Normal modes of the solvent

Here /x and /x are the reduced masses for the normal mode associated with the reaction coordinate and for the th normal mode of the solvent, respectively. Note the different signs of the potential energy terms for the unstable reaction coordinate and the stable solvent coordinates. 

B. The Instantaneous Vibrational Friction and the Instantaneous Normal Modes of the Solvent... 

Resonance Raman (RR) experiments have also provided valuable data on the structure of the electron. RR spectra of aqueous solvated electrons revealed enhancements of the water inter- and intra-molecular vibrations demonstrating that electronic excitation was significantly coupled to these modes. Frequency downshifts of the resonantly enhanced H2O bend and stretch were explained by charge donation into solvent frontier orbitals. RR spectra in primary alcohols (methanol, ethanol, propan-l-ol) revealed strong vibronic coupling of the solvated electron to at least five normal modes of the solvent. The spectra showed enhancements of the downshifted OH stretch. 

For the normal modes of the solvent and their application, see Stratt (1995), Stratt and Maroncelli (1996). 

Most modern investigations of the effects of a solvent on the rate constant, where dynamical fluctuations are included, are based on a classical paper by Kramers from 1940 [1], His theory is based on the transition-state theory approach where we have identified the reaction coordinate as the normal mode of the activated complex that has an imaginary frequency. In ordinary transition-state theory, we assume that the motion in that coordinate is like a free translational motion with no recrossings. This... 

We expand the potential energy surface at the saddle point to second order in the coordinates at the top of the barrier and determine the normal modes of the activated complex one of them is the reaction coordinate y identified as the mode with an imaginary frequency. Since the other normal modes of the activated complex are not coupled to the reaction coordinate in the harmonic approximation, we do not consider them here because they are irrelevant. For the harmonic solvent, we may likewise find the normal modes S. We use these normal modes to write down the Hamiltonian, and then add a linear coupling term representing the coupling between the reaction... 

There is an additional layer of complexity that increases the coupling further. As described above, the universe is external to the solute/solvent system. Perhaps the universe represents some collective normal mode(s) of the solute/solvent system, whose response is separable (or approximately so) from the local solvation of the solvent to the solute. In particular, this occurs when the solute/solvent system contains a large number of solute particles whose properties change as a function of their individual dynamics. In the limit of high enough solute concentrations, the collective (macroscopic) change of these solutes thus leads to a change in the solvation for each of them individually. 

In principle, solvent trapping is also included in the vibrational overlap intergral in equation (25). As noted above, the solvent dipole reorientational motions associated with solvent trapping can be treated as a series of collective vibrations of the medium using approaches devised for treating the collective vibrations of ions or atoms that occur in a crystalline lattice.32-33 However, the problem is mathematically intractable because of the many solvent molecules involved which lead to many normal modes and the existence of a near continuum of energy levels. In addition,... 

If you know nothing about the sample except its solubility, refer to Figure 4-1 and attempt to choose a mode complementary to the polarity of the solvent. For instance, if the sample dissolves in heptane and chloroform, choose a normal-phase mode. If the sample is soluble in methanol or water/... 

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