The importance of the potential surface model has led naturally to a large number of studies on the subject, where the emphasis has usually been placed on lower dimensional problems, such as the reaction dynamics of diatomic to four-atom systems, or conformational problems restricted to few internal rotations. The purposes and methods of this book are, however, somewhat different from those of most studies on potential surface problems. The emphasis here is placed on those fundamental properties of potential energy hypersurfaces that are general for higher dimensions, that is, for larger molecules. The study of these properties requires some of the tools of global analysis that are not among the routine mathematical techniques of quantum chemists: topology, homotopy, and homology. This book provides the reader with an introduction to the fundamentals and to some of the more recent developments in the theory of potential energy hypersurfaces. The text is fairly self-contained. It requires no previous mathematical knowledge from the reader beyond that needed in an undergraduate quantum chemistry course.
The importance of the potential surface model has led naturally to a large number of studies on the subject, where the emphasis has usually been placed on lower dimensional problems, such as the reaction dynamics of diatomic to four-atom systems, or conformational problems restricted to few internal rotations. The purposes and methods of this book are, however, somewhat different from those of most studies on potential surface problems. The emphasis here is placed on those fundamental properties of potential energy hypersurfaces that are general for higher dimensions, that is, for larger molecules. The study of these properties requires some of the tools of global analysis that are not among the routine mathematical techniques of quantum chemists: topology, homotopy, and homology. This book provides the reader with an introduction to the fundamentals and to some of the more recent developments in the theory of potential energy hypersurfaces. The text is fairly self-contained. It requires no previous mathematical knowledge from the reader beyond that needed in an undergraduate quantum chemistry course.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science & Technology
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Maße
Höhe: 230 mm
Breite: 150 mm
ISBN-13
978-0-444-42887-5 (9780444428875)
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Schweitzer Klassifikation
1. The Molecular Energy Expectation Value. Energy, the fundamental quantum mechanical observable. The Born-Oppenheimer approximation and the concept of nuclear geometry. Generalizations of nuclear coordinates. Global and local coordinate systems and the concept of nuclear configuration space. Intersections of Energy Hypersurfaces: adiabatic and diabatic representations. 2. Geometrical Properties of Energy Hypersurfaces. Energy derivatives: forces and force constants. Minima, saddle points and general critical points. Minimum energy path and the intrinsic reaction coordinate. Differential geometry of energy hypersurfaces. 3. Calculation and Representation of Energy Hypersurfaces. The Hartree-Fock-Roothaan-Hall method for the calculation of molecular wavefunctions. The electron correlation problem and the correlation energy. Calculation of semiempirical and empirical potential functions. The force method and calculation of higher derivatives. Minimum search methods for the determination of stable chemical species. Saddle point search methods for the determination of transition structures. Fitting of potential energy hypersurfaces, polynomials, splines and trigonometric functions. 4. The Quantum Chemical Concept of Molecules Revisited. Quantization and continuity. Wave packet topology. The topology of nuclear configurations. 5. Molecular Topology. The reduced nuclear configuration space: metric space M. Catchment regions of potential energy hypersurfaces: the representation of chemical species. Manifold theory of potential energy surfaces and catchment regions. Potential defying chemical species. The role of nuclear charges and relations between potential surfaces: convexity theorems in space w Z. Catchment regions and symmetry. 6. Reaction Topology. Topological reaction paths and quantum chemical reaction mechanisms. The algebraic structure of the complete set of reaction paths. The fundamental group of reaction mechanisms. The reaction globe, the reaction polyhedron, and homology group theory of reaction mechanisms. Quantum chemical reaction networks. The future of computer based quantum chemical synthesis design and molecular engineering. Appendix 1: Review of topological concepts. Appendix 2: Physical units and conversion factors. References. Subject Index.
