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By Mihai V. Putz

Systematic formulations of absolute and chemical electronegativity and hardness are analysed one of the neighborhood and non-local digital density contributions within the body of density practical concept. it really is analytically proved that during all proposed situations could be based the correct stipulations in the absolute and chemical formulations to equalise. There seems new variational notion and time period named as chemical motion performs the unifying position one of the quantum fluctuations of electronegativity and hardness at no matter what point of atomic and molecular structural details. the facility of those proofs is composed in bypassing the information of the whole strength density sensible. this fashion there has been emerged out the hot strategies of HOMO and LUMO chemical activities that neglecting the correlation-exchange phrases account because the strength chemical works of the valence shells whilst changing electrons with the environment.As an software the linked atomic electronegativity, hardness and chemical motion scales are computed and mentioned for every unified quantum photograph with the aid of Slater orbitals. The so referred to as bosonic electronegativity and hardness characterising the fermionic-bosonic combos on valence states emerge out and their affiliate atomic scales are computed. It follows that they demonstrate periodic albeit inverse tendencies than these anticipated from natural fermionic behaviour. This strategy should be came across most respected while explaining the Bose-Einstein condensates and superconductivity of atoms via electronegativity and hardness recommendations. Extension to molecular platforms is prospected by means of using the recursive ideas for electronegativity and hardness abstracted from electronegativity equalisation precept mixed with electronegativity-hardness invariant.In this molecular framework the unified kinds of electronegativity and hardness are used to accomplish the proposed bonding state of affairs according to equality and inequality electronegativity and hardness reactivity rules for a selected sequence of Lewis bases. New index for checking the utmost hardness situation is formulated and utilized to boot. this manner, the entire set of worldwide electronegativity-hardness signs of reactivity of atoms and molecules for numerous physico-chemical stipulations is formulated in a sublime analytical demeanour in the conceptual density practical idea.

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E. to quantify the reactivity. An illustration of the 24 Mihai V. Putz chemical action conceptual reliability will be later presented regarding the electronegativity and hardness density functional formulations. 3. CHEMICAL ACTION THROUGH TOTAL ENERGY [N, V] REPRESENTATION One of the most important issues in DFT regards the N- and V(x)representability of the working electronic density that is used to construct the global density functionals, in particular the total energy [92]. While Nrepresentability properly associates a trial density with the integral constrain (28) the V(x)-representability problem consists in finding the right density that uniquely correlates with the overall potential applied to the electronic system or in which the electronic system evolves [93].

Putz Thus, by combining (54) with (55) there is inferred that the chemical action achieves also the meaning of the averaged chemical work performed on or from the concerned system: C A = CW = ∫ ρ ( x)V ( x)dx (56) From this last quality the chemical action concept relates directly also with the electronic affinity and ionization potential, when the system performs a chemical work to attach or to detach an electron form its current state, respectively: C A+1 = ∫ ρ N +1 ( x)V ( x)dx ≡ EACA ≅ −ε LUMO −CA , (57) C A−1 = ∫ ρ N −1 ( x)V ( x)dx ≡ IPCA ≅ −ε HOMO −CA , (58) within the context of vertical electronic transfers so that the Koopmans’ theorem can be also applied to release the chemical action LUMO and HOMO related orbital energies.

Putz χL = − ηL = Nv + b , a 1 , 2a (85) (86) respectively, being different from that one which explicitly contains the chemical action correction, called hereafter (softness) limited chemical action hardness: η LCA = η L + C A (87) Note that the chemical action correction appears only to the chemical hardness, not to electronegativity, emphasizing on the regulating role that chemical action carries in the chemical bonding scenario, see table 1 and the accompanied discussion, where it is added to the chemical hardness as the averaged quantum fluctuation targeting the final stabilization of bond through the maximum hardness realization.

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