Specific interactions spectral calculations

Now the expectation (mean) value of any physical observable (A(t)) = Yv Ap(t) can be calculated using Eq. (22) for the auto-correlation case (/ = /). For instance, A can be one of the relaxation observables for a spin system. Thus, the relaxation rate can be written as a linear combination of irreducible spectral densities and the coefficients of expansion are obtained by evaluating the double commutators for a specific spin-lattice interaction X in the auto-correlation case. In working out Gm x) [e.g., Eq. (21)], one can use successive transformations from the PAS to the (X, Y, Z) frame, and the closure property of the rotation group to rewrite D2mG(Qp ) so as to include the effects of local segmental, molecular, and/or collective motions for molecules in LC. The calculated irreducible spectral densities contain, therefore, all the frequency and orientational information pertaining to the studied molecular system. 

Assuming an ionic-like interaction potential between the framework atoms and cations, Smirnov et al. performed an MD study to assess the cation dynamics in zeolite A. The calculation of the power spectra for Na" and cations at each site revealed that no specific spectral pattern can be attributed to a particular cation position. Vibrations of cations in all sites occur over a frequency region of 30-300 cm In addition, the spectra calculated with a flexible framework showed a substantial coupling between the cationic and lattice degrees of freedom. The results of this work °° have brought into question the assignments proposed for the bands in the far-infrared spectra of cationic forms of zeolites. 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

Linear prediction is a method to directly obtain the resonance frequencies and relaxation rates from time domain signals, which are a superposition of exponents, by solving the characteristic polynomials. Phases and intensities are calculated interactively using a least-squares procedure. The correlation spectroscopy of a two-dimensional NMR spectrometer employs several specific programs such as RELAY and TOCSY. The recognition of response peaks, the isolations of signals from noise and artifacts, and the spectral position (e.g., chemical shift) are all carried out by computers. 

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