Correlation diagram molecules

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... 

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. 

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. 

Fig. 13.3. Orbital correlation diagram for one ground-state ethene and one excited-state ethene. The symmetry designations apply, respectively, to the horizontal and vertical planes for two ethene molecules approaching one another in parallel planes.

Tabic 6-2. Correlation diagram of the C2/, point group of the isolated T6 molecule (left column) with the C2i, factor group for solid T(, (right column) via the site symmetry C group (center). L, M, and N indicate the principal molecular transition dipole moments, while a, b, and c arc the crystalline axes. 

Fig. 2. Correlation diagram for the formation of cyclobutane from two ethene molecules.

Fig. 3. Correlation diagram for the transition metal catalyzed transformation of two ethene molecules into cyclobutane according to the forbidden-to-allowed concept.

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). 

A good deal of information on small radicals can be obtained from Walsh diagrams (77). These correlation diagrams allow the estimation of molecular geometry from the mere knowledge of the number of valence electrons. The procedure and arguments are similar to those presented by Mulliken (78), who discussed the shapes of ABl molecules in ground and excited states and interpreted their electronic spectra. 

For qualitative discussions, Walsh diagrams (see Sec. I.C.2.) have proved to be very useful, for example, in determining the structures of AB2, AB3, and HAAH molecules in ground and excited states. These correlation diagrams show how MO levels change on passing from one extreme molecular geometry to another. 

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... 

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)... 

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... 

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 local-to-normal transition is governed by the same parameter of Eq. (4.30). The difference is that now the local-to-normal transition occurs simultaneously for the stretching and bending vibrations. The correlation diagram for stretching vibrations is the same as in Figure 4.3. The local-to-normal transition can also be studied for XYZ molecules, for which the Hamiltonian does not have the condition A) = A2 and is... 

Figure 4.16 Linear-bent correlation diagram for triatomic molecules.

Fig. 10. Schematic presentation of the MO-correlation diagram for the electronic state of the AuO molecule (44).

An orbital correlation diagram has been presented for linear and bent M—N—O systems in five-co-ordinate tetragonal molecules, and the diagram can be extended to six-co-ordinate complexes with only minor modifications. From this study, it is concluded that the antibonding nature of the level to be filled under symmetry, and not its composition, lead to distortion and bending of the M—N—O unit, and that v(NO) is not a good guide to the linear... 

Fig. 9. A qualitative correlation diagram for the Jt MO S of a planar E2S2N4 molecule (E here taken to be S ) with the corresponding orbitals of the puckered (Cj ) form...

Fig. 13 a—c. A correlation diagram for the Huckel a MO s of (a) S3N3 and (b) a hypothetical SjNj" ion. In (c), the ab initio HFS energy levels of a planar HjPS Nj molecule are shown. For purposes of clarity, only the n symmetry orbitals are labelled. Unoccupied orbitals are indicated by an asterisk... 

Figure 9.2. Correlation diagram for second-row diatomic molecules. The column on the left shows orbitals for the united atom, those on the right those of the separated atoms.

Fig. 11. Correlation diagram for non-linear MO2 molecules having nineteen valence electrons...

Figure 5.12 A MO correlation diagram for the bent and linear forms of the water molecule...

Fig. 19 State correlation diagram for the dimerization reaction of two ethylene molecules...

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