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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 sensible conception. it truly is analytically proved that during all proposed instances may be based the right kind stipulations in the absolute and chemical formulations to equalise. There seems to be 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 info. the ability of those proofs is composed in bypassing the information of the entire strength density sensible. this manner there has been emerged out the recent techniques of HOMO and LUMO chemical activities that neglecting the correlation-exchange phrases account because the capability chemical works of the valence shells whilst changing electrons with the environment.As an program the linked atomic electronegativity, hardness and chemical motion scales are computed and mentioned for every unified quantum photo with assistance from Slater orbitals. The so referred to as bosonic electronegativity and hardness characterising the fermionic-bosonic combinations on valence states emerge out and their affiliate atomic scales are computed. It follows that they show periodic albeit inverse traits than these anticipated from natural fermionic behaviour. This procedure could be came across most dear while explaining the Bose-Einstein condensates and superconductivity of atoms via electronegativity and hardness techniques. Extension to molecular platforms is prospected via making use of the recursive principles for electronegativity and hardness abstracted from electronegativity equalisation precept mixed with electronegativity-hardness invariant.In this molecular framework the unified different types of electronegativity and hardness are used to accomplish the proposed bonding situation according to equality and inequality electronegativity and hardness reactivity ideas for a selected sequence of Lewis bases. New index for checking the utmost hardness is formulated and utilized besides. this manner, the total 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 concept.

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0 0 ⎦ ( ) ( 2 n+7 / 2 ⎤ ⎡ 4 n+2 3⎞ 2 n +5 / 2 ⎛ + − + e n n n ( 1 ) ⎢ ⎥ ⎜ ⎟ 2⎠ ξ *2 (2n)! exp(2n + 3) ⎢⎣ ⎝ ⎥⎦ Nv ) (116) With expressions (113), (115), and (116) the systematic (softness) limited-, first bosonic-, second bosonic- and chemical action- related electronegativity and hardness, see the sets of equations (85)-(87), (97)-(99), (105)-(107), and (57)-(60), respectively, can be computed since their particular formulations are employed Atomic Electronegativity and Hardness 49 upon a certain atomic system with the relevant parameters, as displayed in the table 6.

To achieve the unification goal the limits (95) and (96) are again considered at different orders so that to release the convergent density functionals versions of absolute and chemical electronegativity and hardness. The unified results are presented in the table 5. However, from it, there outcomes that whereas electronegativity becomes equal expressed in both of its natural versions, as the so called second bosonic electronegativity: ⎛ 1 b ⎞ π ⎞ 1 ⎛ ⎟⎟ − ⎜⎜ C A + ⎟⎟ , χ B[ II ] = ⎜⎜ − N N N 2 a v ⎝ v ⎠ ⎝ v ⎠ (105) the respective hardness expressions still present some inherent differences even in the conditions of the unified frame of electronegativity.

X)VM ( x) ] (39) The minimum of functional (39) establishes in fact a realization of the chemical action principle (38) and optimizes the ordering pairs of the densities with the associate external potentials. More, the chemical action concept and its principle fit with the recommendation of the HK theorems from which the external potential and the electronic density are uniquely correlated for a given eigen-state. 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.

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