Symmetry correlation state

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. 

Fig. 7. Orbital (a), configuration (b), and state (c, d) correlation diagrams for a typical ground-state symmetry-forbidden pericyclic reaction...

The import of diabatic electronic states for dynamical treatments of conical intersecting BO potential energy surfaces is well acknowledged. This intersection is characterized by the non-existence of symmetry element determining its location in nuclear space [25]. This problem is absent in the GED approach. Because the symmetries of the cis and trans conformer are irreducible to each other, a regularization method without a correct reaction coordinate does not make sense. The slope at the (conic) intersection is well defined in the GED scheme. Observe, however, that for closed shell structures, the direct coupling of both states is zero. A configuration interaction is necessary to obtain an appropriate description in other words, correlation states such as diradical ones and the full excited BB state in the AA local minimum cannot be left out the scheme. 

The application of correlation diagrams to photochemical processes goes back to the early work of Laidler and Shuler (1951). More recently, Longuet-Higgins and Abrahamson (1965) showed how orbital-symmetry correlations may be converted into state-symmetry correlations. Here the fundamental consideration is that states of the same symmetry do not cross, i.e. the result is an avoided crossing, while states of different symmetry do cross. The principles involved are illustrated in Fig. 19 for the dimerization of... 

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. 

Figure 11.27 State correlation diagram for the forbidden n2s + n2s cycloaddition. The orbital designations are those defined in Figure 11.15. State symmetry designations refer to the mirror planes a and a of Figure 11.15.

The lowest state of prismane (2B,) cation lies 16 kcal mol-1 above the 2B2 state of the Dewar benzene cation (at the MP2/6-31 G level). This is considerably less than the corresponding energy difference of the neutral systems (37 kcal mol-1). The ground electronic states of prismane and Dewar benzene ions do not correlate their interconversion is forbidden from both state-symmetry and orbital-symmetry considerations. The CIDNP experiments indicate, however, that the actual barrier is quite small. 

The state-symmetry correlation also indicates that electrocyclic radical interconversion favors a conrotatory path from the first excited state and a disrotatory path from the second excited state. Because of the proximity of the energy levels and the violations of the noncrossing rule, it is probable that the excited state process will not be highly stereoselective. The same detailed considerations must be applied to the five-atom five-electron system and yield the results given in Table 1. Differences between the stereochemical predictions of Table 1 and those of others (Woodward and Hoffmann, 1965a Fukui and Fujimoto, 1966b Zimmerman, 1966) tend to be limited to the excited-state reactions of odd-atom radicals. 

Fig. 14. Orbital and state symmetry correlations for the dimerization of ethylene. The orbital symmetry designations in the upper diagram are with respect to the planes of symmetry tjyt and < ...

The coefficients Ck are real and Skk1 =< k k > is the overlap of normalized VB diagrams with identical electron distributions rij. Normalization illustrates the general problem of finding matrix elements between correlated states. We express an operator in second-quantized notation and consider exact eigenstates i> > and x > that may be in the same or different symmetry subspaces. The matrix elements Akk of A are obtained as shown in (11) to give... 

BEBO-based Marcus equation or the hyperbolic relation which is not based on theory but is easier to use and gives about the same answer. The reduction in isotope effect predicted by the Westheimer transition state symmetry arguments is harder to correlate, yet the wide range of isotope effects virtually requires this explanation, in contrast to the case in proton transfers. 

Various approximations allow one to draw diabatic surfaces that connect the electronic states of the reactant with those of conceivable photoproducts and symmetry considerations (Section 4.4) are extremely helpful in this respect. We first consider state symmetry correlation diagrams.331 If the molecules of interest are symmetric (perhaps ignoring some substituents), we consider a reaction coordinate leading from reactant to... 

The significance of electron correlation and of state symmetries in the interaction of strong laser pulses with He Is [122]... 

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