National Academies Press: OpenBook
Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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.

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Page viii Cite
Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×
   

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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.

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
×

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

Suggested Citation:"Front Matter." National Research Council. 1995. Mathematical Challenges from Theoretical/Computational Chemistry. Washington, DC: The National Academies Press. doi: 10.17226/4886.
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Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.

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