Large amplitude motions (LAMs) such as torsional and inversion motions are present in a variety of molecular systems ranging from small non-rigid molecules to polymers and play a crucial role in nuclear dynamics. This dissertation presents theoretical studies of LAM dynamics present in small molecules and polymers based on the quantum and classical approaches. On the small molecular side, high-level quantum calculations are performed to calculate high quality torsion-inversion potential energy surfaces for CH3XH2 (X=C, N, O). The torsion-inversion coupling is found to be in the range 280 ¿¿¿¿¿¿¿ V1,3 ¿¿¿¿¿¿¿ 450 cm-1. Torsion-inversion Hamiltonian is constructed and torsion-inversion energy levels as well as spectroscopic parameters are calculated for these molecular species. The frequency calculation at each stationary point of the surface is performed as well as the calculation of the two-dimensional torsion-inversion force constant surface. On the polymer side, nuclear dynamics are studied performing classical molecular dynamics (MD) simulations. The force field required for the MD simulations are derived from ab initio calculations. Both static and dynamical properties of poly(3-hexylthiophene) (P3HT), a promising solar cell material, are calculated. These properties include structural parameters, density, surface tension, glass transition temperature and melting temperature.