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EXECUTIVE SUMMARY

1

Overview

Conclusions and Recommendations

2

Reference

5

INTRODUCTION

7

References

10

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

21

Numerical Analysis

22

Distance Geometry

23

25

Mathematics and Fullerenes

26

27

Quasicrystals

28

Chemical Topology

Combinatorics, Graph Theory, and Chemical Isomer Enumeration

Analysis of Molecular Spectra by Using Cayley Trees

29

Group Theory, Topology, Geometry, and Stereochemistry

Topology of Polymers

30

Knot, Links (Catenanes), and DNA

31

32

Graph Theory

34

Application of Graph Theory to Organizing Chemical Literature

Application of Graph Theory to Representation of Chemical Reactions

37

38

X-Ray Crystallography

40

Remark

42

4

MATHEMATICAL RESEARCH OPPORTUNITIES FROM THEORETICAL/COMPUTATIONAL CHEMISTRY

43

Introduction

Numerical Methods for Electronic Structure Theory

The N- and V-Representability Problems

48

" Front Matter ." Mathematical Challenges from Theoretical/Computational Chemistry . Washington, DC: The National Academies Press, 1995 .

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