Rotation time, solvent molecules

In an adiabatic electron transfer reaction in aqueous solution the transfer coefficient k is 1 and e c lli ion frequency between two uncharged reactants is 10 M s (1). If other solvents are used, Z may increase in value because it depends on the time of the concerted rotations of solvent molecules. If k is smaller than 1 we speak of nonadiabatic reactions their theoretical treatment is difficult ang will not be attempted here (4). The free energy of activation (AG ) can be divided into four important parts ... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

The rotational relaxation of low-viscosity solvents takes place in times of ps. This can be observed through time-resolved spectroscopy when the dipole moment of the excited molecule differs substantially from that of the ground state species. Table 8.2 gives a few values of these relaxation times the alcohols show rather slow relaxation because of the hydrogen bonds which associate the solvent molecules. 

The V-B coupling Hamiltonian to first order in the three HOD dimensionless normal coordinates is Hv b = —2, c], l , where F, is the inter-molecular force due to the solvent exerted on the harmonic normal coordinate, evaluated at the equilibrium position of the latter. This force obviously depends on the relative separations of all molecules, and on their relative orientations. In the most rigorous quantum description of rotations, this term would depend on the excited molecule rotational eigenstates and of the solvent molecules. Instead rotation was treated classically, a reasonable approximation for water at room temperature. With this form for the coupling, the formal conversion of the Golden Rule formula into a rate expression follows along the lines developed by Oxtoby (2,53), with a slight variation to maintain the explicit time dependence of the vibrational coordinates (57),... 

Even in the case of strong interactions between solvent and solute, the life time of each solvate is brief since there is continuous rotation or exchange of the solvent shell molecules. The time required for reorientation of hydrates in water is of the order 10 ... 10 " s at 25 °C [91]. If the exchange between bulk solvent molecules and those in the inner solvation shell of an ion is slower than the NMR time scale, then it is possible to observe two different resonance signals for the free and bound solvent. In this... 

Other spectroscopic methods have also been used to study the statics and dynamics of solvation shells of ions and molecules [351-354], In this respect, solvation dynamics refers to the solvent reorganization e.g. rotation, reorientation, and residence time of solvent molecules in the first solvation shell) in response to an abrupt change in the solute properties, e.g. by photoexcitation of the solute with ultra-short laser-light pulses. Provided that this excitation is accompanied by an electron transfer or a change in the dipole moment, then the dynamics of this process correspond to how quickly the solvent molecules rearrange around the instantaneously created charge or the new dipole. 

Another matter concerns the time of reaction between a set of water molecules after an ion has just pushed its way into the middle of them. Thus, if the lifetime of molecules in the primary solvation shell is sufficiently short, there must be somejumps in which the ion is bare or at least only minimally clothed. How is the hydration number affected by the time needed for the solvent molecules buried in the solvent layer to break out of that attachment and rotate so that their dipoles are oriented toward the ion to maximize the energy of interaction (cos 0 = 1) ... 

The effective time of such a relaxation is much higher than the rotation time of solvent dipoles. In the frame work of the transition state theory, when the inner-sphere reorganization can be neglected, v is related to the rotation time of solvent molecules in the dielectric medium, 1 1. by... 

---