Symmetry and electronic states

The presence of an unpaired electron in radical cations has significant consequences for symmetric compounds. This becomes clear if one considers the transformation of an open shell symmetric compound into another compound of a different symmetry. In such cases, the symmetry of the singly occupied molecular orbital (SOMO) determines the overall electronic states of the reactant and the product. If the two electronic states do not correlate, i.e., do not share a common symmetry element, a symmetry-preserving pathway from reactant to product is not possible. Any adiabatic reaction leading from the reactant to the product therefore has to involve the loss of symmetry. This problem obviously does not occur for the case of closed-shell molecules, where all orbitals are doubly occupied, leading to a common electronic Ai state for all molecules. 

A case where both effects are important is the ring opening of the cyclobutene radical cation l +.13 This reaction was studied experimentally by Bally and coworkers, who found that, in contrast to the thermal reaction, only the trans-1,3-butadiene radical cation, trans-2 +, is formed in a matrix isolation experiment.14,15 This surprising result can be explained by considering the electronic states of the species involved in the reaction, which are shown in Fig. 1. 

The cyclobutere radical cation l + has a C2v symmetry and a 2B ground state. Following a conrotatory pathway leads to the first excited state of cis-2 +, which also has a C2v symmetry and a 2BX state. Conversely, the 2A2 ground state of cis-2 + correlates to the second excited state of 1 +. Thus, a direct, symmetry conserving reaction of the group state of l + to the ground state of cis-2 + is not possible. 

In contrast, trans-2 + has a C2h symmetry and a 2Bg ground state, therefore in principle allowing a symmetry preserving pathway to correlate it with the ground state of 1 +. The corresponding C2-symmetric transition structure has, at the QCISD(T)//QCISD level of theory and using a 6-31G basis set, an activation energy of 23.4 kcal/mol. However, a frequency analysis of this transition structure 

Similar results are also obtained for the next higher homologue of the reaction, the ring closing reaction of the 1,3,5-hexatriene radical cation 6 + to give the 1,3-cyclohexadiene radical cation 7 +. Even though 6 + is spectroscopically well 

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Estimate of Cp and for free radicals may be made to within 2 cal/mole- K by taking the values for closely related compounds and making corrections for symmetry and electronic states (Table D.l) to Thus Cp and /S for NH3 and CH3 are probably very close to each other. In similar ffu hion the values of and S (properly corrected) are probably also within 2 cal/mole-°K for the radicals H—H—C=(), and H—O—6 and the molecules IIC N and UNO (a correction of about 3 cal/mole- K may be made to for nonlinearity). The methods of partial bond and atom contributions may also be used to estimate (fp and /S for radicals to about the same reliability as indicated for the molecular species. 

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