M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 49
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The main idea in their work is that symmetry phenomenamay play as important a role in chemical reactions as they do in theconstruction of molecular orbitals or in molecular spectroscopy. It iseven possible to make certain symmetry based “selection rules” forthe “allowedness” and “forbiddenness” of a chemical reaction, just asis done for spectroscopic transitions.The series of articles written by Woodward and Hoffmann in themiddle of the 1960s caused a considerable stir in the organic chemistrycommunity.
For decades afterwards organic chemists were checkingand trying out reactions proposed by the orbital symmetry rules. In2003, the first paper of their series [14] was the 88th most cited paperin the Journal of the American Chemical Society [15].M. Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed.,C Springer Science+Business Media B.V. 2009DOI: 10.1007/978-1-4020-5628-4 7, 3133147 Chemical ReactionsBefore describing the symmetry rules for chemical reactions,however, we would like to mention some limitations.
Symmetry rulescan usually be applied to comparatively simple reactions, the so-calledconcerted reactions. In a concerted reaction all relevant changes occursimultaneously; the transformation of reactants into products happensin one step with no intermediates.At first sight it would seem logical that symmetry rules can beapplied only to symmetrical molecules. However even nonsymmetricreactants can be “simplified” to related symmetrical parent molecules.As Woodward and Hoffmann put it, they can be “reduced to theirhighest inherent symmetry” [16]. This is, in fact, a necessary criterion if symmetry principles are to be applied.What does this mean? For example, propylene, H2 C=CHCH3 , mustbe treated as its “parent molecule”, ethylene. The reason is that it isthe double bond of propylene which changes during the reaction, andit nearly possesses the symmetry of ethylene. Salem calls this feature“pseudosymmetry” [17].The statement: a chemical reaction is “symmetry allowed” or“symmetry forbidden,” should not be taken literally.
When a reactionis symmetry allowed, it means that it has a low activation energy. Thismakes it possible for the given reaction to occur, though it does notmean that it always will. There are other factors which can imposea substantial activation barrier. Such factors may be steric repulsions, difficulties in approach, and unfavorable relative energies oforbitals. Similarly, “symmetry forbidden” means that the reaction,as a concerted one, would have a high activation barrier.
However,various factors may make the reaction still possible; for example, itmay happen as a stepwise reaction through intermediates. In this case,of course, it is no longer a concerted reaction.Most of the symmetry rules explaining and predicting chemicalreactions deal with changes in the electronic structure. However, achemical reaction is more than just that. Breakage of bonds and formation of new ones are also accompanied by nuclear rearrangements andchanges in the vibrational behavior of the molecule. (Molecular translation and rotation as a whole can be ignored.)As has been shown previously, both the vibrational motion and theelectronic structure of the molecules strongly depend on symmetry.This dependence can be fully utilized when discussing chemicalreactions.7.1. Potential Energy Surface315Describing the structures of both reactant and product moleculeswith the help of symmetry would not add anything new to our previousdiscussion. What is new and important is that certain symmetry rulescan be applied to the transition state in between the reactants and products.
This is indeed the topic of the present Chapter.7.1. Potential Energy SurfaceThe potential energy surface is the cornerstone of all theoreticalstudies of reaction mechanisms [18]. The topography of a potentialenergy surface contains all possible information about a chemicalreaction.
However, how this potential energy surface can be depictedis another matter.The total energy of a molecule consists of the potential and thekinetic energy of both the nuclei and the electrons. The coulombicenergy of the nuclei and the electronic energy together representthe whole potential energy under whose influence the nuclei carryout their vibrations. Since the energies of the (ground and variousexcited) electronic states are different, each state has its own potentialenergy surface.
We are usually interested in the lowest energy potential surface which corresponds to the ground state of the molecule.An N atomic molecule has 3N–6 internal degrees of freedom (alinear molecule has 3N–5). The potential energy for such a moleculecan be represented by a 3N–6-dimensional hypersurface in a 3N–5dimensional space. Clearly the actual representation of this surface isimpossible in our limited dimensions.There are ways, however, to plot parts of the potential energy hypersurface. For example, the energy is plotted with respect to the changeof two coordinates during a reaction and molecular rearrangement inFigure 7-1a and b.
Such drawings help to visualize the real potential energy surface. It is like a rough topographic map with mountainsof different heights, long valleys of different depths, mountain pathsand holes. Since energy increases along the vertical coordinate, themountains correspond to energy barriers and the holes and valleys todifferent energy minima.Studying reaction mechanisms means essentially finding the mosteconomical way to go from one valley to another. Two adjacentvalleys are connected by a mountain path: this is the road that the316(a)7 Chemical Reactions(b)Figure 7-1. Three-dimensional potential energy surfaces: (a) Energy hypersurfacefor FSSF ⇔ SSF2 isomerization (detail).
Reproduced with permission [19] copyright (1977) American Chemical Society; (b) Potential energy surface of the molecular rearrangement of AgI3 , with the corresponding structures indicated on the sides[20]. Copyright (2005) American Chemical Society.reactant molecules must follow if they want to reach the valley on theother side, which will correspond to the product(s). The top of thepass is called the saddle point or col. The name saddle point refersto the saddle on a horse.
Starting from the center of the saddle, it isgoing up in the direction of the head as well as the tail, and it is goingdown in the direction of both sides. The configuration of nuclei at thesaddle point is sometimes called a transition state, sometimes a transition structure, in other cases an activated complex, and yet in othercases, a supermolecule. Transition state is the most commonly usedterm, although it is somewhat ambiguous (see Section 7.1.1).7.1.1. Transition State, Transition StructureThe region of the potential energy surface indicating the transitionstate is illustrated in Figure 7-2, while a modern sculpture reminiscentof a potential energy surface at and around the saddle point is shownin Figure 7-3.The term transition state is sometimes used interchangeably withthe term transition structure, although in a strict sense the two arenot identical.
Transition state is the quasi-thermodynamic state of7.1. Potential Energy Surface317Figure 7-2. Potential energy surface by Williams in the region of the transitionstructure in different representations [21]: (a) Three-dimensional representation ofthe saddle-shaped potential energy surface; (b) Two-dimensional potential energycurve produced by a vertical cut through the surface in (a) along the reaction path(indicated by bold dashed line) from reactants (R) to products (P); (c) Energycontours produced by horizontal cuts through the potential energy sufrace in (a).Adapted with permission from Reference [21].Figure 7-3. Saddle-shaped sculpture in Madrid, Spain.
Photograph by the authors.3187 Chemical Reactionsthe reacting system as defined by Eyring [22]. The transition structure, on the other hand, is the molecular structure at the saddle point.As was shown by Houk et al. [23], when a reaction has a largeactivation barrier and a slowly varying entropy in the region of thepotential energy maximum, the transition-state geometry and the transition structure are about the same.
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