Correlation diagrams illustrated

Figure 1.1. Orbital correlation diagram illustrating the distinction between normal electron demand (leftside) and inverse electron demand (right side) Diels-Alder reactions.

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

The situation is reversed for the tt2s + n4s addition. Figure 11.16 illustrates this case now the bonding orbitals all transform directly to bonding orbitals of the product and there is no symmetry-imposed barrier. As with the electrocyclic processes, the correlation diagrams illustrate clearly the reason for the striking difference observed experimentally when the number of electrons is increased from four to six. The reader may verify that the 4s + 4s reaction will be forbidden. Each change of the total number of electrons by two reverses the selection rule. 

Figure 2.3. The Walsh correlation diagram illustrating the changes in the n, n, and a orbital energies as thiophosgene is distorted from a planar to a pyramidal conformation.

Fig. 2.2 Correlation diagrams illustrating the accuracy of the DFTB approach for typical organic functional groups relevant for epoxide and polyurethane adhesive systems. Structural parameters (top distances ...

Use the correlation diagram illustrated in Figure 10.56 to determine which vertices will be vacant from the parent deltahedral structure. 

The corresponding state correlation diagrams illustrate this feature very nicely. The ground state of the trigonal bipyramid is 62, characterized by the configuration (xy)(xz)(z -y2) - that is by the occupation of the three lowest orbitals by one electron. The first excited state, is characterized by the occupation (xy)(xz)... 

FIGURE 48.2 Orbital correlation diagram illustrating the a-cleavage of acetone. A linear acyl radical (left) is predicted to be photochemically generated from the nit excited state of acetone. The orbital symmetry is represented by the letters a (asymmetric) and s (symmetric), with respect to the o mirror plane. 

The complementary relationship between thermal and photochemical reactions can be illustrated by considering some of the same reaction types discussed in Chapter 11 and applying orbital symmetry considerations to the photochemical mode of reaction. The case of [2ti + 2ti] cycloaddition of two alkenes can serve as an example. This reaction was classified as a forbidden thermal reaction (Section 11.3) The correlation diagram for cycloaddition of two ethylene molecules (Fig. 13.2) shows that the ground-state molecules would lead to an excited state of cyclobutane and that the cycloaddition would therefore involve a prohibitive thermal activation energy. 

Correlation diagrams include the product orbitals while perturbation approaches require knowledge of the empty orbitals of the reactant. However, the occupied molecular orbitals of diazirine (II), compared with those of cyclopropene (I), do seem to give some indication of a preferred thermal decomposition of (II) compared with the rearrangement of (I). Moreover these molecular orbitals are a typical illustration of the localization obtained in the presence of an electronegativity perturbation. 

Fig. 4.9. A schematic diagram illustrating the attosecond dynamics of the strongly correlated nuclear and electron wavepackets that lead to HHG in H2 and/or D2. When the internuclear distance is large, HHG is suppressed...

In official documents of the Emopean Commission it is stated that accreditation should be seen by public authorities, by the accreditors, by the certifiers and by the industry as the highest level of control of conformity assessment activities, from a technical point of view. The diagram illustrates the correlation of various activities and the role of the stakeholders. Accreditation provides the highest level of recognition of activities within conformity assessment. 

Fig. 18 Energy diagram for the first step of an electrophilic substitution reaction illustrating the crossing of DA and D +A" configurations. The effect of a substituent that stabilizes the D + A configuration (e.g. by improving the arene donor ability) is indicated by the dotted line. The diagram illustrates the correlation between AAv, the difference in excitation energies for the perturbed and unperturbed systems, and AE, the difference in activation energy for the two systems. (Avoided crossing deleted for clarity)...

The application of correlation diagrams to photochemical processes goes back to the early work of Laidler and Shuler (1951). More recently, Longuet-Higgins and Abrahamson (1965) showed how orbital-symmetry correlations may be converted into state-symmetry correlations. Here the fundamental consideration is that states of the same symmetry do not cross, i.e. the result is an avoided crossing, while states of different symmetry do cross. The principles involved are illustrated in Fig. 19 for the dimerization of... 

Answer to 2(d). This question illustrates that it is the number of electrons, not the number of nuclei, that is important. The orbital correlation diagram is shown in Figure 14.2. In disrotatory opening, a mirror plane of symmetry is preserved. This correlation is with bold symmetry labels and solid correlation lines. Italic symmetry labels and dotted correlation lines denote the preserved rotational axis of symmetry for conrotatory ring opening. For the cation, the disrotatory mode is the thermally allowed mode. It corresponds to a a2s + 05 pericyclic reaction. 

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. 

The electronic configuration is thus different. We can illustrate this by a correlation diagram for the orbitals ... 

Figure 11.16 Symmetry, basis orbitals, and correlation diagram for the it2s + tt4s cycloaddition. Symmetry classifications are with respect to the mirror plane illustrated.

Fig. 4. Topological correlation diagram for the interconversion of M(A-B)2(C-C) isomers by a twist mechanism. Twist motions about the P-C3 and one of the i-C3 axes of A and AcC are illustrated. From Ref.30)...

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