Abstract
The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems.
Highlights
In Walter Kohn’s lecture, with the occasion of receiving his Nobel Prize in Chemistry [1], back in1998, for density functional theory (DFT) theory [2,3,4], there was formulated a quite provoking assertion affirming that, heuristically, the general eigen-wave-function Ψ (r1,..., rN ) associated to a system of N electrons fails to be a legitimate scientific concept when N ≥ N0 ≈ 103.this affirmation may be at any time turned in a theorem, eventually as Kohn’s zeroDFT theorem, with a proof following the van Vleck prescription of the so called „exponential wall”, leaving with the applicability limits of the conceptually eigen-wave function of multi-electronics systems
Taken together relations (11) and (12) generate, by direct summation, the evidence of the contradiction [2]: E1 [ ρ ] + E 2 [ ρ ] < E1 [ ρ ] + E 2 [ ρ ]. The removal of such contradiction could be done in a single way, namely, by abolishing, in a reverse phenomenologically order, the fact that two eigen-functions, two Hamiltonians and respectively, two external potential exist for characterizing the same ground state of a given electronic system
Since the terms of total energy are involved in bonding and reactivity states of many-electronic systems, i.e. the kinetic energetic terms in electronic localization functions (ELF) topological analysis or the exchange and correlation density functionals in chemical reactivity in relation with either localization and chemical potential or electronegativity, worth presenting various schemes of quantification and approximation of these functionals for better understanding their role in chemical structure and dynamics
Summary
In Walter Kohn’s lecture, with the occasion of receiving his Nobel Prize in Chemistry [1], back in. The above described conceptual project was unfolded in 1963 when Walter Kohn met in Paris (at École Normale Supérieure), during his sabbatical semester, the mate Pierre Hohenberg who was working at the description of the metallic alloys (specially the CuxZn1-x systems) by using quantum traditionally methods of averaging crystalline periodic field. Studies of this type of problems often start from the level of the uniform electronic density referential upon which specific perturbation treatments are applied. The present work likes to review some fundamental aspects of density functional theory highlighting on the primer conceptual and computational consequences in electronic localization and chemical reactivity
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