Dynamical effects, from molecular spectra

As we have seen, the expressions for the rate constant obtained for different models describing the lattice vibrations of a solid are considerably different. At the same time in a real situation the reaction rate is affected by different vibration types. In low-temperature solid-state chemical reactions one of the reactants, as a rule, differs significantly from the molecules of the medium in mass and in the value of interaction with the medium. Consequently, an active particle involved in reaction behaves as a point defect (in terms of its effect on the spectrum and vibration dynamics of a crystal lattice). Such a situation occurs, for instance, in irradiated molecular crystals where radicals (defects) are formed due to irradiation. Since a defect is one of the reactants and thus lattice regularity breakdown is within the reaction zone, the defect of a solid should be accounted for even in cases where the total number of radiation (or other) defects is small. 

Much remains to be done in this area. The role of the many-body polarizability has yet to be explored, a simple dynamical model has yet to be presented, and a microscopic justification of Eq. (14.2.5) has yet to be developed. Moreover the important practical question concerning the collision-induced scattering from molecular liquids has yet to be answered. Only after this effect is assessed can it be subtracted from the depolarized scattering in such a manner that the remaining spectrum gives information about molecular tumbling. 

As discussed in this section, the tube-dilation effect, i.e. M J/Me > 1, mainly occurs in the terminal-relaxation region of component two in a binary blend. This effect means that the basic mean-field assumption of the Doi-Edwards theory (Eq. (8.3)) has a dynamic aspect when the molecular-weight distribution of the polymer sample is not narrow. This additional dynamic effect causes the viscoelastic spectrum of a broadly polydisperse sample to be much more complicated to analyze in terms of the tube model, and is the main factor which prevents Eq. (9.19) from being applied... 

In the absence of significant molecular motion the spectra can be calculated simply as a powder-like super-imposition of the individual molecular static lines of Lorentzian shape from all over the sample. These lines are then positioned into the spectrum according to Eq. (5) as in Ref. [6j. To include also dynamic effects, such as fluctuations of molecular long axes (defining the scalar order parameter S and the director n) and translational molecular diffusion, it is convenient to use a semi-classical approach with the time-dependent deuteron spin Hamiltonian [25] where the H NMR line shape I cj) is calculated as the Fourier transform of... 

The dynamic properties of the Mossbauer nucleus which can be monitored as a result of their effect on the Mossbauer spectrum can arise from the lattice dynamics of the solid in which the nucleus is situated. It can also result from the motion of a localised part of the system, such as a molecular motion, or from motion of the whole system within its environment. As the effect on the spectrum depends only on the actual motion of the nucleus and not on its origin it is not possible to distinguish directly between the possible sources of any such motion. Since the motion is often related to the internal energy of the system under investigation it is frequently studied as a function of the various parameters which determine the behaviour of the system, and particularly the temperature. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

The COSMO solvent model has been used to simulate the influence of water on the electronic spectrum of A -methylacetamide [81], and the results was compared with the results of molecular dynamics simulations (where the electronic spectrum were calculated as an average over 90 snapshots from MD simulations). Most of the hydration effects were found to come from the first solvation shell hydrogen-bonded water molecules, and the continuum model does not properly account for these effects. The rotatory strengths were not calculated directly in ref. [81]. However, the results were used to model ECD spectra of peptides via the coupled oscillator model, with satisfactory result. 

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