Solvent effects spectral density

There are a number of considerations that must be addressed when formulating quantitative 13c NMR procedures - these include solvent effects, spectral overlap, line widths, dynamic and nuclear Overhauser effects and detailed assignments. The steps required to develop sound quantitative methods will be the subject of this chapter. It is imperative that excellent quantitative methods be established so that NMR can be utilized in studies of polymer structure-property relationships. Polymer molecular structure needs to be related to the incipient solid state structure and ultimately to observed solid state physical properties such as density, flexural moduli, environmental stress cracking behavior, to name a few. 

Since the stochastic Langevin force mimics collisions among solvent molecules and the biomolecule (the solute), the characteristic vibrational frequencies of a molecule in vacuum are dampened. In particular, the low-frequency vibrational modes are overdamped, and various correlation functions are smoothed (see Case [35] for a review and further references). The magnitude of such disturbances with respect to Newtonian behavior depends on 7, as can be seen from Fig. 8 showing computed spectral densities of the protein BPTI for three 7 values. Overall, this effect can certainly alter the dynamics of a system, and it remains to study these consequences in connection with biomolecular dynamics. 

The extinction coefficient and emission rate are defined through the spectral density function G (v) that combines the effects of solvent-induced inhomogeneous broadening and vibrational excitations of the donor-acceptor complex. A substantial simplification of the description can be achieved if the two types of nuclear motions are not coupled to each other. The spectral density G (v) is then given by the convolution ... 

Figure 41. Solvent viscosity effects on low-frequency motions of alanine dipeptide. The normalized spectral density for the dihedral angle is plotted versus frequency (ps 1) for (a) dynamics on a vacuum potential surface (see Fig. 58a) (6) dynamics with a potential of mean force (see Fig. 58b) in a solvent of viscosity, y = 1.0 cP (c) dynamics with a potential of mean force (see Fig. 586) in a solvent of viscosity, ij > 1.0 cP.

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

The Golden Rule formula (9.5) for the mean rate constant assumes the Unear response regime of solvent polarization and is completely equivalent in this sense to the result predicted by the spin-boson model, where a two-state electronic system is coupled to a thermal bath of harmonic oscillators with the spectral density of relaxation J(o)) [38,71]. One should keep in mind that the actual coordinates of the solvent are not necessarily harmonic, but if the collective solvent polarization foUows the Unear response, the system can be effectively represented by a set of harmonic oscillators with the spectral density derived from the linear response function [39,182]. Another important point we would like to mention is that the Golden Rule expression is in fact equivalent [183] to the so-called noninteracting blip approximation [71] often used in the context of the spin-boson model. The perturbation theory can be readily applied to... 

The theory of localised solvent-solute complexes, proposed by Gendell, Freed and FraenkeF, has been shown to provide an interpretation of solvent effects upon electron spin resonance spectra, which is acceptable to chemical intuition and which correctly predicts, at least in a qualitative fashion, most of the observed trends in spectral parameters. Further progress towards a quantitative understanding would seem to await a theory, for the calculation of spin densities, which explicitly includes the spatial distribution of solvent molecules around the solute, as has indeed been recently attempted. ... 

The effect of the medium denoted here as implicit reflects the influence of the solvent on the transition densities (i.e., spectral properties) of the D/A units, which determine the direct coupling Vs. The solvent explicitly enters into the definition of the coupling through the term T Xpiicit in (2.4), which describes an interaction between the two chromophores mediated by the medium, that generally leads to an overall reduction (i.e., a screening) of the D/A coupling. 

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