Correlation diagram, definition

State Correlation Diagram (SCO) approach 27-8 statistical copolymerization see copolymerization statistical copolymers sea also copolymers definition 333... 

FIGURE 20. Top Definition of the phase relationship of the three localized basis 7r-orbitals of a norbornadiene molecule with an exocyclic double bond in position 7. Bottom Correlation diagram of the experimental orbital energies j = —/ of norbornadiene 75, 7-methylidenenorbornadiene 196 and 7-isopropylidenenorbomadiene 206, with those of the corresponding monoenes... 

With this definition, due to Child and Halonen (1984), local-mode molecules are near to the = 0 limit, normal mode molecules have —> 1. The correlation diagram for the spectrum is shown in Figure 4.3, for the multiplet P = va + vb = 4. It has become customary to denote the local basis not by the quantum numbers va, vh, but by the combinations... 

The concepts discussed regarding the symmetry restrictions and their removal can be described in a number of ways. Complete correlation diagrams can be constructed and the forbiddenness illustrated by sharp orbital crossings 20). Although definitive, this approach would not as clearly illustrate the nature of the restraints to reaction. 

A similar correlation diagram can be drawn to interpret the exclusive observation of BaOH chemiluminescence in the reaction of Ba(6s6p P) with water [172]. Here again, the reaction of excited barium can be explained by H-atom migration and formation of the intermediate HBaOH. This mechanism definitely carries some generality since it has been used also by Oberlander and Parson to account for re-... 

The abscissas of the correlation diagrams can be quantified. The quantification is thus far only an ex post facto device with power to classify but not yet to predict. It does not yet have a microscopic interpretation. Nevertheless it satisfies the needs of a theory of the equilibrium behavior of melting and freezing of clusters. Only the existence and not the definition of the nonrigidity parameter or the details of its origins is used in stage 2. However, we make a brief aside here to explain the definition in order to clarify just what information it carries. To understand the order parameter y (not to be confused with the surface tension), it is useful to examine how nonrigidity is traditionally characterized in diatomic and linear, particularly triatomic molecules. For... 

In general, an abstract Boolean diagram with a dimension greater than three underlies these semilattices. The reaction lattices as well as the reaction semilattices contain dynamic sublattices or semilattices. The abstract diagrams on which they are based allow the definition of a norm to describe the reaction path continuously by eigenvalue correlation diagrams. The normed lattice can be... 

The formal definition of a correlation diagram for two boreholes is as follows (Guberman 1987). Let X be the absolute height of the roof of some layer in the first borehole and y be the absolute height of the roof of the same layer in the second... 

While photocycloadditions are typically not concerted, pericyclic processes, our analysis of the thermal [2+2] reaction from Chapter 15 is instructive. Recall that suprafacial-suprafacial [2+2] cycloaddition reactions are thermally forbidden. Such reactions typically lead to an avoided crossing in the state correlation diagram, and that presents a perfect situation for funnel formation. This can be seen in Figure 16.17, where a portion of Figure 15.4 is reproduced using the symmetry and state definitions explained in detail in Section 15.2.2. The barrier to the thermal process is substantial, but the first excited state has a surface that comes close to the thermal barrier. At this point a funnel will form allowing the photochemical process to proceed. It is for this reason that reactions that are thermally forbidden are often efficient photochemical processes. It is debatable, however, whether to consider the [2+2] photochemical reactions orbital symmetry "allowed". Rather, the thermal forbiddenness tends to produce energy surface features that are conducive to efficient photochemical processes. As we will see below, even systems that could react via a photochemically "allowed" concerted pathway, often choose a stepwise mechanism instead. 

The /i-bond diagrams of (f>(r 2) cannot contain any articulation pairs, and so the diagrams connecting the root point 2 with the n h-bonds connected to root point 1 do not have nodal points. This definition is just of the (n + l)-particle direct correlation function c(r2, r2,..., r +2) and one has... 

There is most definitely a positive correlation between An,ax and the maximum Also, an inverse correlation between the transition energy, hw, and jSjjj predicted by the two-state model holds if the maximum attainable values for one particular transition energy are considered. There are many compounds, however, that fall much below this line. They are more cyanine-like (close to Class II, low Aju.) and combine low transition energies with low second-order polarizabilities. They are, unfortunately, often omitted in similar diagrams found in the literature which show only a selection of the more successful structures specifically optimized for NLO applications. 

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