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Properties of Chemically Interesting Potential Energy Surfaces : Eurographicseminars - D. Heidrich

Properties of Chemically Interesting Potential Energy Surfaces



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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.- 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.

ISBN: 9783540542865
ISBN-10: 3540542868
Series: Eurographicseminars
Audience: General
Format: Paperback
Language: English
Number Of Pages: 183
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 1.07
Weight (kg): 0.33