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.

Format:

Book

Author/Creator:

National Research Council (U.S.). Committee on Mathematical Challenges from Computational Chemistry.

Language:

English

Subjects (All):

Chemistry, Physical and theoretical--Mathematics.

Chemistry, Physical and theoretical.

Physical Description:

1 online resource (143 p.)

Edition:

1st ed.

Place of Publication:

Washington, D.C. : National Academy Press, 1995.

Language Note:

English

Summary:

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.

Contents:

Mathematical Challenges from Theoretical/Computational Chemistry

Copyright

REFERENCES

Contents

Executive Summary

OVERVIEW

CONCLUSIONS AND RECOMMENDATIONS

Reference

1 Introduction

References

2 The Emergence of Computational Chemistry

3 Examples of Constructive Cross-Fertilization Between the Mathematical Sciences and Chemistry

USE OF STATISTICS TO PREDICT THE BIOLOGICAL POTENCY OF MOLECULES LATER MARKETED AS NEW DRUGS AND AGRICULTURAL CHEMICALS

NUMERICAL ANALYSIS

DISTANCE GEOMETRY

MATHEMATICS AND FULLERENES

QUASICRYSTALS

CHEMICAL TOPOLOGY

Combinatorics, Graph Theory, and Chemical Isomer Enumeration

Analysis of Molecular Spectra by Using Cayley Trees

Group Theory, Topology, Geometry, and Stereochemistry

Topology of Polymers

Knots, Links (Catenanes), and DNA

GRAPH THEORY

Application of Graph Theory to Organizing Chemical Literature

Application of Graph Theory to Representation of Chemical Reactions

X-RAY CRYSTALLOGRAPHY

Remark

4 Mathematical Research Opportunities from Theoretical/Computational Chemistry

INTRODUCTION

NUMERICAL METHODS FOR ELECTRONIC STRUCTURE THEORY

THE N-AND V-REPRESENTABILITY PROBLEMS

MELDING OF QUANTUM MECHANICS WITH SIMPLER MODELS

MOLECULAR DYNAMICS ALGORITHMS

Enhanced Sampling

Numerical Methods for Solving Ordinary Differential Equations

Symplectic Integrators

The Time Step Problem in Molecular Dynamics

Implicit Integration Schemes

Future Prospects

N-AND V-REPRESENTABILITY PROBLEMS IN CLASSICAL STATISTICAL MECHANICS

IMPLICATIONS OF TOPOLOGICAL PHASES

THEORETICAL AND COMPUTATIONAL CHEMISTRY IN SPACES OF NONINTEGER DIMENSION.

References

MULTIVARIATE MINIMIZATION IN COMPUTATIONAL CHEMISTRY

Introduction

Problem Classification

The Complexity of Computational Chemistry Problems

Local Optimization Methods

Global Optimization Methods

Perspective

LOCATING SADDLEPOINTS

SAMPLING OF MINIMA AND SADDLEPOINTS

EFFICIENT GENERATION OF POINTS THAT SATISFY PHYSICAL CONSTRAINTS IN A MANY-PARTICLE SYSTEM

Prototypical Problem

Variations on the Prototypical Problem

Simplest Strategy

Metropolis Monte Carlo Method

Relationship of These Problems to More General Optimization Problems

MOLECULAR DIVERSITY AND CORNBINATORIAL CHEMISTRY IN DRUG DISCOVERY

Overview of the Drug Discovery Process

Sources of Molecular Diversity

Current Computational Approaches to Compound Selection

Opportunities for Improvements in Computational Approaches to Compound Selection

STATISTICAL ANALYSES OF FAMILIES OF STRUCTURES

QUANTUM MONTE CARLO SOLUTION OF THE SCHRÖDINGER EQUATION

Variational Monte Carlo (VMC)

Diffusion Monte Carlo (DMC)

Green's Function Monte Carlo (GFMC)

Research Opportunities

NONADIABATIC PHENOMENA

EVALUATION OF INTEGRALS WITH HIGHLY OSCILLATORY INTEGRANDS: QUANTUM DYNAMICS WITH PATH INTEGRALS

Discussion of the Problem

Stationary-Phase Monte Carlo Methods

Alternative Approaches to the Prototype Problem

Other Formulations and Solutions of the Basic Problem

FAST ALGEBRAIC TRANSFORMATION METHODS

5 Cultural Issues and Barriers to Interdisciplinary Work

MOTIVATION AND CONNECTIONS

EFFECTS OF DISCIPLINARY BOUNDARIES

EFFECTS OF THE CURRICULUM

LANGUAGE DIFFERENCES

TOWARD A FRUITFUL COLLABORATION

6 Conclusions and Recommendations

Afterword.

Glossary.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

ISBN:

9786610193394

9780309176620

030917662X

9781280193392

1280193395

9780309560641

0309560640

9780585143897

0585143897

OCLC:

44957784