In this work two different areas of study are discussed. First, a novel model is presented for the quantum mechanics of large amplitude motion in floppy hydrides. A framework is developed for converged quantum mechanical calculations on large amplitude dynamics in polyatomic hydrides (XH_n ) based on a relatively simple, but computationally tractable, "particles-on-a-sphere" (POS) model for the intramolecular motion of the light atoms. The model assumes independent 2D angular motion of H atoms imbedded on the surface of a sphere with an arbitrary interatomic angular potential, which permits systematic evolution from "free rotor" to "tunneling" to "quasi-rigid" polyatomic molecule behavior for small but finite values of total angular momentum J. Simple tri- and tetra- atom hydrides act as a test suite for the POS model. After successfully modeling these systems, the model is used on systems with 4 and 5 hydrogens surrounding a central heavy atom, with the final focus on the theoretically and experimentally challenging CH₅⁺ molecule.

Next, novel methods are introduced for computing multistate potential energy surfaces for the abstraction of hydrogen by fluorine in two different experimentally important systems: F(²P) + HCl → HF + Cl( ²P) and F(²P) + H₂O → HF + OH( ²Σ). A novel method of dynamically adjusted weighting factors in state-averaged multiconfigurational self-consistent field calculations (SA-MCSCF) is developed and tested on the F(²P) + H₂O → HF + OH (²Π) reaction. Using the DW-MCSCF approach a new multistate electronic potential energy surface for the F(²P) + HCl → HF + Cl(²P) reaction is calculated in full dimensionality. The thesis concludes with nonadiabatic quantum nuclear dynamics calculations for the F(²P) + HCl → HF + Cl(²P) reaction.