature.

- "Current address: Glaxo-Wellcome, Greenford, Middlesex, UB6 OHE, U.K. (Electronic mail: arl22958@ggr.co.uk) *Current address: University of Texas, Austin, TX 78712. (Electronic mail: cmao771@charon.cc.utexas.edu)

Contributors to Previous Volumes X ~ X

VOLUME 3

Tamar Schlick, Optimization Methods in Computational Chemistry.

Harold A. Scheraga, Predicting Three-Dimensional Structures of Oligopep- tides.

Andrew E. Torda and Wilfred F. van Gunsteren, Molecular Modeling Using NMR Data.

David F. V. Lewis, Computer-Assisted Methods in the Evaluation of Chemical Toxicity.

VOLUME 4

Jerzy Cioslowski, Ab lnitio Calculations on Large Molecules: Methodology and Applications.

Michael L. McKee and Michael Page, Computing Reaction Pathways on Mo- lecular Potential Energy Surfaces.

Robert M. Whitnell and Kent R. Wilson, Computational Molecular Dynamics of Chemical Reactions in Solution.

Roger L. DeKock, Jeffry D. Madura, Frank Rioux, and Joseph Casanova, Computational Chemistry in the Undergraduate Curriculum.

VOLUME 5

John D. Bolcer and Robert B. Hermann, The Development of Computational Chemistry in the United States.

Rodney J. Bartlett and John F. Stanton, Applications of Post-Hartree-Fock Methods: A Tutorial.

Steven M. Bachrach, Population Analysis and Electron Densities from Quan- tum Mechanics.

Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade, Brock A. Luty, and J. Andrew McCammon, Biological Applications of Electro- static Calculations and Brownian Dynamics Simulations.

xx Contributors to Previous Volumes

K. V. Damodaran and Kenneth M. Merz Jr., Computer Simulation of Lipid Systems.

Jeffrey M. Blaney and J. Scott Dixon, Distance Geometry in Molecular Model- ing.

Lisa M. Balbes, S. Wayne Mascarella, and Donald B. Boyd, A Perspective of Modern Methods in Computer-Aided Drug Design.

VOLUME 6

Christopher J. Cramer and Donald G. Truhlar, Continuum Solvation Models: Classical and Quantum Mechanical Implementations.

Clark R. Landis, Daniel M. Root, and Thomas Cleveland, Molecular Me- chanics Force Fields for Modeling Inorganic and Organometallic Compounds.

Vassilios Galiatsatos, Computational Methods for Modeling Polymers: An In- troduction.

Rick A. Kendall, Robert J. Harrison, Rik J. Littlefield, and Martyn F. Guest, High Performance Computing in Computational Chemistry: Methods and Ma- chines.

Donald B. Boyd, Molecular Modeling Software in Use: Publication Trends.

Eiji Osawa and Kenny B. Lipkowitz, Published Force Field Parameters.

VOLUME 7

Geoffrey M. Downs and Peter Willett, Similarity Searching in Databases of Chemical Structures.

Andrew C. Good and Jonathan S. Mason, Three-Dimensional Structure Database Searches.

Jiali Gao, Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials.

Contributors to Previous Volumes xxi

Libero J. Bartolotti and Ken Fiurchick, An Introduction to Density Functional Theory.

Alain St-Amant, Density Functional Methods in Biomolecular Modeling.

Danya Yang and Arvi Rauk, The A Priori Calculation of Vibrational Circular Dichroism Intensities.

Donald B. Boyd, Compendium of Software for Molecular Modeling.

CHAPTER 1

Computations in Treating Fullerenes and Carbon Aggregates

ZdenEk Slanina,” 1 Shyi-Long Lee,’’ and Chin-hui Yut ”Department of Chemistry, National Chung-Cheng University, Ming-Hsiung, Chia- Yi 621 , Taiwan, and ?Department of Chemistry, National Tsing Hua University, Hsinchu 30043, Taiwan

INTRODUCTION

Fullerenes became known to chemists recently enough for computational chemistry, and especially molecular mechanics and semiempirical quantum chemistry, to have provided useful information during the surge of interest in these molecules. If in 1942 Hahn and his co-workers2 had been able to find higher carbon aggregates (their upper limit was CIS), there would have been little help at that time from theoretical chemistry for those trying to understand the structures, reactivities, spectra, and energetics of fullerene-type molecules. [Although the Hiickel molecular orbital (HMO) method was available, compu- tational hardware was certainly very modest and symmetry reduction not com- mon.] Similarly, experimental studies3 of carbon vapor in the 1950s and 1960s would have received better theoretical support if the methodologies and computers had been available. Even then, use of inert gases and proper temperature-pressure regimes were not implemented and thus, only small car- bon aggregates were observed. As Kratschmer4 however stresses, fullerene mol-

Reviews in Computational Chemistry, Volume 8 Kenny B. Lipkowitz and Donald B. Boyd, Editors

VCH Publishers, Inc. New York, 0 1996

2 Computations in Treating Fullerenes and Carbon Aggregates

ecules belong to a frequently overlooked molecular species in carbon chemistry. The small aggregates were given the best theoretical treatment then possible by Pitzer and Clementi,s and later by Hoffmanns and others.’ However, the golden age of Hiickel studies of aromatic systems neglected a suggestion by Jones8 and missed the instructive and prophetic visualization of c60 by Osawa.9 Hence, Hiickel calculations of c60 were somewhat delayed.10>11 As is now known, the early calculations were unknown to the discoverers of c60.

Owing to the tremendous development of computational hardware in the 1970s and 1980s, computational chemistry could well follow the c60 discovery by Kroto, Smalley, and others12 and even supply useful support to further advances. The “synthetic” physicists Huffman and Kratschmer indeed re- called13 the role of the four computationally predicted IR bands in establishing the historical carbon arc C,o synthesis14 (they explicitly quoted six quantum chemical papers’s-20 in their report). Vibrational analysis using semiempirical molecular orbital theory of c60 was certainly close to the limit of what was possible computationally in 1985-1986. Also reported at that time21 was the vibrational analysis of C70. However, within five years of C60’s discovery to its routine synthesis, computational hardware and software underwent another substantial increase in performance (expected from Moore’s law on the dou- bling of integrated-circuit capacity every 18 months22). Hence, the second, permanent wave23 of research interest in fullerenes coincided with the arrival of computational chemistry at a stage of maturity adequate for the task. This is particularly well demonstrated by the landmark semiempirical calculations of Bakowies and Thie124 and ab initio correlated treatment by H b e r et al.25

Computational chemistry now plays the role of a real partner in fullerene research where theory and experiment are mutually complementary tools. Therefore, this fresh research field is, inter a h , exemplary of the role of compu- tations in modern chemical research. Exponential growth of fullerene re- search23 ensures that a survey can hardly be exhaustive. Thus, a custom of specialized and personalized reviews has been adopted26-61 in the literature, though there is one singularity-the last comprehensive review in the field, written by Weltner and van Zee26 during the first, presynthetic wave. In this chapter we stress the interplay between theory and experiment together with an overview of important methodological developments.

RELEVANT METHODOLOGY

Hypersurface Stationary Points Although molecular dynamics simulations within complete potential hy-

persurfaces would be highly useful for understanding the mechanisms of full- erene formation, such quantum chemical hypersurfaces are not available. Typ-

Relevant Methodology 3

ically, molecular dynamics treatments have employed simple phenomenological potentials,62-67 and higher quality potential functions are an exception.68Jj9 Hence, basically all quantum chemical computations on fullerenes have been performed at stationary points of the potential hypersurfaces. Standard tech- niques for stationary point location, mostly with analytical first energy deriva- tives, have been applied. However, with respect to the computational demands, they are not always followed by a vibrational analysis based on the second energy derivatives from a numerical differentiation, Computational techniques for stationary point location and characterization, which are well described elsewhere,70-74 are not modified when applied to fullerenes.

Fullerenes were originally defined as purely carbonaceous aggregates C,: ( n even) built from five- and six-membered rings and three-coordinated carbon atoms (c60 in Figure 1 serves as an example).75 Topological reasoning, based on Euler’s formula (for convex bodies, otherwise the rules can be different), leads to proof that any such polyhedron always contains exactly 12 five- membered rings, whereas the number of six-membered rings is simply given as n / 2 - 10 (n 2 20, # 22). The exceptional case of n = 22 points out that the 12-pentagon rule is a necessary, not a sufficient condition. The limitation to n being even is not relevant now, however, inasmuch as large carbon cages with n odd are known from both experiment76-78 and theory.79 Also, the limitation of the five- and six-membered rings is not required, for other types of rings have

Figure 1 The C,, molecule, buckminsterfullerene: an example from the first wave (1985-1986) of fullerene structure optimizations. Shown are the AM1 results from Ref.’s

4 Computations in Treating Fullerenes and Carbon Aggregates

been considered. For example, Shibuya and Yoshitaniso examined an ico- sahedral structure for C60, a truncated dodecahedron instead of a truncated icosahedron. The former isomer is composed of three- and ten-membered rings but is rather unstable.80 Recently, Taylor81 proposed four-membered rings as a possible significant pattern for some fullerene structures and suggested c48 as a prototype compound. The truncated cuboctahedron-like structure (Figure 2) is however located more than 200 kcal/mol above a pentagonlhexagon c 4 8 struc- ture.82 Haymet83 discussed a polyhedron, archimedene, built from four-, six-,

Figure 2 three views of the AM1-optimizedsz 41618 0, structure of C,, (the truncated cuboctahedron-like structure).

Example of a pattern different from the standard pentagonihexagon route:

Relevant Methodology 5

and ten-membered rings. Odd-numbered rings, different from pentagons, are also of interest, Murry and Scuseria84 computed a mechanism for the cage opening and considered nine- and thirteen-membered rings. They also pointed out the importance of triplet potential hypersurfaces for lowering potential barriers in fullerene kinetics. Three- and seven-membered rings appear in the c6, s t ru~tures .~9

A high symmetry has frequently been associated with fullerenes and espe- cially the icosahedral Ih symmetry of c60 (Figure 1; or Oh symmetry of c48 in Figure 2), although species with no symmetry are also possible. BabiC et al.85 discussed fullerenes in the original pentagonihexagon sense up to C70 and constructed polyhedrons with the following symmetries: C1, Ci, C,, C,, C3, Czy, C ~ V , C2h9 C3h, D29 D3, D 5 , D2h, D3h, D5h, D6h, D2d, D3d9 D5d9 D6d, s4, s6,

T, Td, and Ih . Because fullerenes with these symmetries are derived purely from geometrical reasoning, it is obvious that not all of them will necessarily have a corresponding local energy minimum on the C, hypersurfaces.

The Jahn-Teller distortion is an important factor that causes symmetry reduction, and CZ0 serves as a good example86187 of a species that undergoes such distortion. In fact, C20 is the smallest possible fullerene, containing 12 pentagons and no hexagons. The high symmetry polyhedron built from 12 regular pentagons is the dodecahedron. In the molecule, however, the frontier orbitals are degenerate and partially filled, requiring a symmetry lowering in accord with the Jahn-Teller theorem. At the Hartree-Fock level with a split valence basis set of Gaussian-type orbitals (HF/6-3 lG") , for example, the sym- metry is lowered to C2 according to computations of Raghavachari et a1.88 (an experimental test would be of considerable interest89).

The c60 is the smallest possible fullerene with all pentagons isolated (Le., each pentagon is surrounded by five hexagons). The structural pattern has been well recognized since the very night of discovery,35 on September 9/10, 1985, and later formalized in the so-called isolated-pentagon rule90 (IPR). The lim- ited computational experience available9*-95 supports the belief that the IPR structures are more stable than structures with joined pentagons.

The c 6 0 cage, the best experimentally characterized fullerene, has been studied with various computational methods. Methods of all types, including molecular mechanics, semiempirical, and ab initio molecular orbital theories, reproduce well the two bond lengths (r6-5 and r6-6 between hexagon and pentagon and between two hexagons, respectively) in c60 (Table 1),95-98 This is even true for two HMO deductions of the bond distances.99>100 In fact, Murry et a1.95 compared molecular mechanics (MM3) with ab initio self- consistent field (SCF) computations of fullerene geometries and concluded that M M 3 can effectively reproduce fullerene structures. The IR spectrum of c60 (in contrast to the Raman spectrum) consists of only four bands owing to the symmetry selection rules. The frequencies are reasonably well reproduced at various levels of computations (cf. Table 2).14196,1001101 The performance of the simple H M O estimation by Cyvin et a1.100 is especially remarkable. One

Tab

le 1

H

eat

of F

orm

atio

n H

f (kc

al/m

ol) a

nd B

ond

Len

gths

(A) o

f C

6,

Met

hods

u

MN

DO

St

anda

rd

MN

DO

Mod

ifie

d SC

FbI

STO

-3G

M

PZ

C/T

ZP

A

M1

PM

3 P

aram

eter

s P

aram

eter

s II

Bd

Exp

.

AH

f 62

5.00

97

2.39

81

0.81

86

8.22

59

9.43

59

9.43

e B

ond

leng

ths

‘6--

5

1.46

3 1.

446

1.46

4 1.

458

1.47

4 1.

465

1.45

8f

1.40

1f

‘6

6

1.37

6 1.

406

1.38

5 1.

384

1.40

0 1.

392

Err

ore

0.01

5 0.

009

0.01

1

0.00

9 0.

009

0.00

8 ~

~~

~~

.SC

F/S

TO

-3G

, sel

f-co

nsis

tent

fie

ld/S

late

r-ty

pe or

bita

l ap

prox

imat

ed b

y th

ree

Gau

ssia

ns; M

PZ/T

ZP,

sec

ond-

degr

ee M

elle

r-P

less

et/t

ripl

e-ze

ta

hRef

eren

ce 9

5.

CR

efer

ence

25.

dR

efer

ence

96.

.R

efer

ence

97.

fR

efer

ence

98.

nA

vera

ge o

f ab

solu

te d

iffer

ence

s be

twee

n th

eory

and

exp

erim

ent

for

the two

bond

leng

ths.

plus

pol

ariz

atio

n ba

sis

set;

AM

1, A

usti

n M

odel

1;

PM

3, P

aram

etri

c M

etho

d 3;

MN

DO

, mod

ifie

d ne

glec

t of

diat

omic

diff

eren

tial o

verl

ap.