The writing of this book is motivated by recent advances in the field of theoretical reaction dynamics since the mid-1980's.  Prior to the mid-1980's, the field of reactive scattering was dominated by model theoretical studies of collinear atom-diatom reactive scattering and approximate three dimensional atom-diatom reactive scattering including only two effective degrees of freedom. The post mid-1980's period has been marked by rapid progress in the development of rigorous quantum mechanical methods for computation of molecular reactive scattering in the gas-phase.  The rapid development in computational methodology was motivated in part by the availability of new and faster computers to theoretical chemists.  The new theoretical and computational development has quickly eclipsed collinear atom-diatom scattering calculations and made exact 3D atom-diatom reactive scattering calculations routine applications in the gas-phase.  For the first time exact quantum dynamics calculations have enabled theoretical chemists to make accurate dynamics predictions for some simple triatomic reactions.  Such exact quantum dynamics methods provide rigorous theoretical tools for analyzing reaction dynamics at an unprecedented level of detail and accuracy.  Exact dynamics calculations can be regarded as ``simulated experiments", especially when coupled with {\it ab initio} quantum chemistry calculation.

Although this book is motivated by recent theoretical advances, it is not written simply to describe the progress in the field of chemical reaction dynamics.  Rather, the book is intended to provide a balanced presentation of both fundamental dynamics theories and their applications to realistic chemical dynamics problems. From my personal knowledge and experience, there is a real need for a book that can combine both the abstract theory on quantum scattering and practical methodologies that are tailored for numerical applications to realistic molecular systems.  Currently, there are basically two categories of books that are being read by graduate students and researchers in the field. On the one side are books on abstract scattering theory mainly written by and for theoretical physicists.  These books are usually quite abstract and mainly describe theories on elastic scattering with few, if any, discussions of treatment of reactive or arrangement scattering problems that are relevant to reaction dynamics.  On the other side are monographs and proceedings on very specific topics in quantum reactive scattering that are mainly tailored for those specialists who are already experts in the field.

In view of the above considerations, the contents of this book are specially organized to contain three main parts: (1) fundamental theory of scattering (2) development of practical computational methodologies based on fundamental theory and (3) applications of theory to specific benchmark molecular systems.  In particular, the section dealing with scattering theory in the book is written in a coherent fashion.  The central theme of the theory is based on the time-dependent picture in order to help the reader visualize the dynamical process and gain a physically intuitive picture.  This is in contrast to most traditional books on scattering theory that tend to focus on the abstract time-independent theory of scattering.  I believe that the time-dependent theme will make the topic of scattering theory much easier to understand and grasp by graduate students and anyone who is new to the field.  The presentation of the theory in this book is then generally followed by applicable computational methods, and in addition, efforts are made to show specific applications of theories or methods to chemical problems.  Besides the main topics in quantum dynamics, the book also has other useful contents including an introductory chapter on Hartree-Fock theory for electron structure and a chapter on the basic theoretical treatment of separation of electronic and nuclear degrees offreedom.  There is also an appendix at the end of the book to provide the reader with many useful mathematical formulas and relations that are frequently encountered in theoretical studies and computation of quantum molecular dynamics problems.  Taken as a whole, this book is thus intended to be a comprehensive treatment of quantum scattering theory and its application in molecular reaction dynamics.

This book is organized as follows; Chapter 1 describes the basic theory and treatment for molecular systems with both electronic and nuclear degrees of freedom.  Chapter 2 introduces the basic theory of the Hartree-Fock equations for solving electronic problems.   This is followed by a description of theoretical methodologies to solve general bound state problems for molecules in Chapter 3.  The fundamental theory of quantum scattering is presented in detail in Chapter 4.  Chapter 5 focuses on the development of time-independent computational methodologies to solve gas phase reactive scattering problems with specific applications to prototype atom-diatom reactive scattering.  Chapter 6 presents the time-dependent wavepacket approach for solving large scale quantum dynamics problems with specific applications to benchmark tetraatomic reactions.  Chapter 7 describes various equivalent forms of state-to-state S matrix elements and their applications.  It also presents a general reactant-product decoupling (RPD) approach to computing state-to-state $S$ matrix elements for large systems.  The theory and phenomena of dynamical resonances and relation of the exact quantum mechanical rate constant to the transition state theory are given in Chapter 8.  Chapter 9 introduces basic theory for molecular interactions with the radiation field and presents methodologies for calculating fragmentation dynamics of molecules.  Theoretical models with applications to molecular reactions on rigid solid surfaces are presented in Chapter 10.  Finally, Chapter 11 presents general theories of semiclassical approximation in quantum mechanics.

This book is written as a self-contained and comprehensive yet very compact book that is suitable for a variety of readers including graduate students, researchers and/or other professionals who are interested in the theory and applications in the field of molecular reaction dynamics.

Many people have contributed to my writing of this book.  I especially thank Prof. Donald J. Kouri and Prof. William H. Miller from whom I have learned many of the theories presented in the book while I was a graduate student and postdoctoral fellow.  Many of the research topics and specific applications presented in the book are results of years of research work done by my former students and postdoctoral fellows.  Here I would like to thank Dr. Donghui Zhang, Dr. Jiqiang Dai, Dr. Wei Zhu for their contributions to the research topics presented in the book.  I thank my colleague Prof. Henry Brenner for careful reading of the manuscript and for correcting errors.  The writing of this book began while I was on sabbatical for one semester at Hong Kong University of Science and Technology in 1997.