Introduction
The so-called reaction path (RP) with respect to the potential energy or the Gibbs energy ("free enthalpy") is one of the most fundamental concepts in chemistry. It significantly helps to display and visualize the results of the complex microscopic processes forming a chemical reaction. This concept is an implicit component of conventional transition state theory (TST). The model of the reaction path and the TST form a qualitative framework which provides chemists with a better understanding of chemical reactions and stirs their imagination. However, an exact calculation of the RP and its neighbourhood becomes important when the RP is used as a tool for a detailed exploring of reaction mechanisms and particularly when it is used as a basis for reaction rate theories above and beyond TST. The RP is a theoretical instrument that now forms the "theoretical heart" of "direct dynamics". It is particularly useful for the interpretation of reactions in common chemical systems.
A suitable definition of the RP of potential energy surfaces is necessary to ensure that tbe reaction theories based on it will possess sufficiently high quality. Thus, we have to consider three important fields of research:
- Analysis of potential energy surfaces and the definition and best calculation of the RPs or - at least - of a number of selected and chemically interesting points on it.
- The further development of concrete versions of reaction theory beyond TST which are applicable for common chemical systems using the RP concept.
- The investigation of chemical reactions with RP concepts and theories based on it.
These fields are treated in this book. The present volume begins with an "Introduction to the Nomenclature and Usage of the RP concept" (D.Heidrich). The brief chapter tries to find a common language and better understanding between chemists when they are dealing with the RP and its applications.
Then, four contributions are grouped together (those from P.G.Mezey, X.Chapuisat, T.lwai and A. Tachibana, and from W. Quapp) which are related to important aspects or new developments of the reaction path theory.
The next block of chapters (by T.Helgaker, K.Ruud and P.R.Taylor, by W.Quapp, O.Imig, and D.Heidrich, and by G.Seifert and K.Krüger) is dedicated to the mathematical and quantum chemical techniques of calculating points on the RP. The last of these chapters includes a review of applications of the density functional theory in chemistry.
The following two chapters (written by D.G. Truhlar, and by A.D.Isaacson) are devoted to the description and application of current versions of reaction theories based on the RP concept ("direct dynamics" methods) for the ground state.
Finally, in the contribution of A.L.Sobolewski and W.Domcke, the "state of art" in treating the RP in excited states (of hydrogen transfer processes) are brought into focus. The last contribution by V.Engel gives us insights into the RP regions gained by modern time-resolved femtosecond syectroscopy and reviews literature in this field.
I asked the authors of the chapters to use clear and instructive introductions as well as more illustrations. So, in part, the book aims at a deepening of theoretical insights for the average chemist. If our book contributes to a better understanding of the RP concept and to encouraging theoreticians to fill or futther develop the existing grey zones between quantum mechanic scattering theory and trajectory calculations, on the one hand, and conventional TST, on the other hand, then it has served its purpose.
I would like to thank the authors for their valuable contributions. Special personal are dedicated to Prof.P.G.Mezey and Prof.D.G.Truhlar for their stimulating discussions and friendly support. The interdisciplinary "Naturwissenschaftlich- Theoretisches Zentrum" (NTZ) of the Leipzig University has greatly promoted our activities. Finally, I am very grateful to Dr.W.Quapp for his support in preparing the book and Margo Eastlund and Mike Cloud for corrections in our English text.
Dietmar Heidrich, Leipzig, March 1995
Table of Contents
An Introduction to the Nomenclature and Usage of the Reaction Path Concept
Dietmar Heidrich
From Reaction Path to Reaction Mechanism: Fundamental Groups and Symmetry Rules
Paul G. Mezey
Loose Definitions of Reaction Paths
Xavier Chapuisat
Role and Treatment of Zero Eigenvalues of Rotation in the Cartesian Force Constant Matrix along Reaction Path
Akitomo Tachibana and Toshihiro Iwai
The Invariance of the Reaction Path Description in any Coordinate System
Wolfgang Quapp
Second-Order Methods for the Optimization of Molecular Potential Energy Surfaces
Trygve Helgaker, Kenneth Ruud and Peter R. Taylor
Gradient Extremals and their Relation to the Minimum Energy Path
Wolfgang Quapp, Olaf Imig and Dietmar Heidrich
Density Functional Theory - Calculations of Potential Energy Surfaces and Reaction Patbs
Gotthard Seifert and Kerstin Krüger
Using the Reaction Path Concept to Obtain Rate Constants from ab initio Calculations
Alan D.Isaacson
Direct Dynamics Method for the Calculation of Reaction Rates
Donald G. Truhlar
Ab intio Studies of Reaction Paths in Excited-State Hydrogen Transfer Processes
Andrzej L.Sobolewski and Wolfgang Domcke
Viewing the Readion Path with the Help of Time-Resolved Femtosecond Spectroscopy
Christoph Meier and Volker Engel
Index
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