One of the biggest challenges in Chemical Dynamics is describing the behavior of complex systems accurately. Classical MD simulations have evolved to a point where calculations involving thousands of atoms are routinely carried out. Capturing coherence, tunneling and other such quantum effects for these systems, however, has proven considerably harder. Semiclassical methods such as the Initial Value Representation (SC-IVR) provide a practical way to include quantum effects while still utilizing only classical trajectory information. For smaller systems, this method has been proven to be most effective, encouraging the hope that it can be extended to deal with a large number of degrees of freedom. Several variations upon the original idea of the SCIVR have been developed to help make these larger calculations more tractable; these range from the simplest, classical limit form, the Linearized IVR (LSC-IVR) to the quantum limit form, the Exact Forward-Backward version (EFB-IVR). In this thesis a method to tune between these limits is described which allows us to choose exactly which degrees of freedom we wish to treat in a more quantum mechanical fashion and to what extent. This formulation is called the Tuning IVR (TIVR). We further describe methodology being developed to evaluate the prefactor …

The thesis is concerned with the relation between a microscopic approach and a macroscopic approach to the study of the nuclear binding energy as a function of neutron number, proton number and nuclear deformations. First of all we give a general discussion of the potential energy of a system which can be divided into a bulk region and a thin skin layer. We find that this energy can be written down in the usual liquid drop type of expression, i.e., in terms of the volume, the surface area and other macroscopic properties of the system. The discussion is illustrated by a study of noninteracting particles in an orthorhombic potential well with zero potential inside and infinite potential outside. The total energy is calculated both exactly (a microscopic approach) and also from a liquid drop type of expression (a macroscopic approach). It turns out that the latter approach reproduces the smooth average of the exact results very well. We next make a digression to study the saddle point shapes of a charged conducting drop on a pure liquid drop model. We compare the properties of a conducting drop with those of a drop whose charges are distributed uniformly throughout its volume. …