Cyclization Reactions of Polyunsaturated Systems

For a systematic study of many related systems, a practical but nevertheless reliable approach had to be identified. It is clear that the reactions of the type depicted in Fig. 8.5 inherently have some diradical and hence multi-determinantal character. Therefore, semiempirical, HF and MP2 methods are unsuitable approaches because a single-reference will not be able to describe all the species involved equally well. DFT may be an option but it is also single-reference however, as it is not the wavefunction that is the operand but the electron density, DFT may still do a reasonable job in describing these reactions. The simple take on this is that the density may be well-behaved even if the wavefunction is not. For instance, DFT has been proven to work exceptionally well for carbenes although singlet carbenes are 

Of course, a proper treatment would utilize multireference methods, but these are very time consuming and limited to model stmctures only [36, 88). Furthermore, dynamic electron correlation is also very important in these reactions so that, for instance, simple CASSCF (complete active space SCF) computations are meaningless, as they mostly include static correlation. Perturbative corrections to CASSCF wavefunctions such as CASPT2 (CAS perturbation theory of second order) are necessary however, multireference perturbation methods do not improve significantly the singlet-triplet energy separations of many biradicals as compared to CASSCF results [89]. 

As demonstrated in Fig. 8.6, the quality of the results is further improved by single-point energy computations on the BLYP/6-31G structures utilizing the Briickner-doubles coupled cluster approach including triple excitations perturba-tively BCCD(T), also called BD(T) based on BS-UHF reference wavefunctions. In contrast, coupled-duster computations with unmodified UHF molecular orbi- 

With this validated methodology at hand, our research group has systematically computed new reaction modes of polyunsaturated carbon-ridi systems. For instance, we evaluated alternatives to the experimentally known cyclization modes 

These conclusions bear important implications for thermal reactions of unsaturated hydrocarbons and carbon-rich stmctures. For instance, irregularities in carbon nanotubes such as Stone-Wales defects play a significant role in determining the properties of these fascinating structures [102]. 

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