Quantum dynamics of hydrogen/metal clusters and O...H...O fragment of protonated water dimer

This dissertation is divided into two parts. Part I presents a systematic study of the quantum vibrational dynamics of hydrogen/metal clusters, ranging from the simplest H/M₂ cluster which can be solved exactly by variational method, to the large H/M₇ system in which rigid body approximations are employed. For all the systems under considerations, great efforts are made to elucidate the quantum nature of the vibrational motion of the light hydrogen atom in the heavy metal clusters. Diffusion Monte Carlo (DMC) method is also used to study the ground state properties of this many-body system. A novel iterative method combining with 3D DVR variational calculations with a normal mode treatment is developed beyond rigid body approximation (RBA) treatment. Several case studies show that the DVR/NM scheme works quite well for a quantum particle moving on a predominantly classical cluster, and that it can be applied to some other systems, such as vibrational dynamics of hydrogen on surfaces.; In Part II, three-dimensional bound state calculations are reported for the vibration dynamics of fragment of the protonated water dimer in hyperspherical coordinate. This rigorous quantum treatment of the subspace provides the most accurate description to date of the vibrational spectrum of the above system. Detailed dynamics results as well as some lower dimensional adiabatic treatments are discussed.