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.
