Potential Energy Surfaces: Proceedings Of The Mariapfarr Workshop In Theoretical Chemistry (lecture Notes In Chemistry)

**Potential Energy Surfaces** is a collection of lectures given at the 1996 Mariapfarr Workshop in Theoretical Chemistry, organized by Alexander F. Sax. The Mariapfarr Workshops' aim is to discuss in-depth topics in Theoretical Chemistry. The target group of these workshops is graduate students and postdocs. Hypersurfaces and Coordinate Systems 1 Preliminaries 2 Metric spaces 3 Vector spaces 4 Affine and Euclidian spaces 5 Manifolds 6 Coordinate systems used for molecules References The Idea of a Potential Energy Surface 1 Introduction 2 The removal of translational motion 3 Distinguishing electronic and nuclear motions 4 The body-fixed Hamiltonian 5 Separating electronic and nuclear motions 6 The clamped nucleus Hamiltonian 7 The Potential Energy Function 8 Conclusions References Interpolation and fitting of potential energy surfaces: Concepts, recipes and applications 1 Introduction 2 General functional forms 3 Specific forms for diatomic and polyatomic systems 4 Combination of theoretical and experimental data 5 Comparison of different fits in some test cases 6 Formulae for Lagrange-, Hermite-and spline-interpolations 7 Acknowledgments and literature 8 Appendix Empirical Classical Force Fields for Molecular Systems 1 Introduction 2 Choice of the explicit degrees of freedom 3 Force field terms 4 Conclusion References The Born-Oppenheimer Expansion: Eigenvalues, Eigenfunctions and Low-Energy Scattering 1 Introduction 2 Spectral Asymptotics 3 Low energy scattering for diatomic molecules References. Front Matter....Pages i-viii Hypersurfaces and Coordinate Systems....Pages 1-60 The Idea of a Potential Energy Surface....Pages 61-96 Interpolation and fitting of potential energy surfaces: Concepts, recipes and applications....Pages 97-175 Empirical Classical Force Fields for Molecular Systems....Pages 177-214 The Born-Oppenheimer Expansion: Eigenvalues, Eigenfunctions and Low-Energy Scattering....Pages 215-233 Back Matter....Pages 235-236 This volume contains the lectures given at the theoretical chemistry workshop in 1996 in Mariapfarr, Austria. Topics addressed include: hypersurfaces and coordinate systems; interpolation and fitting; empirical force fields; and the Born-Oppenheimer expansion.