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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