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 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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