Transition structure symmetry

Transition structures can be dehned by nuclear symmetry. For example, a symmetric Spj2 reaction will have a transition structure that has a higher symmetry than that of the reactants or products. Furthermore, the transition structure is the lowest-energy structure that obeys the constraints of higher symmetry. Thus, the transition structure can be calculated by forcing the molecule to have a particular symmetry and using a geometry optimization technique. 

As mentioned above, a structure with a higher symmetry than is obtained for the ground state may satisfy the mathematical criteria defining a reaction structure. In a few rare (but happy) cases, the transition structure can be rigorously defined by the fact that it should have a higher symmetry. An example of this would be the symmetric Sn2 reaction ... 

In this case, the transition structure must have symmetry, with the two F atoms arranged axially and the H atoms being equatorial. In fact, the transition structure is the lowest energy compound that satisfies this symmetry criteria. 

For systems where the transition structure is not defined by symmetry, it may be necessary to ensure that the starting geometry does not have any symmetry. This helps avoid converging to a solution that is an energy maximum of some other type. 

Try quasi-Newton calculations starting from structures that look like what you expect the transition structure to be and that have no symmetry. This is a skill that improves as you become more familiar with the mechanisms involved, but requires some trial-and-error work even for the most experienced researchers. 

One way to do so is to look at the normal mode corresponding to the imaginary frequency and determine whether the displacements that compose it tend to lead in the directions of the structures that you think the transition structure connects. The symmetry of the normal mode is also relevant in some cases (see the following example). Animating the vibrations with a chemical visualization package is often very useful. Another, more accurate way to determine what reactants and products the transition structure coimects is to perform an IRC calculation to follow the reaction path and thereby determine the reactants and products explicity this technique is discussed in Chapter 8. 

Let us finally consider two Z-matrices for optimization to transition structures, the Diels-Alder reaction of butadiene and ethylene, and the [l,5]-hydrogen shift in Z-1,3-pentadiene. To enforce the symmetries of the TSs (Cj in both cases) it is again advantageous to use dummy atoms. 

Mezey, P.G. (1991) New symmetry theorems and similarity rules for transition structures. In Theoretical and Computational Models for Organic Chemistry, Formosinho, SJ. Csizmadia, I.G. and Amaut, L.G. (Eds.), Kluwer Academic Publishers, Dordrecht. 

The triplet instability of both RB3LYP and RHF solutions is responsible for the difference in the symmetry of the ethylene-peroxynitrous acid transition structure. In general, an unsymmetrical transition structure with alkene epoxidation when an alternative symmetrical structure is possible, appears to be associated with an unstable wave function. 

Another important contribution by Landau is related to symmetry changes accompanying phase transitions. In second-order or structural transitions, the symmetry of the crystal changes discontinuously, causing the appearance (or disappearance) of certain symmetry elements, unlike first-order transitions, where there is no relation between the symmetries of the high- and low-temperature phases. If p(x, y, z) describes the probability distribution of atom positions in a crystal, then p would reflect the symmetry group of the crystal. This means that for T> T p must be consistent with... 

The rearrangement occurs at least partially with antarafacial allylie participation and was estimated to be concerted in the sense of orbital-symmetry conservation control. Transition-structures appropriate to concerted pathways were judged likely to have exorbitantly high energies as a result of poor orbital overlap and unfavorable steric interactions. 

Polymetallic anions, prepared by dissolution of alloys of the alkali and post-transition metals in amine solvents (often with a complexand for the alkali metal cation), have been characterized in crystalline and solution phases. Clusters TlSng3, Ge92 (with 20 skeletal bonding electrons), Sn93- (21 skeletal e) and Bi95+ (22 skeletal e) possess a tricapped trigonal prismatic structure, symmetry D3A, with variations of dimensional detail which correlate with the electron population.291 292 This structure is a ctoso-deltahedron, and with 20 (2h + 2) skeletal electrons can be construed to be three-dimensionally aromatic.292 The 22e clusters M94 (M = Ge, Sn, Pb) occur as the C4v monocapped square antiprism, a nido polyhedron. 

There are other stereochemical features which have nothing to do with the symmetry of the orbitals, and are much less powerfully controlled. In many cycloadditions, there are two possible all-suprafacial approaches one having what is called the extended transition structure 2.102, in which the conjugated systems keep well apart, and the other called the compressed 2.103, where they lie one above the other. Both are equally allowed by the rules that we shall see in Chapter 3, but one will usually be faster than the other. This type of stereochemistry applies only when the conjugated systems have at least three atoms in each component it is therefore only rarely a consideration. It shows up in the cycloadditions of allyl cations to dienes, where the two adducts 2.56 and 2.57 on p. 13 are the result of the compressed transition structure 2.104 and the extended 2.105, respectively, with the former evidently lower in energy. 

The reaction is symmetry-allowed when it is suprafacial on all three components, but there are two reasonably accessible transition structures for an all-suprafacial reaction, chair-like 5.52 and boat like 5.53, both of which are [ g+ g+ J. In the reaction 5.48 - 5.49, it must be boat-like to give two cis double bonds in the product, but this is probably constrained by the... 

It is frequent but not invariable that where a longer conjugated system has a geometrically accessible and symmetry-allowed transition structure like that in 5.90, the longer system is used. Thus, the [8+2] and [6+4] cycloadditions on pp. 15 16, and the [14+2] cycloaddition on p. 44 take place rather than perfectly reasonable Diels Alder reactions, and the 8-electron electrocyclic reactions of 4.51 and 4.54 takes place rather than disrotatory hexatriene-to-cyclohexadiene reactions. This kind of selectivity is called periselectivity. 

---