In many ultrafast electron transfer reactions, the reactant population decays as a multi-exponential function of time and the traditional assumption of well-separated time scales is invalid. The dynamics of electron transfer depends, in general, on the complicated dynamical properties of the dielectric medium and needs to be described by a detailed reactant population relaxation rather than just a rate constant. Our aim is to develop new theories and computational tools to characterize the dynamics of ultrafast electron transfer reactions. For a generic model of electron transfer, the spin-boson Hamiltonian, our recent strategy is to map the discrete quantum degrees of freedom onto continuous variables and the resulting dynamical problem is studied using the semiclassical initial value representation.

For homogeneous dielectric fluids, a simple dielectric continuum theory adequately describes their dielectric response. For example, using the dielectric response of water we were able to successfully describe aqueous solvation dynamics measured by time-dependent Stokes shift experiments and by photon-echo experiments. However, for inhomogeneous dielectric materials, such as proteins, micellar systems and zeolites, dielectric fluctuations are severely restricted due to the inherent constraints of the materials. Constraints give rise to rough energy landscapes with many pertinent length scales. Traditional dielectric continuum theory assumes that there is only one intrinsic microscopic length scale. Hence, such theory is questionable when applied to inhomogeneous dielectric materials.

On other hand, atomistic molecular dynamics simulations' computational cost is extremely
high for large proteins. To overcome these shortcomings, we try to constructe physically well-justified models to avoid the high computational cost and yet to describe the inhomogeneous response. In a recent model, a collection of structurally constrained polarizable dipoles embedded in a dielectric continuum solvent to describe the dielectric response of a protein using the actual molecular structure at the atomic level from protein data bank. The main assumption of our model is the existence of a set of  intrinsic polarizabilities for each residue, portable to all proteins in nature. The polarizabilities can be obtained by performing detailed molecular dynamics simulations for small proteins. The dielectric response of large proteins can be computed from these  intrinsic parameters.

Three-dimensional atomic structures of proteins form the foundation of our molecular understanding of biology. X-ray crystallography is the major and  sometimes only tool for the determination of these detailed protein structures. The bottleneck of this method is to grow
a large and good quality crystal used in diffraction.  For membrane proteins which carry out some of the most fundamental processes in biology such as photosynthesis, vision and nerve communications, it is exceedingly difficult to find the optimal crystallization conditions because of their peculiar molecular properties.  This difficulty is in no small part due to the lack of a transparent and reliable theoretical model to describe the crystallization process. Our research goal is to develop such a theoretical model and to explore the physical principles of finding optimal crystallization conditions. By studying the relationship between the crystallization conditions
and the physical parameters of the protein solution, we should be able to provide  useful guidance to the search for protein crystallization conditions.