Ehrenfest Statistical Dynamics in Chemistry: Study of Decoherence Effects.

In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to nonadiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.

Bethe approximation for a model of polymer solvation.

The phase diagram of a recently proposed model for the solvation of monomers and polymers in water is studied in the homopolymer case, and several thermodynamic quantities are computed by means of pair approximation of the cluster variation method, i.e., the Bethe approximation. The model takes into account the water degrees of freedom in a simplified way, so that they can be integrated out analytically. The resulting effective Hamiltonian contains only a temperature-dependent water-monomer interaction and its phase diagram can be easily studied thanks to the simplicity of the Bethe approximation and exhibits, for a hydrophobic polymer, both cold and warm unfolding transitions in a wide region of the parameter space. This suggests that the present one might be a toy-model description of the phase behavior observed experimentally in water solutions of hydrophobic polymers, such as poly-N-isopropylacrylamide (PNIPAM), as well as a step to understand the mechanism of cold unfolding in proteins.

Model for the hydration of nonpolar compounds and polymers.

We introduce an exactly solvable statistical-mechanical model of the hydration of nonpolar compounds, based on grouping water molecules in clusters where hydrogen bonds and isotropic interactions occur; interactions between clusters are neglected. Analytical results show that an effective strengthening of hydrogen bonds in the presence of the solute, together with a geometric reorganization of water molecules, are enough to yield hydrophobic behavior. We extend our model to describe a nonpolar homopolymer in aqueous solution, obtaining a clear evidence of both "cold" and "warm" swelling transitions. This suggests that our model could be relevant to describe some features of protein folding.

Modeling hydration water and its role in polymer folding.

The hydrophobic effect is the dominant force which drives a proteintowards its native state, but its physics has not been thoroughlyunderstood yet. We introduce an exactly solvable model of the solvation ofnon-polar molecules in water, which shows that the reduced number ofallowed configurations of water molecules when the solute is present isenough to give rise to hydrophobic behaviour. We apply our model to anon-polar homopolymer in aqueous solution, obtaining a clear evidence ofboth `cold' and `warm' collapse transitions that recall those of proteins.Finally we show how the model can be adapted to describe the solvation ofaromatic and polar molecules.