Correlation diagrams construction

Application of continuous wave techniques and line shape analysis to wide-line n.m.r. spectra Cf D-xylose, D-mannose, D-glucose, D-fructose, and D-sorbose suggests that the lattice is effectively rigid in all except possibly D-fructose. Previously published C n.m.r. data for arabinosides and ribosides have been tabulated with correlation diagrams constructed in such a way that the data on new compounds can be used to assign the anomerlc configurations and ring size. Measurements of self-diffusion coefficients of carbo-... 

A more detailed analysis [2,5] is summarized in Fig. 10, the local state correlation diagram constructed for the quadrangle of harpooning intersections 1) 3), 1) 4),... 

An example of a correlation diagram constructed from the collision of two Aluminum atoms is shown in Figure 2.8. This shows the modification in the core level MOs formed from the 2p levels as the two Aluminum atoms approach each other to zero interatomic distance (for the sake of clarity, the other levels are not shown). Zero distance is used as this allows for the extrapolation of the MO energies to those of Iron (the nucleus that would be formed). The understanding of how the MOs are modified allows for the prediction of which core holes are most likely formed during such collisions, as well as the minimum energy and distance required (Figure 2.8). 

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

The cyclobutene-butadiene interconversion can serve as an example of the reasoning employed in construction of an orbital correlation diagram. For this reaction, the four n orbitals of butadiene are converted smoothly into the two n and two a orbitals of the ground state of cyclobutene. The analysis is done as shown in Fig. 11.3. The n orbitals of butadiene are ip2, 3, and ij/. For cyclobutene, the four orbitals are a, iz, a, and n. Each of the orbitals is classified with respect to the symmetiy elements that are maintained in the course of the transformation. The relevant symmetry features depend on the structure of the reacting system. The most common elements of symmetiy to be considered are planes of symmetiy and rotation axes. An orbital is classified as symmetric (5) if it is unchanged by reflection in a plane of symmetiy or by rotation about an axis of symmetiy. If the orbital changes sign (phase) at each lobe as a result of the symmetry operation, it is called antisymmetric (A). Proper MOs must be either symmetric or antisymmetric. If an orbital is not sufficiently symmetric to be either S or A, it must be adapted by eombination with other orbitals to meet this requirement. 

Correlation diagrams can be constructed in an analogous fashion for the disrotatory and conrotatory modes for interconversion of hexatriene and cyclohexadiene. They lead to the prediction that the disrotatory mode is an allowed process whereas the conrotatory reaction is forbidden. This is in agreement with the experimental results on this reaction. Other electrocyclizations can be analyzed by the same method. Substituted derivatives of polyenes obey the orbital symmetry rules, even in cases in which the substitution pattern does not correspond in symmetiy to the orbital system. It is the symmetry of the participating orbitals, not of the molecule as a whole, that is crucial to the analysis. 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon... 

Show, by constructing a correlation diagram, whether each of the following disrotatory cyclizations is symmetiy allowed ... 

Application to the Construction of Frontier Orbitals and to Correlation Diagrams... 

Conjugated chains, 14, 46 Correlation diagrams, 44, 50 Cyclobutadiene, 171 Cyclobutane, 47, 222 orbital ordering, 26 through-space interactions, 26 Walsh orbitals, 27 Cyclobutene, 200 Cyclohexane, 278 Cyclohexene (half-boat), 274 Cyclopen tadiene, 225 Cvclopen tadienone, 269 Cyclopentadienyl anion, 237 Cyclopentane, 254 Cyclopen ten e, 241 Cyclopropane, 41, 47, 153 construction of orbitals, 19, 22 Walsh orbitals, 22, 36, 37 Cyclopropanone, 48, 197 bond lengths, 38 Cyclopropen e, 49, 132 reactivity, 40... 

Construct a state correlation diagram for the conrotatory butadiene-cyclobutene system. 

The techniques which can be used for the construction of orbital correlation diagrams are well known 2,5,8,20) an(j neeq not be reviewed... 

Burdett has also applied the AOM to the rationalisation of the geometries of main group molecules (38). Correlation diagrams (analogous to Walsh diagrams) can be constructed to show the angular dependence of MO energies, and the shapes of simple... 

On the basis of the above the following correlation diagram can be constructed showing correlation between orbitals of the same symmetry having minimal differences in a disrotatoiy interconversion. The lines connecting the orbitals show similar symmetry. 

The same arguments can be applied to construct the correlation diagram for the conrotatory process in the transformation of cyclobutene v " butadiene system. In such a case, as we have seen, a C2 symmetry is maintained throughout. 

The plane indicated serves to construct the orbital correlation diagram using the methylene ground state or o -configuration, the lowest singlet being Ai or (see Fig. 8). 

When the electronic states of both the reactants and products have been determined and characterized, a correlation diagram may be constructed by connecting the states according to the following rules ... 

This question requires you to construct an orbital correlation diagram of the Woodward-Hoffmann type. 

Construction of an orbital correlation diagram (7) discloses that concerted cis elimination of R-R from ci -ML4RR is not forbidden by symmetry considerations thus, there appears to be no advantage for the asymmetric elimination... 

These relationships show that far fewer individual correlation diagrams need be constructed from scratch than might have first been anticipated. 

Finally, let us look at the corresponding state correlation diagram, as shown in Figure 7.18. In constructing this, we use the direct product rules ... 

The second principle, which has been used earlier (page 194) in constructing the correlation diagrams for the Woodward-Hoffmann rules, and which has its ultimate origin in the phenomenon of configuration interaction (page 179) is called the noncrossing rule ... 

The methods illustrated above for working out the correlation diagrams of d2 ions in octahedral and tetrahedral environments can be applied to all dn configurations for 2 < n 9. However, the labor involved increases extraordinarily fast as the number of electrons increases. Fortunately, several kinds of relationships make it possible to obtain certain diagrams from others which are more readily constructed. 

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