M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 51
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(7-8) is fulfilled. Thisalso means that at the maximum point the symmetry of the excitedstate may differ from that of the ground state. However, any minutedistortion will remove the system from the saddle point. The reaction coordinate must then become again totally symmetric. Howcan this happen? Obviously, this can happen by changing the pointgroup of the system. By reducing the symmetry, nonsymmetric vibrational modes may become symmetric, and the reaction coordinatemay become totally symmetric.
This reasoning may even help inpredicting how the symmetry will be reduced; we just have to findthe point group in which the reaction coordinate becomes totallysymmetric.Two examples will illustrate how these rules work. One involves thereduction of symmetry which occurs when a linear molecule becomesbent [41]. The other example involves transforming a planar moleculeinto a pyramidal one.For a linear AX2 molecule of D∞h symmetry the normal mode thatreduces it to C2v is the u bending mode (Figure 7-5a). In the C2vpoint group, this normal mode becomes totally symmetric.
(The othercomponent of the u mode becomes the rotation of the molecule.)For an AX3 planar molecule the symmetry is D3h . The puckeringmode (Figure 7-5b) of A2 symmetry reduces it to C3v . In the C3v pointgroup, the symmetry of this vibration is A1 .Concerning the energy integral in Eq. (7-7), Bader called attentionto an interesting phenomenon [42]. If the excited state ⌿i lies veryclose to the ground state ⌿0 , a distortion occurs that will push thetwo states apart. This phenomenon is similar to the Jahn–Teller effect(but it is not the same) and is called the pseudo Jahn–Teller effect (seeChapter 6).
The symmetry of the distortion is predicted by Eq. (7-7).3247 Chemical ReactionsFigure 7-5. The effect of symmetry lowering on the reaction coordinate: (a)Bending of a linear AX2 molecule [2 (u ) → 2 (A1 )]; (b) Puckering of a planarAX3 molecule [2 ( A2 ) → 2 (A1 )].7.2. Electronic Structure7.2.1. Changes During a Chemical ReactionA chemical reaction is a consequence of an interaction betweenmolecules. The electronic aspects of these interactions can bediscussed in much the same way as the interaction of atomic electrondistributions forming molecules. The difference is that while MOs areconstructed from the AOs of the constituent atoms, in describing achemical reaction the MOs of the product(s) are constructed fromthe MOs of the reactants. Before a reaction takes place (i.e., whilethe reacting molecules are still far apart), their electron distribution is unperturbed.
When they approach each other, their orbitalsbegin to overlap, and distortion of the original electron distributiontakes place. There are two requirements for a constructive interactionbetween molecules: symmetry matching and energy matching. Thesetwo factors can be treated in different ways. The approaches of Fukui[43, 44], and of Woodward and Hoffmann [45, 46] differ somewhat.Since those are the two most successful methods in this field, we shall7.2. Electronic Structure325concentrate on them. First, the basis of each method will be presentedbriefly, followed by a few classical examples, each of which will betreated in some detail.7.2.2.
Frontier Orbitals: HOMO and LUMOA successful chemical reaction requires both energy and symmetrymatching between the MOs of the reactants. The requirements areessentially the same as in case of constructing MOs from AOs; onlyorbitals of the same symmetry and comparable energy can overlapsuccessfully. The strongest interactions occur between those orbitalswhich are close to each other in energy. However, the interactionbetween filled MOs is destabilizing since the energy of one orbitalincreases by about as much—actually a little more—as that of theother decreases (see Figure 7-6a). The most important interactionsoccur between the filled orbitals of one molecule and the vacantorbitals of the other.
Moreover, since the interaction is strongest forenergetically similar orbitals, the most significant interactions can beexpected between the highest occupied molecular orbital (HOMO) ofone molecule and the lowest unoccupied molecular orbital (LUMO)of the other (Figure 7-6b). The labels HOMO and LUMO were incorporated by Fukui into a descriptive collective name: frontier orbitals.The first article in this topic appeared in 1952 [47], and the idea hasFigure 7-6. (a) Interaction of two filled orbitals.
The interaction is destabilizing,and so the reaction will not occur; (b) Interaction of the highest occupied MO(HOMO) of one molecule with the lowest unoccupied MO (LUMO) of anothermolecule.3267 Chemical Reactionsbeen extended to a host of different reactions in the succeeding years(see, e.g., References [48] and [49]).Fukui recognized the importance of the symmetry properties ofHOMOs and LUMOs perhaps for the first time in connection with theDiels-Alder reaction.
According to his Nobel lecture [50], however,it was only after the appearance of the papers by Woodward andHoffmann in 1965 that he “became fully aware that not only thedensity distribution but also the nodal property”—that is, symmetry—“of the particular orbitals have significance in . . . chemical reactions.”The concept of frontier orbitals simplifes the MO description ofchemical reactions enormously, since only these MOs of the reactantmolecules need to be considered. Several examples of this approachwill be given in Section 7.3.7.2.3. Conservation of Orbital SymmetryThe first papers by Woodward and Hoffman outlining and utilizing theidea of conservation of orbital symmetry appeared in 1965 [51–53].Salem [54] called the discovery of orbital symmetry conservation arevolution in chemistry:It was a major breakthrough in the field ofchemical reactions in which notions preexistingin other fields (orbital correlations by Mulliken,and nodal properties of orbitals in conjugatedsystems, by Coulson and Longuet-Higgins) wereapplied with great conceptual brilliance to afar-reaching problem.
Chemical reactions weresuddenly adorned with novel significance.The idea and the principles of drawing correlation diagrams followsdirectly from the atomic correlation diagrams of Hund [55] andMulliken [56]. They are very useful for predicting the “allowedness”of a given concerted reaction. In constructing correlation diagrams,both the energy and the symmetry aspects of the problem must beconsidered.
On one side of the diagram the approximate energy levelsof the reactants are drawn, while on the other side those of theproduct(s) are indicated. A particular geometry of approach mustbe assumed. Furthermore, the symmetry properties of the molecularorbitals must be considered in the framework of the point group of7.2. Electronic Structure327the supermolecule. In contrast to the frontier orbital method, it isnot necessarily the HOMOs and LUMOs that are considered.
Instead,attention is focused upon those molecular orbitals which are associated with bonds that are broken or formed during the chemical reaction. We know that each acceptable molecular orbital must belongto one irreducible representation of the point group of the system.At least for nondegenerate point groups, this MO must be eithersymmetric or antisymmetric with respect to any symmetry elementthat may be present. (The character under any operation is either1 or –1.)Among all possible symmetry elements, those must be considered which are maintained throughout the approach and which bisectbonds that are either formed or broken during the reaction.
Theremust always be at least one such symmetry element. The next stepis to connect levels of like symmetry without violating the so-callednoncrossing rule. According to this rule, two orbitals of the samesymmetry cannot intersect [57]. Thus, the correlation diagram iscompleted. These diagrams yield valuable information about the transition state of the chemical reaction. The method will be illustratedwith examples in Section 7.3.7.2.4.
Analysis in Maximum SymmetryIn the analysis in maximum symmetry approach two points areconsidered when predicting whether or not a chemical reaction canoccur. One such point involves the allowedness of an electron transferfrom one orbital to another. The other involves consideration of thereaction-decisive normal vibration. In both cases symmetry argumentsare used. This approach, developed by Halevi, [58–60] is thoroughand rigorous. It is similar in part to the Bader–Pearson method andin part to the Woodward–Hoffmann method. It incorporates severalfeatures of each of these methods.
First, the transformation of both themolecular orbitals (electronic structure) and the displacement coordinates (vibrations) are examined in the context of the full symmetrygroup of the reacting system. All ways of breaking the symmetry ofthe system are explored, and no symmetry elements which are retainedalong the pathway are ignored. The correlation diagrams are called“correspondence diagrams” in this approach to distinguish them fromthe Woodward–Hoffmann diagrams.3287 Chemical ReactionsHalevi’s method to determine whether a chemical reaction isallowed or forbidden considers both the electronic and vibrationalchanges in the molecule.
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