Relaxation molecules

In Table 30.1, we have compared the electronically relaxed hardness and softness descriptors for the geometrically rigid and relaxed molecules, respectively. As intuitively expected, relaxing the nuclear positions decreases the electronic hardness (increases softness) of the molecular system under consideration. This electronic... 

A new property appears in the conversion of a linear DNA molecule into a closed circular molecule. The axis of the double helix can itself be twisted into a superhelix (Figure 5.18B). A circular DNA molecule without any superhelical turns is known as a relaxed molecule. Supercoiling is biologically important for two reasons. First, a supercoiled DNA molecule has a more compact shape than does its relaxed counterpart. Second, supercoiling may hinder or favor the capacity of the double helix to unwind and thereby affects the interactions between DNA and other molecules. These topological features of DNA will be considered further in Section 27.3. 

Check it 5.2.1.6 also shows that it is possible to include relaxation induced effects into simulations which might be a source of perturbation in a real experiment. The overall pulse sequence time, especially in the long sequences used in nD experiments, becomes a very important, restrictive variable in the development of new pulse sequences. For fast relaxing molecules such as macromolecules the overall pulse sequence time is crucial because if the nuclei start to relax before the data acquisition there will be a loss in signal intensity. It is also important that for maximum signal intensity the spin system returns to thermal equilibrium between scans. 

The relay COSY experiments has to contend with reduced signal intensity during the long relay step. In contrast in a TOCSY experiment because of the different effective rate constant during the spinlock period relaxation effects are minimized [5.143] and TOCSY experiments can be successfully performed on fast relaxing molecules such as polymers or organic macromolecules. 

The first pubUshed criticism of the binary collision model was due to Fixman he retained the approximation that the relaxation rate is the product of a collision rate and a transition probabihty, but argued that the transition probability should be density dependent due to the interactions of the colliding pair with surrounding molecules. He took the force on the relaxing molecule to be the sum of the force from the neighbor with which it is undergoing a hard binary collision, and a random force mA t). This latter force was taken to be the random force of Brownian motion theory, with a delta-function time correlation ... 

The interpretation of one- and two-dimensional spectra of large biomolecules such as proteins and nucleic acids is usually impossible due to the large number of highly degenerated peaks. Hence, even for the medium-sized molecules, it is necessary to use isotopic enrichment with and nuclei, and to perform triple-resonance 3D NMR experiments for resonance assignment and extraction of structural constraints. However, as we pointed out above, the resolution of conventionally acquired 3D spectra, is limited by sampling requirements. Therefore, it is rarely possible to obtain line widths close to the natural ones in a reasonable time, even for very fast-relaxing molecules. The conventional 4D spectra, such as or... 

The apparent oxygen absorption linewidth pressure dependence in air derived from the fitting to this simple model showed an effect of greater FM deviation as it became comparable with the narrower spectral line at low pressures. This phenomenon is because of the interaction between the electric field of the modulated wave and that of the relaxing molecule during its transition (ref. 15, p. 139, and ref 20) see Section 1.2. The effect is to increase the measured spectral absorption linewidth because the molecules are oriented in LTE with the instantaneous electric field due to the source, as they relax after a collision. As the FM deviation increases, so therefore does the bandwidth of the radiation field they experience, and this causes an increase to the linewidth. 

Suppose that some of the high energy levels of the relaxing molecule may transform themselves, for example as in a predissociation, into another species equation (2.2) for the evolution of the populations then becomes... 

A simple well-known extension of a collinear Landau-Teller model is provided by the breathing sphere (BSP) model of Schwartz, Slawsky and Herzfeld [13] which fully retains the Landau-Teller exponential factor. More consistent treatment, which approximately takes into account the anisotropic character of the atom-molecule interaction, is based on the so-called infinite order sudden approximation (lOSA) [14] with respect to rotational transitions that accompany the vibrational transition. Within this approximation the rotation of the relaxing molecule plays the role of a spectator, which insignificantly modifies the exponent in Eq. (8) through quite unimportant redefinition of a. If, in addition, the quasiclassical correction to the semiclassical Landau-Teller exponent is small and the effect of the attractive part of the potential is weak, one can write the following simple expression for the deactivation rate constant within BSP or lOSA approximation ... 

The possible direct monitoring of the population change of different vibrational levels of relaxing molecules using kinetic spectroscopy will also be mentioned. 

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