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Über dieses Buch

Contemporary chemical reaction theory is the characterization of Potential Energy Hypersurfaces (PES). The authors critically analyze chemically and mathematically suitable reaction path definitions. The book presents a simple mathematical analysis of stationary and critical points of the PES. It provides tools for studying chemical reactions by calculating reaction paths and related curves. A further aspect of the book is the dependence of PES properties on approximations used for the analysis. Recent quantum chemical calculations, particularly of single proton transfer processes, and experimental data are compared. The book addresses students and researchers in Theoretical Chemistry, Chemical Kinetics and related fields.



1. GuideLines in the Development of the Theory of Chemical Reactivity Using the Potential Energy Surface (PES) Concept

The PES concept forms the basis for a variety of theories, models and methods for the study of chemical reactivity. These methods represent a variety of classical, semiclassical, and completely quantum-mechanical methodologies with different degrees of accuracy and applicability to perform calculations of microscopic and macroscopic attributes of chemical reactions. Beyond the investigation of reaction mechanisms, problems which arise from multiphoton excitations in a hypothetical mode-specific chemistry may also be analysed on the basis of the FES concept. Its realization depends on the extent of the intramolecular vibrational redistribution (IVR) which may also be attributed to special PES properties
D. Heidrich, W. Kliesch, W. Quapp

2. Analysis of Multidimensional Potential Energy Surfaces — Stationary and Critical Points —

As outlined in the introducing chapter, the minimizers and the saddle points of index one of the energy functional are corner-stones of most reaction theories in chemistry. Thus the applicability of these theories strongly depends on the availability of mathematical methods, which compute such points in an effective manner. Therefore the current chapter is engaged in the presentation of methods, which enable to compute minima and/or saddles of a PES.
D. Heidrich, W. Kliesch, W. Quapp

3. Analysis of Multidimensional Potential Energy Surfaces — Paths —

We assume a chemical reaction along a valley path crossing a saddle point (SP1) of the PES. We at first also assume no occurrence of zero eigenvalues of the Hessian orthogonal on the path, which would exclude valley path bifurcation. Starting from a minimum in the direction of the eigenvector of the weakest positive eigenvalue of H(x) upwards in the energy mountains, a simple and deep valley will be traced.
D. Heidrich, W. Kliesch, W. Quapp

4. Quantum Chemical PES Calculations: The Proton Transfer Reactions

In this chapter we discuss
  • ▸ the characterization and visualization of selected reaction PES (proton transfer reactions, Sect. 4.1),
  • ▸ how approximations in the quantum chemical methods may determine the quality of reaction PES (Sect. 4.2), both along with
  • ▸ recent results for bimolecular single proton transfer reactions in comparison to experimental data.
D. Heidrich, W. Kliesch, W. Quapp


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