UC Berkeley

Semiclassical approaches to chemical dynamics show great promise as methods to obtain practical results for a wide range of problems. In this dissertation we make these approaches more practical, by improving the efficiency of the calculations, and apply them to a wider range of problems, by developing techniques to explore new kinds of problems.

The approaches to improve the efficiency of semiclassical calculations essentially fall into two categories: we can reduce the number of trajectories we need in order to converge the calculation, or we can make each trajectory easier to calculate. (Of course, these two are not mutually exclusive.)

In this work, we have made attempts on both sides. Our efforts to reduce the number of trajectories required have been focused on finding ways to make the Monte Carlo sampling more efficient. The first method uses time-dependent information in order to reduce the sampling space. The second explores the idea of histogramming the phase of the contribution to the integrand. Although only the first of these shows real promise as a way to speed up semiclassical calculations, both methods can provide insights on the nature of the quantum effects we observe.

In an effort to make each trajectory easier to calculate, we developed a new method for calculating the monodromy matrix, which serves as the input to calculating the semiclassical prefactor. Calculating the semiclassical prefactor is the most computationally expensive part of generating a trajectory for a semiclassical calculation. Our new method doesn't break open the bottleneck, but it does make a meaningful improvement.

Finally, we step beyond simple improvements in efficiency. The dynamics of fermions provide a challenge for semiclassical methods. We present a method for generating a semiclassical Hamiltonian from a second-quantized fermionic Hamiltonian. This technique is applied to a simple model of a molecular transistor, and the results are in excellent agreement with the exact quantum calculations.