Friday, March 25, 2011

Overdamped quantum molecular dynamics

How do quantum states in organic molecules couple to their environment (e.g., a solvent and/or protein)?
Is the dynamics of excited states quantum or classical or something in between?

These questions are not just of fundamental scientific interest. Dye molecules are now widely used as a means to monitor biomolecules and nanoconfined water.

A nice way to investigate the above questions experimentally is with ultrafast laser spectroscopy.  For example, to optically excite a molecule and monitor the emission (fluorescence) in real time. A nice combined theoretical/experimental study is in the paper
Femtosecond fluorescence upconversion studies of barrierless bond twisting of auramine in solution by van der Meer, Zhang, and M. Glasbeek.

Upon photoexcitation the auramine dye molecule (below) is believed to undergo twisting of the phenyl (benzene) rings on the left and right side of the central C=NH2 bridge. With increasing time [1-100 psec] this leads to redshift in the light emission frequency [dynamic Stokes shift] and a reduction in the intensity of emission. As the temperature decreases and the viscosity of the solvent increases the time scale on which these changes occur increases.

Here are a few of the key ideas and things I found interesting about the paper.

They consider four alternative physical models to explain the experiments and rule out three of them. The best model consists has the excited state being a superposition of a two diabatic states: one fluorescent F and one dark D. As the reaction proceeds (the molecule twists) the character of the state changes from F to D.

Dynamics on the excited state potential energy surface is described by a Schmoluchowski equation with a rotational diffusion constant Dr.

Comparing the predictions of the model with experimental data they find that the diffusion constant Dr  increases with the temperature and with the inverse of the solvent viscosity. The magnitude of this dependence is consistent with the Einstein-Stokes relation. This shows that the twisting motion of the molecule is overdamped by collisions with the solvent molecules. [Since the solvent is non polar dielectric relaxation is not involved].

A key next step is to provide a quantum chemical justification for the model, both the existence of the dark excited state and the relevant parameters in the effective Hamiltonian for the excited state.

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