Properties of Chemically Interesting Potential Energy Surfaces

ISBN-13: 9783540542865 / Angielski / Miękka / 1991 / 183 str.

D. Heidrich; Dietmar Heidrich; Wolfgang Kliesch

Opis

This is a summary of modern chemical reaction theories in the light of the reaction path concept of potential energy hypersurfaces (PES). It presents a simple mathematical analysis of stationary and critical points of the PES and aims to provide the tools necessary for studying chemical reactions.

Spis treści

1 Guidelines in the Development of the Theory of Chemical Reactivity using the Potential Energy Surface (PES) Concept.- 1.1 The Potential Energy Surface (PES) Concept.- 1.2 The Dimensionality Problem.- 1.3 On the Definition of a Reaction Path (RP).- 1.4 The Hierarchy and Competition of Reaction Theories.- 1.5 What about the Calculation of Absolute Reaction Rates?.- 1.6 Potential Energy Calculation and Gradient Revolution.- 1.7 The “State of the Art” in Everyday Study of Chemical Reactivity.- References.- 2 Analysis of Multidimensional Potential Energy Surfaces — Stationary and Critical Points.- 2.1 Basic Definitions and Notations.- 2.2 Geometrical Properties of PES.- 2.3 Stationary Points.- 2.4 Location of Stationary Points.- 2.4.1 The Newton Process and its Modifications.- 2.4.2 Update Methods.- 2.4.3 Quasi-Newton Methods.- 2.4.4 Descent Methods.- 2.4.5 A Global Newton-like Method.- 2.5 Testing of Numerical Procedures.- 2.6 Zero Eigenvalues of the Hessian.- 2.6.1 Translational and Rotational Invariance.- 2.6.2 “True” Zero Eigenvalues: Catastrophe Points.- 2.6.3 Flat Bottoms and Double Minimum Potentials.- References.- 3 Analysis of Multidimensional Potential Energy Surfaces — Paths —.- 3.1 the Simple Valley Floor Line.- 3.2 Mathematics of Valley Floors.- 3.2.1 Gradient Extremals (GE).- 3.2.2 GE and Bifurcation Points.- 3.2..3 GE for Higher-Dimensional Cases.- 3.3 Steepest Descent Paths.- 3.4 The Independence of Steepest Descent Paths from Parameterization and Coordinate System.- 3.4.1 Parameterization.- 3.4.2 Invariance from Coordinate System.- 3.4.3 Mass-Weighted Cartesian Coordinates.- References.- 4 Quantum Chemical Pes Calculations: The Proton Transfer Reactions.- 4.1 The Problem in Visualization of PES Properties.- 4.1.1 RP Energy Profiles and Surfaces Derived from Usual PES Sections.- 4.1.2 Graphical Presentation of Three-center Problems.- 4.1.3 Interaction Surface of an Attacking Species with a Fixed Valence System.- 4.1.4 Empirically Derived Diagrams of more Complex Reactions PES.- 4.1.5 Energy Profiles from Mathematically Defined RP Calculations.- 4.1.6 Summary.- References.- 4.2 PES Properties Along the Bimolecular Single Proton Transfer.- 4.2.1 Formulation of the Reaction Mechanisms.- 4.2.2 The Proton Transfer Energy.- 4.2.3 Discussion of most Recent PES Data of Bimolecular Single Proton Transfer.- 4.2.4 Gas-Phase Results and Medium Influenced Experimental Data.- 4.2.5 Theoretical Approach to Medium Influence and the PES Concept.- 4.2.6 Proton Transfer, Transition State Theory, and Quantum Chemistry.- References.