Correlation diagrams rules

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. 

In a concerted reaction, orbital and state symmetry is conserved throughout the course of the reaction. Thus a symmetric orbital in butadiene must transform into a symmetric orbital in cyclobutene and an antisymmetric orbital must transform into an antisymmetric orbital. In drawing the correlation diagram, molecular orbitals of one symmetry on one side of the diagram are connected to orbitals of the same symmetry on the other side, while observing the noncrossing rule. 

The formulation and systematization of these rules came in a series of famous papers by Woodward and Hoffmann (8), whose arguments soon merged with the correlation diagram formalism of Longuet-Higgins and Abrahamson (9) into a now well accepted and far-reaching theory (10). 

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

The most widely used qualitative model for the explanation of the shapes of molecules is the Valence Shell Electron Pair Repulsion (VSEPR) model of Gillespie and Nyholm (25). The orbital correlation diagrams of Walsh (26) are also used for simple systems for which the qualitative form of the MOs may be deduced from symmetry considerations. Attempts have been made to prove that these two approaches are equivalent (27). But this is impossible since Walsh s Rules refer explicitly to (and only have meaning within) the MO model while the VSEPR method does not refer to (is not confined by) any explicitly-stated model of molecular electronic structure. Thus, any proof that the two approaches are equivalent can only prove, at best, that the two are equivalent at the MO level i.e. that Walsh s Rules are contained in the VSEPR model. Of course, the transformation to localised orbitals of an MO determinant provides a convenient picture of VSEPR rules but the VSEPR method itself depends not on the independent-particle model but on the possibility of separating the total electronic structure of a molecule into more or less autonomous electron pairs which interact as separate entities (28). The localised MO description is merely the simplest such separation the general case is our Eq. (6)... 

This rule can be understood from the orbital correlation diagram shown in Scheme 7.22, where the symbols S and A denote symmetric and antisymmetric orbitals, respectively (Bellville and Bauld 1982, Bauld et al. 1983). 

To generate the correlation diagram, let us assemble the states of the united and separated atoms, and connect them according to the rules ... 

Problem 9-15. Could the same predictions be made from a simple electron repulsion argument If n pairs of electrons must be accommodated in the valence-shell molecular orbitals, then assume simply that they will be as far apart as possible. Up to four electrons will push each other as far apart as possible, to create linear geometry more than four must be distributed more densely, so that the angle between the substituents will be less that 180°. Does this simple hypothesis explain everything that Walsh s rules do Is there any advantage to using Walsh s correlation diagram analysis ... 

The photochemical disrotatory closure of butadiene to cyclobutene has been described with a state-correlation diagram, like that shown in Figure 21.4. It is based on the familiar orbital-correlation diagram of Woodward and Hoffmann," from which the intended correlations indicated by the dashed lines can readily be deduced. The solid lines indicate that there is an avoided crossing, which is put in as a result of the quantum mechanical noncrossing rule. It says that two states of the same total symmetry cannot cross. Instead, as they approach each other in energy, they will mix and separate, as the solid lines indicate. 

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 ... 

Chapter 14 deals with orbital correlation diagrams following Woodward and Hoffmann [3]. State wave functions and properties of electronic states are deduced from the orbital picture, and rules for state correlation diagrams are reviewed, as a prelude to an introduction to the field of organic photochemistry in Chapter 15. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

The photochemical dimerization of unsaturated hydrocarbons such as olefins and aromatics, cycloaddition reactions including the addition of 02 ( A ) to form endoperoxides and photochemical Diels-Alders reaction can be rationalized by the Woodward-Hoffman Rule. The rule is based on the principle that the symmetry of the reactants must be conserved in the products. From the analysis of the orbital and state symmetries of the initial and final state, a state correlation diagram can be set up which immediately helps to make predictions regarding the feasibility of the reaction. If a reaction is not allowed by the rule for the conservation of symmetry, it may not occur even if thermodynamically allowed. 

Once the two sides of a correlation diagram have been established, the states of the same symmetry and multiplicity are connected by straight lines in such a way as to observe the non-crossing rule identical states cannot cross as the strength of the interaction is changed. When this is done we have completed the correlation diagram. 

One of the most important applications of correlation diagrams concerns the interpretation of the spectral properties of transition-metal complexes. The visible and near ultra-violet spectra of transition-metal completes can generally be assigned to transitions from the ground state to the excited states of the metal ion (mainly d-d transitions). There are two selection rules for these transitions the spin selection rule and the Laporte rule. 

It is now possible to draw a correlation diagram between the states, as shown in Figure 7.13. The crucial feature to note here is that the Ax to Ax correlations which would seem to follow from direct orbital,correlations cannot and do not actually occur, because of what is called the noncrossing rule. Two states of the same symmetry cannot cross, in the manner indicated by the dotted lines, because of electron repulsion. Instead, as they approach they turn away from each other so that the lowest 4, states on each side are correlated with each other as shown by the full lines. The repulsive interaction is similar in essence to that involved in configuration interaction in naphthalene, as discussed in Section 7.6. Indeed, the noncrossing rule is no more than a special but straightforward instance of configuration interaction. 

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 ... 

A second selection rule states that anv transition for which S 0 is forbidden, i.e.. in order to be allowed, a transition must involve no change in spin stale. Looking at the correlation diagram for a d configuration in an octahedral field (Fig. 11.35). we note that the ground stale has a multiplicity of 3 (5 = I) and that there are three excited stales with this same multiplicity 372) . and Ttu (from the 3P). Thus we can envision three transitions that are spin allowed ... 

In order to use the correlation diagrams shown in Fig. 11.37 or simplifications of them, it is necessary to know the selection rules that govern electronic transitions. 

The ligand field treatment has been extended by means of angular overlap calculations and ensuing correlation diagrams.37 A similar treatment has been made for d6 complexes, such as those of Co111 and Rh111.38 39 The photolysis rules, incidentally, are not as strongly obeyed with such complexes. 

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