Fukui function descriptors of Hirshfeld reactants

Let us again examine the A-B reactive system and its A°-B° promolecule reference, the latter consisting of the free reactant densities brought to their current positions in A-B, for the finite separation between the two subsystems. It should be observed, that this hypothetical state also corresponds to the electrostatic stage of the interaction between reactants, when the electron distributions and internal subsystem geometries are held frozen at finite inter-reactant separations. When the subsequent Hirshfeld partitioning of the known overall ground-state density of A-B is performed, one obtains the uniquely defined, equilibrium subsystems in the reactive system. 

Both A°-B° and A-B constitute a collection of the uniquely defined reactant subsystems, before and after their density relaxation at finite distances, respectively. It is of interest in the theory of chemical reactivity to determine how the reactivity indices of reactants, e.g. FF, change as a result of their interaction one would also like to know how their response properties relate to those of the system as a whole, at both these limits the molecular, in A-B, and the corresponding quantities, in A°-B° [28], 

Let us first examine the promolecule A°-B°, defined by the subsystem densities p° = (pa, Ph ) generating the promolecular density p° = pA + pB. A number of related FF-type derivatives of the electronic densities, with respect to either N° = (TVa, iVB) or TV0 = N% + iVB, can be defined for this reference system  

Analogous derivatives, with respect to either A/11 = (WA, AB) or N = Aa + AB = N°, can be defined for the reactive system A-B, consisting of the corresponding Hirshfeld reactant densities, pH = (pA, p ), which sum up to the overall molecular density p = pA + Pb  

A similar relation can be derived for the partitioning of the promolecular FF, by reversing the roles of the Hirshfeld and the free reactant densities in the minimum entropy deficiency principle, so that now pH(r) play the role of the reference densities, while p°(r) are the optimum densities satisfying the constraint XaP°(r) = P°(r)  

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