Mathematical Frontiers in Computational Chemical Physics

This IMA Volume in Mathematics and its Applications MATHEMATICAL FRONTIERS IN COMPUTATIONAL CHEMICAL PHYSICS is in part the proceedings of a workshop which was an integral part of the 1986-87 IMA program on SCIENTIFIC COMPUTATION. We are grateful to the Scientific Committee: Bjorn Engquist (Chairman), Roland Glowinski, Mitchell Luskin and Andrew Majda for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizer, Donald Truhlar, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with atomic and molecular structure for a fruitful exchange of ideas. Willard Miller, Jr. Hans Weinberger MATHEMATICAL FRONTIERS IN COMPUTATIONAL CHEMICAL PHYSICS PREFACE The Workshop on Atomic and Molecular Structure and Dynamics was held June 15-July 24, 1987 at the Institute for Mathematics and Its Applications on the University of Minnesota Twin Cities campus as part of the 1986-87 I. M. A. Pro­ gram on Scientific Computation. There were over 70 participants, including the eleven plenary lecturers whose contributions form the chapters of this volume. The chapters discuss a wide variety of topics in the subject area of the Workshop. Each chapter includes expository material that is especially prepared to introduce the subject to a mathematical audience interested in studying frontier areas in math­ ematical chemical physics, and in addition each chapter also discusses challenging problem areas where additional mathematical progress is necessary and desirable for the advancement of the field.

Introductory Chapters.- The Born-Oppenheimer Approximation in Molecular Quantum Mechanics.- Electronic Structure Theory.- Spectral Theory.- Spectra of Atoms and Spectral Theory of Atomic Hamiltonians.- Stieltjes Methods for Schrödinger Spectra: Hilbert-Space Approximations to the Discrete and Continuum Eigenstates of Spatially Anisotropie Hamiltonian Operators.- Classical Many-Body Systems.- Classical Molecular Dynamics Simulations: Algorithms and Applications, Stochastic Dynamics, and Free Energies.- Collective Phenomena in Statistical Mechanics and the Geometry of Potential Energy Hypersurfaces.- Quantum Dynamics.- Quantum Evolution in External Electromagnetic Fields: Exact Results and Asymptotic Approximations.- New Time-Dependent and Time-Independent Computational Methods for Molecular Collisions.- Dynamical Groups.- Lie Algebraic Approach to Molecular Structure and Dynamics.- Lie Algebraic Approach to the Many-Electron Correlation Problem.- Unitary Group Approach to Configuration Interaction Calculations of the Electronic Structure of Atoms and Molecules.