In general, quantum-chemical methods for prediction of the outcome of cycloaddition reactions can be classified into three groups, depending on the particular reaction steps. The least used first group comprises the reactivity indexes, which are based on the analysis of stationary states of substrates. The second group contains the indirect methods of determination of activation energy, such as PMO, FMO and BL. The third group includes the methods relying on finding and characterization of critical structures on the corresponding potential energy hypersurface. BL and PMO methods can be applied only for the reactions that obey the principle of non-intercrossing of the energy profiles. These methods are mutually complementary and are used for description of different reaction stages of [2+3] cycloadditions. In the case of a late transition state, the activation energy is controlled primarily by the electronic effects related to formation of new bonds, rather than by the weak donor-acceptor interactions of substrates that are the basis for PMO and FMO methods. Reverse situation occurs when the activation barrier is controlled by an early transition state whose structure resembles substrates. Despite some reported successes, BL method has not become so popular as PMO. This results probably from the narrower scope of potential applications of the former method compared to the later one as well as from the BL method formalism. BL is used for explanation of specific aspects of [2+3] cycloadditions rather than for the reactivity predictions in the literal sense. Availability of fast computers and advanced quantum-chemical software has caused the [2+3] cycloaddition analysis based on localization and characterization of critical points on the potential energy hypersurface has gained popularity in recent years. Such analysis affords information about reactivity of the reagents, reaction mechanism, and, regio-, stereo- and periselectivity of practically any kind of reactions. By this method, transition state geometry and its physicochemical parameters, such as charge distribution, ionization potential, or dipole moment, can be determined. The transition state dipole moment can be used for prediction of the reaction course in solvents of different polarity. Moreover, there are procedures for direct calculations in the presence of a simulated dielectric medium, such as a solvent.
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