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 -- References -- NUMERICAL ANALYSIS -- References -- DISTANCE GEOMETRY -- References -- MATHEMATICS AND FULLERENES -- References -- QUASICRYSTALS -- References -- 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 -- References -- GRAPH THEORY -- Application of Graph Theory to Organizing Chemical Literature -- Application of Graph Theory to Representation of Chemical Reactions -- References -- X-RAY CRYSTALLOGRAPHY -- Remark -- References -- 4 Mathematical Research Opportunities from Theoretical/Computational Chemistry -- INTRODUCTION -- References -- NUMERICAL METHODS FOR ELECTRONIC STRUCTURE THEORY -- THE N-AND V-REPRESENTABILITY PROBLEMS -- References -- MELDING OF QUANTUM MECHANICS WITH SIMPLER MODELS -- References -- 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 -- References -- N-AND V-REPRESENTABILITY PROBLEMS IN CLASSICAL STATISTICAL MECHANICS -- References -- 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 -- References -- LOCATING SADDLEPOINTS -- References -- 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 -- References -- 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 -- References -- NONADIABATIC PHENOMENA -- References -- EVALUATION OF INTEGRALS WITH HIGHLY OSCILLATORY INTEGRANDS: QUANTUM DYNAMICS WITH PATH INTEGRALS -- Prototypical Problem -- Discussion of the Problem -- Stationary-Phase Monte Carlo Methods -- Alternative Approaches to the Prototype Problem -- Other Formulations and Solutions of the Basic Problem -- References -- FAST ALGEBRAIC TRANSFORMATION METHODS -- References -- 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 -- References -- 6 Conclusions and Recommendations -- References -- Afterword.

Glossary.