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Mathematical Challenges from Theoretical/Computational Chemistry MATHEMATICAL CHALLENGES FROM THEORETICAL/COMPUTATIONAL CHEMISTRY Committee on Mathematical Challenges from Computational Chemistry Board on Mathematical Sciences and Board on Chemical Sciences and Technology Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1995
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Mathematical Challenges from Theoretical/Computational Chemistry NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. Support for this project was provided by the National Science Foundation, Air Force Office of Scientific Research, Department of Energy, Army Research Office, and Ciba-Geigy Corporation. Library of Congress Catalog Card Number 95-68040 International Standard Book Number 0-309-05097-9 Copyright 1995 by the National Academy of Sciences. All rights reserved. Available from: National Academy Press 2101 Constitution Avenue, NW Box 285 Washington, DC 20055 B-515 Available on the Internet via the World Wide Web at the URL: http://www.nas.edu/. Printed in the United States of America COVER ILLUSTRATION: The catalytic binding site of the enzyme purine nucleoside phosphorylase, which plays a key rule in immune function, is shown in gray as a space-filling model. An inhibitor of the enzyme is shown in white. A tight fit between the enzyme and the inhibitor is required for binding and inhibitory activity, and a goal of structure-based drug discovery is the design of inhibitors that are geometrically (and chemically) complementary to an enzyme binding site. The figure was computer generated and resulted from a study that involved calculating geometries of potential inhibitors "docked" in the enzyme binding site (Montgomery et al., 1993). The study involved energy minimization and Monte Carlo-like conformational searching using the MacroModel computational chemistry software (Mohamadi et al., 1990). Such a computationally intensive task could not have been carried out 10 years ago and was an integral part of a structure-based drug design effort (Montgomery, 1993; see also Bugg et al., 1993). Figure courtesy of W. Guida, Pharmaceuticals Division, Ciba-Geigy Corporation. References Bugg, C.E., W.M. Carson, and J.A. Montgomery, 1993, Drugs by design, Scientific American 269:92–98. Mohamadi, F., N.G.J. Richards, W.C. Guida, R. Liskamp, M. Lipton, C. Caufield, G. Chang, T. Hendrickson, and W.C. Still, 1990, MacroModel—An integrated software system for modeling organic and bioorganic molecules using molecular mechanics, J. Comput. Chem. 11:440–467. Montgomery, J.A., 1993, Purine nucleoside phosphorylase: A target for drug design, Medicinal Research Reviews 13:209–228. Montgomery, J.A., S. Niwas, J.D. Rose, J.A. Secrist, Y.S. Babu, C.E. Bugg, M.D. Erion, W.C. Guida, and S.E. Ealick, 1993, Structure-based design of inhibitors of purine nucleoside phosphorylase 1. 9-(arylmethyl) derivatives of 9-deazaguanine, J. Med. Chem. 36:55–69.
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Mathematical Challenges from Theoretical/Computational Chemistry Committee on Mathematical Challenges from Computational Chemistry FRANK H. STILLINGER, AT&T Bell Laboratories, Chair HANS C. ANDERSEN, Stanford University LOUIS AUSLANDER, City University of New York DAVID L. BEVERIDGE, Wesleyan University ERNEST R. DAVIDSON, Indiana University WAYNE C. GUIDA, Ciba-Geigy Corporation PETER A. KOLLMAN, University of California at San Francisco WILLIAM A. LESTER, JR., University of California at Berkeley YVONNE C. MARTIN, Abbott Laboratories GEORGE C. SCHATZ, Northwestern University TAMAR SCHLICK, New York University and Howard Hughes Medical Institute L. RIDGWAY SCOTT, University of Houston DEWITT L. SUMNERS, Florida State University PETER G. WOLYNES, University of Illinois at Urbana-Champaign Board on Chemical Sciences and Technology Liaison KENDALL N. HOUK, University of California at Los Angeles SCOTT T. WEIDMAN, Study Director TAÑA L. SPENCER, Project Assistant
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Mathematical Challenges from Theoretical/Computational Chemistry Board on Mathematical Sciences AVNER FRIEDMAN, University of Minnesota, Chair JEROME SACKS, National Institute of Statistical Sciences, Vice Chair LOUIS AUSLANDER, City University of New York HYMAN BASS, Columbia University PETER E. CASTRO, Eastman Kodak Company R. DUNCAN LUCE, University of California at Irvine PAUL S. MUHLY, University of Iowa GEORGE NEMHAUSER, Georgia Institute of Technology ANIL NERODE, Cornell University INGRAM OLKIN, Stanford University RONALD PEIERLS, Brookhaven National Laboratory DONALD ST. P. RICHARDS, University of Virginia MARY F. WHEELER, Rice University ROBERT J. ZIMMER, University of Chicago JON KETTENRING, Bellcore, Ex Officio Member JOHN R. TUCKER, Director JACK ALEXANDER, Program Officer RUTH E. O'BRIEN, Staff Associate BARBARA W. WRIGHT, Administrative Associate
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Mathematical Challenges from Theoretical/Computational Chemistry Board on Chemical Sciences and Technology ROYCE C. MURRAY, University of North Carolina, Co-Chair EDWIN P. PRZYBYLOWICZ, Rochester Institute of Technology, Co-Chair PAUL S. ANDERSON, The Du Pont Merck Pharmaceutical Company DAVID C. BONNER, Premix, Inc. PHILIP H. BRODSKY, Monsanto Company MARVIN H. CARUTHERS, University of Colorado GREGORY R. CHOPPIN, Florida State University FRED P. CORSON, Dow Chemical Company MOSTAFA EL-SAYED, Georgia Institute of Technology JOANNA S. FOWLER, Brookhaven National Laboratory BERTRAM O. FRASER-REID, Duke University JUDITH C. GIORDAN, Henkel Corporation JOSEPH G. GORDON II, IBM Almaden Research Center L. LOUIS HEGEDUS, W.R. Grace & Co. GEORGE J. HIRASAKI, Rice University DOUGLAS A. LAUFFENBERGER, Massachusetts Institute of Technology MARSHA I. LESTER, University of Pennsylvania W. HARMON RAY, University of Wisconsin GABOR A. SOMORJAI, University of California at Berkeley JOHN J. WISE, Mobil Research and Development Corporation DOUGLAS J. RABER, Director MARIA P. JONES, Administrative Secretary SYBIL A. PAIGE, Administrative Associate TAÑA L. SPENCER, Senior Secretary SCOTT T. WEIDMAN, Senior Program Officer TAMAE M. WONG, Program Officer
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Mathematical Challenges from Theoretical/Computational Chemistry Commission on Physical Sciences, Mathematics, and Applications RICHARD N. ZARE, Stanford University, Chair RICHARD S. NICHOLSON, American Association for the Advancement of Science, Vice Chair STEPHEN L. ADLER, Institute for Advanced Study SYLVIA T. CEYER, Massachusetts Institute of Technology SUSAN L. GRAHAM, University of California at Berkeley ROBERT J. HERMANN, United Technologies Corporation RHONDA J. HUGHES, Bryn Mawr College SHIRLEY A. JACKSON, Rutgers University KENNETH I. KELLERMANN, National Radio Astronomy Observatory HANS MARK, University of Texas at Austin THOMAS A. PRINCE, California Institute of Technology JEROME SACKS, National Institute of Statistical Sciences L.E. SCRIVEN, University of Minnesota A. RICHARD SEEBASS III, University of Colorado LEON T. SILVER, California Institute of Technology CHARLES P. SLICHTER, University of Illinois at Urbana-Champaign ALVIN W. TRIVELPIECE, Oak Ridge National Laboratory SHMUEL WINOGRAD, IBM T.J. Watson Research Center CHARLES A. ZRAKET, MITRE Corporation (retired) NORMAN METZGER, Executive Director
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Mathematical Challenges from Theoretical/Computational Chemistry CONTENTS EXECUTIVE SUMMARY 1 Overview 1 Conclusions and Recommendations 2 Reference 5 1 INTRODUCTION 7 References 10 2 THE EMERGENCE OF COMPUTATIONAL CHEMISTRY 13 3 EXAMPLES OF CONSTRUCTIVE CROSS-FERTILIZATION BETWEEN THE MATHEMATICAL SCIENCES AND CHEMISTRY 19 Use of Statistics to Predict the Biological Potency of Molecules Later Marketed as New Drugs and Agricultural Chemicals 19 References 21 Numerical Analysis 21 References 22 Distance Geometry 23 References 25 Mathematics and Fullerenes 26 References 27 Quasicrystals 27 References 28 Chemical Topology 28 Combinatorics, Graph Theory, and Chemical Isomer Enumeration 28 Analysis of Molecular Spectra by Using Cayley Trees 29 Group Theory, Topology, Geometry, and Stereochemistry 29 Topology of Polymers 30 Knot, Links (Catenanes), and DNA 31 References 32 Graph Theory 34 Application of Graph Theory to Organizing Chemical Literature 34 Application of Graph Theory to Representation of Chemical Reactions 37 References 38 X-Ray Crystallography 40 Remark 42 References 42 4 MATHEMATICAL RESEARCH OPPORTUNITIES FROM THEORETICAL/COMPUTATIONAL CHEMISTRY 43 Introduction 43 References 43 Numerical Methods for Electronic Structure Theory 43 The N- and V-Representability Problems 48
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Mathematical Challenges from Theoretical/Computational Chemistry References 50 Melding of Quantum Mechanics with Simpler Models 51 References 53 Molecular Dynamics Algorithms 54 Enhanced Sampling 54 Numerical Methods for Solving Ordinary Differential Equations 54 Symplectic Integrators 54 The Time Step Problem in Molecular Dynamics 55 Implicit Integration Schemes 56 Future Prospects 57 References 57 N- and V-Representability Problems in Classical Statistical Mechanics 59 References 63 Implications of Topological Phases 63 Theoretical and Computational Chemistry in Space of Noninteger Dimension 65 References 67 Multivariate Minimization in Computational Chemistry 68 Introduction 68 Problem Classification 69 The Complexity of Computational Chemistry Problems 69 Local Optimization Methods 71 Global Optimization Methods 72 Perspective 73 References 74 Locating Saddlepoints 77 References 78 Sampling of Minima and Saddlepoints 80 Efficient Generation of Points That Satisfy Physical Constraints in a Many-Particle System 85 Prototypical Problem 85 Variations on the Prototypical Problem 85 Simplest Strategy 86 Metropolis Monte Carlo Method 87 Relationship of These Problems to More General Optimization Problems 87 Molecular Diversity and Combinatorial Chemistry in Drug Discovery 87 Overview of the Drug Discovery Process 87 Sources of Molecular Diversity 88 Current Computational Approaches to Compound Selection 89 Opportunities for Improvements in Computational Approaches to Compound Selection 90 References 91 Statistical Analyses of Families of Structures 93 Quantum Monte Carlo Solution of the Schrödinger Equation 94 Variational Monte Carlo (VMC) 95 Diffusion Monte Carlo (DMC) 95 Green's Function Monte Carlo (GFMC) 96 Research Opportunities 96 References 96 Nonadiabatic Phenomena 96 References 99
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Mathematical Challenges from Theoretical/Computational Chemistry Evaluation of Integrals with Highly Oscillatory Integrands: Quantum Dynamics with Path Integrals 99 Prototypical Problem 100 Discussion of the Problem 100 Stationary-Phase Monte Carlo Methods 101 Alternative Approaches to the Prototype Problem 102 Other Formulations and Solutions of the Basic Problem 102 References 104 Fast Algebraic Transformation Methods 105 References 108 5 CULTURAL ISSUES AND BARRIERS TO INTERDISCIPLINARY WORK 109 Motivation and Connections 109 Effects of Disciplinary Boundaries 110 Effects of the Curriculum 112 Language Differences 112 Toward a Fruitful Collaboration 114 References 115 6 CONCLUSIONS AND RECOMMENDATIONS 117 References 119 AFTERWORD 121 GLOSSARY 123
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Mathematical Challenges from Theoretical/Computational Chemistry The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Robert M. White is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council.
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Mathematical Challenges from Theoretical/Computational Chemistry LIST OF BOXES BOX 2.1 The Schrödinger Wave Equation 14 BOX 2.2 Molecular Mechanics/Molecular Dynamics 15 BOX 2.3 Chemist, Mathematician, or Physicist? 16 BOX 3.1 Rational Drug Design 20 BOX 3.2 Research Opportunities in Parallel Computing 22 BOX 3.3 Protein Microtutorial 24 BOX 3.4 Clique Detection 36 BOX 4.1 Electronic Phase Transitions 52 BOX 4.2 Tutorial on Statistical Mechanics and the Importance of Minima and Saddlepoints in Condensed Matter Systems 60 BOX 4.3 Implications of Dynamic Chaos for Quantum Mechanical Systems 64 BOX 4.4 Nodal Properties of Wave functions 66 BOX 4.5 Automatic Differentiation 70 BOX 4.6 Comments on the Ambiguous Concept of ''Structure'' for Complex Molecules and Macromolecules 82 BOX 4.7 Implications of Dynamical Chaos at the Classical Level 84 BOX 4.8 Possibility of Intelligent Algorithms to Detect Novel Phenomena Automatically 90 BOX 5.1 American Chemical Society Curriculum Standards for Mathematical Course Work 111 BOX 5.2 Information Sources About Theoretical/Computational Chemistry 113 BOX 5.3 Information Sources About the Mathematical Sciences 114
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