Theoretical Advances toward Understanding Recent Experiments in Biophysical Chemistry

Several theoretical advances are presented, with the common theme of helping better understand and guide recent experiments in biophysical chemistry. In Chapter 2, I consider a recent criticism of the Jarzynski equality, notably that a breakdown in the connection between work and changes in the Hamiltonian for time-dependent systems causes the Jarzynski equality to produce unphysical results. I discuss the relationship between two possible definitions of free energy and demonstrate that it is indeed possible to obtain physically relevant free energy profiles from the Jarzynski equality, thereby resolving the recent questions in the literature. Next, I consider several aspects of coherent resonance energy transfer. In Chapter 3, I present a theory for coherent resonance energy transfer based on classical electrodynamics and demonstrate how it is able to capture dynamics in the coherent regime, the incoherent regime, and in between these two limits. In Chapter 4, I present a quantum theory for resonant energy transfer based on using a variational polaron transform to optimally split the Hamiltonian into a zeroth-order part and a perturbation. I then apply a quantum master equation to obtain the dynamics of energy transfer for various parameters. Finally, in Chapter 5, I examine whether it is possible to use the known exact equilibrium state of the system to improve the variational procedure. Thesis Supervisor: Robert J. Silbey Title: Class of 1942 Professor of Chemistry