Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Multiple proton translocation in biomolecular systems: concerted to stepwise transition in a simple model

In this paper we study a simple model potential energy surface (PES) useful for describing multiple proton translocation mechanisms. The approach presented is relevant to the study of more complex biomolecular systems like enzymes. In this model, at low temperatures, proton tunnelling favours a concerted proton transport mechanism, while at higher temperatures there is a crossover from concerted to stepwise mechanisms; the crossover temperature depends on the energetic features of the PES. We illustrate these ideas by calculating the crossover temperature using energies taken from ab initio calculations on specific systems. Interestingly, typical crossover temperatures lie around room temperature; thus both concerted and stepwise reaction mechanisms should play an important role in biological systems, and one can be easily turned into another by external means such as modifying the temperature or the pH, thus establishing a general mechanism for modulation of the biomolecular function by external effectors.

Optimal basis set for electronic structure calculations in periodic systems

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a single (i.e., common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from k.p-approximation theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analyzed for a test calculation on a 16-atom Na supercell.