Coherent corrected diffusivity

One expects that Dg and Dt will have a different concentration dependence. Comparisons between PFG NMR, QENS, and MD simulations could only be made in the past at the level of Dg. At equihbriiun, one can now obtain experimentally Dt using coherent neutron scattering. From equihbrium MD simulations, one cannot derive Dt, but one can determine the corrected diffusivity Do. These two diffusivities are linked by considering that the driving force for diffusion is the chemical potential gradient, and not the concentration gradient... 

Coherent QENS measurements and MD simulations have been performed for N2 and CO2 in silicalite [30,31]. It has been found that the self-diffusivities of the two gases decrease with increasing occupancy, while the transport diffusivities increase. For a comparison with other systems, it is appropriate to remove the influence of the thermodynamic correction factor and to discuss the collective mobility in terms of the corrected diffusivity (also called Maxwell-Stephan diffusivity). Dq(c) is directly obtained from the Simula-... 

For the moment, assume that the VE picture is correct and inertial solvent motion causes negligible dephasing. Diffusive motion must be the primary cause of coherence decay. In the VE theory, the diffusive motion is the relaxation of stress fluctuations in the solvent by viscous flow. The VE theory calculates both the magnitude Am and lifetime z0J of the resulting vibrational frequency perturbations. A Kubo-like treatment then predicts the coherence decay as a function of the viscosity of the solvent. Figure 19 shows results for typical solvent parameters. At low viscosity, the modulation is in the fast limit, so the decay is slow and nearly exponential. Under these conditions, the dephasing time is inversely proportional to the viscosity, as in previous theories [Equation (19)]. As the viscosity increases, the modulation rate slows. The decay becomes faster and approaches a... 

We have presented several approaches to calculate the rate constants of electron transfer occurring in solvent from the weak to strong electronic couplings. In the fast solvent relaxation limit, the approach based on the nonadiabatic transition state theory can be adopted. It is related to the Marcus formula by a prefactor and referred as a modified Marcus formula. When the solvent dynamics begin to play a role, the quantum Kramers-like theory is applicable. For the case where the intramoleeular vibrational motions are much faster than the solvent motion, the extended Sumi-Mareus theory is a better ehoice. As the coherent motion of eleetron is ineorporated, such as in the organic semiconductors, the time-dependent wavepaeket diffusion approach is proposed. Several applications show that the proposed approaches, together with electronic structure calculations for the faetors eontrolling eleetron transfer, can be used to theoretically predict electron transfer rates correctly. 

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