Spin Effects on Chemical Reactivity

Accordingly, the following constructions of the electronic density will be considered 

Therefore, the density functional of the total energy of a system placed in an external potential, with an oriented magnetic field which activate  

one expresses the total differential of the total functional energy, extending (3.98), as  

By evaluating the last two functional derivatives under the integrals of (3.413) with the aid of the total spin energy and by using the Euler relations (3. 412), one can re-rewrite the last total differential as  

On the other hand, another form of the total differential (3.414) can be obtained through considering the total energy as a function of variables 

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