Correlation Schematic

Although in some cases a consistent analysis of LS or DS spectra was carried out by applying the asymptotic laws of MCT, there are strong indications that these features are not completely appropriate to quantitatively describe, for example, DS as well as LS spectra. As discussed above, this is by now well known for PC and glycerol, at least. In order to tackle the problem of different experimental probes in a more realistic fashion, several MCT approaches have been published [265,380,400]. In a two-correlator schematic model, in which the dynamics of some probe (e.g., molecular reorientation in a dielectric experiment) is coupled to the overall structural relaxation in a simple manner, a simultaneous description of LS, DS, and NS spectra was possible even below Tc. Some of the results are... 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

Figure Bl.9.12. The schematic diagram of the relationships between the one-dimensional electron density profile, p(r), correlation fiinction y (r) and interface distribution fiinction gj(r).

Figure Bl.10.12. Schematic diagram of a two-dimensional histogram resulting from the triple coincidence experiment shown in figure BLIP. 10. True triple coincidences are superimposed on a imifomi background and tliree walls corresponding to two electron correlated events with a randomly occurring third electron.

Figure Bl.16.22. Schematic representations of CIDEP spectra for hypothetical radical pair CH + R. Part A shows the A/E and E/A RPM. Part B shows the absorptive and emissive triplet mechanism. Part C shows the spin-correlated RPM for cases where J and J a.. ...

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

The AeroSizer, manufactured by Amherst Process Instmments Inc. (Hadley, Massachusetts), is equipped with a special device called the AeroDisperser for ensuring efficient dispersal of the powders to be inspected. The disperser and the measurement instmment are shown schematically in Figure 13. The aerosol particles to be characterized are sucked into the inspection zone which operates at a partial vacuum. As the air leaves the nozzle at near sonic velocities, the particles in the stream are accelerated across an inspection zone where they cross two laser beams. The time of flight between the two laser beams is used to deduce the size of the particles. The instmment is caUbrated with latex particles of known size. A stream of clean air confines the aerosol stream to the measurement zone. This technique is known as hydrodynamic focusing. A computer correlation estabUshes which peak in the second laser inspection matches the initiation of action from the first laser beam. The equipment can measure particles at a rate of 10,000/s. The output from the AeroSizer can either be displayed as a number count or a volume percentage count. 

Figure 4-7. Schematic dependence (log-log plot) otTi and as functions of To, the correlation time. The minimum in Ti occurs at t = l/ojo.

Figure 1.5 Schematic state correlation diagram for radical addition to a carbon-carbon double bond showing configuration energies as a function of the reaction...

We will conclude this section on theory with such a case. In Section 8.3 it was shown that the influence of substituents on the rate of dediazoniation of arenediazonium ions can be treated by dual substituent parameter (DSP) methods, and that kinetic evidence is consistent with a side-on addition of N2. We will now discuss these experimental conclusion with the help of schematic orbital correlation diagrams for the diazonium ion, the aryl cation, and the side-on ion-molecule pair (Fig. 8-5, from Zollinger, 1990). We use the same orbital classification as Vincent and Radom (1978) (C2v symmetry). 

Fig. 12. Schematic representation of variations in dehydration rates (ft) with prevailing water vapour pressure (Ph2o) These examples include Smith—Topley behaviour and indicate correlations with phase stability diagrams. (After Bertrand et al. [596], reproduced with permission, from Journal of Inorganic and Nuclear Clemistry.)...

Figure 4.18. Peak-size correlation in an HPLC-chromatogram. The impurity profile of a chemical intermediate shown in the middle contains peaks that betray the presence of at least two reaction pathways. The strength of the correlation between peak areas is schematically indicated by the thickness of the horizontal lines below the chromatogram. The top panel gives the mean and standard deviation of some peak areas (n = 21) the two groups of peaks immediately before and after the main peak were integrated as peak groups.

Figure 5. A schematic model for the structure in TEOS-PTMO hybrid systems, (A) PTMO chain, (B) linear species based on partially condensed TEOS, (C) cluster formed by highly condensed TEOS. 1/s corresponds to the correlation length observed in SAXS profiles.

In the methyl radical, the reaction takes place in the direction of SO (2pn of central carbon) extension, that is to say, the direction perpendicular to the molecular plane. Walsh 76> correlated the remarkable localization of SO at the nitrogen atom in NO 2 to the experimental results indicating that NO 2 abstracts hydrogen from other molecules to form HNO2 rather than HONO, combines with NO to form ON—NO2, dimerizes to produce O2N—NO2, and so forth. Also he pointed out that the SO MO of C1CO is highly localized at the carbon atom, which is connected with the production of CI2CO in the reaction with CI2. The SO extension of NO 2 is schematically shown below 103>. 

Fig. 40. (a) A schematic correlation diagram illustrating the role of quantized bot-... 

Fig. 16. Schematic of the repulsive surface correlating to the triplet products illustrating...

Fig. 3 Structure-photophysical property relationship of coumarin derivatives, (a) Schematic representation of the correlation between electronic effect of substituents at the C-3 and C-7 position and photophysical properties (b) Structure and their emission maxima of various coumarins...

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Figure 2 Schematic representation of carbon spin-lattice relaxation time, T,c, and spin-spin relaxation time under CPMAS or DDMAS condition, T2C, as a function of correlation times.

Figure 36 Schematic representation of dynamic picture of bR in monomer. See the correlation times for the cytoplasmic and extracellular loops and transmembrane a-helices are significantly shortened as compared with those in 2D crystal as shown in Figure 24.

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