Rare-event phenomena are ubiquitous in nature. We propose a new strategy, kappa-dynamics, to model rare event dynamics. In this methodology we only assume that the important rare-event dynamics obey first-order kinetics. Exact rates are not required in the calculation and the reaction path is determined on the fly. kappa-dynamics is highly parallelizable and can be implemented on computer clusters and distributed machines. Theoretical derivations and several examples of atomic scale dynamics are presented. With single-molecule (SM) techniques, the individual molecular process can be resolved without being averaged over the ensemble. However, factors such as apparatus stability, background level, and data quality will limit the amount of information being collected. We found that the correlation function calculated from the finite-size SM rotational diffusion trajectory will deviate from its true value. Therefore, care must be taken not to interpret the difference as the evidence of new dynamics occurred in the system. We also proposed an algorithm of single fluorophore orientation reconstruction which converts three measured intensities {I₀,I₄₅,I₉₀} to the dipole orientation. Fluctuations in the detected signals caused by the shot noise result in a different prediction from the true orientation. This difference should not be interpreted as the evidence of the nonisotropic rotational motion. Catalytic reactions are also governed by the rare-events. Studying the dynamics of catalytic processes is an important subject since the more we learn, the more we can improve current catalysts. Fuel cells have become a promising energy source in the past decade. The key to make a high performance cell while keeping the price low is the choice of a suitable catalyst at the electrodes. Density functional theory calculations are carried out to study the role of geometric relaxation in the oxygen-reduction reaction for nanoparticle of various transition metals. Our calculations of Pt nanoparticles show that the structural deformation induced by atomic oxygen binding can energetically stabilize the oxidized states and thus reduces the catalytic activity. The catalytic performance can be improved by making alloys with less deformable metals. / text