Chemical reactivity spin hardness

We discussed mainly some of the possible applications of Fukui function and local softness in this chapter, and described some practical protocols one needs to follow when applying these parameters to a particular problem. We have avoided the deeper but related discussion about the theoretical development for DFT-based descriptors in recent years. Fukui function and chemical hardness can rigorously be defined through the fundamental variational principle of DFT [37,38]. In this section, we wish to briefly mention some related reactivity concepts, known as electrophilicity index (W), spin-philicity, and spin-donicity. 

The optical spectra of radicals provide important data for testing open-shell methods. Until about 1960 open-shell MO studies were rather rare. An intensive development of open-shell MO theory started in the early sixties and was followed by chemical apphcations and systematic studies in the late sixties. At present it is possible to state that the physicochemical properties of radicals are predicted with an accuracy comparable to that attained for closed-shell molecules. This is important not only from the viewpoint of the electronic spectra, which can hardly be interpreted without MO theory, but also from the viewpoint of the general theory of reactivity, since radicals and excited states offer the means to overcome spin and S5unmetry restrictions in certain chemical reactions. 

DFT based reactivity indices have proven to be of great use in the interpretation of a variety of experimental and theoretical results, either as such, or used within the context of three main principles electronegativity equalization, the principle of maximum hardness and the hard and soft acids and bases principle. The majority of reactivity indices emerge as response functions of the system s energy E with respect to the number of electrons N and/or the external potential v(r). In this contribution, we have outlined the spin-polarized extension of conceptual DFT or chemical DFT,... 

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