Structure, biradicaloid zwitterionic

In connection with Eq. (22), yet another important factor differentiates our approach from usual quantum chemical analyses of reaction mechanisms. This difference concerns the fact that while a quantum chemical approach is in principle independent of any external information (all participating species appear automatically as various critical points on the PE hypersurface), in our model that is more closely related to classical chemical ideas some auxiliary information about the structure of the participating molecular species is required. This usually represents no problem with the reactants and the products since their structure is normally known, but certain complications may appear in the case of intermediates. This complication is not, however, too serious since in many cases the structure of the intermediate can be reasonably estimated either from some experimental or theoretical data or on the basis of chemical intuition. Thus, for example, in the case of pericyclic reactions that are of primary concern for us here, the intermediates are generally believed to correspond to biradical or biradicaloid species with the eventual contributions of zwitterionic structures in polar cases. 

The structural dependence of biradicaloid minima discussed in Section 4.3.3 on an example of twisting of a double bond A=B can be extended to take solvent effects into account. Not only the nature of the atoms A and B but also polar solvents and counterions affect the stability of zwitterionic states and states of charged species. Then, depending on the solvent, a biradicaloid minimum can represent either an intermediate or a funnel for a direct reaction. 

If all atoms involved in the reaction lie in the same plane, the unpaired electron of the acyl radical may be either in an orbital that is symmetric with respect to this plane or in an orbital that is antisymmetric—that is, either in a 0 or in a r orbital, whereas only a o orbital is available for the unpaired electron of radical R. Instead of just one singlet and one triplet covalent biradicaloid structure (Figure 4.5), there are now two of each, which may be denoted as B and B respectively. Similarly, there are also different zwitterionic structures to be expected. The increase in complexity and the number of states that results from the presence of more than two active orbitals on the atoms of a dissociating bond has been formalized and used for the development of a classification scheme for photochemical reactions ( topicity ), as is outlined in more detail in Section 6.3.3. 

The diagonalization of the one-particle density matrix P on the Cl level yields the natural orbitals (NOs) and the occupation numbers of the molecule. In an RHF-SCF calculation, all occupation numbers are either 0 or 2, which means that an MO is either doubly occupied by 2 electrons or not occupied. If we invoke a Cl calculation, the mixing of configurations results in fractional occupation numbers of the NOs. Still in a normal molecule, such as ethane, water, ammonia, etc., the occupation numbers for the ground state will be close to 0 or 2. The occupation numbers of at least two NOs of excited states usually deviate from the values 0 and 2. In a biradicaloid structure occupation numbers will change and typically two of them will be close to 1. However, this method cannot characterize zwitterions since occupation numbers should be close to 0 and 2, respectively, in this case. The approach by Jug and Poredda yields both zwitterionic and diradical character of species, based on the valence criterion of Gopinathan and Jug. The valence is defined according to equation (5), which can be reformulated as equation (6). 

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