Chemical action and chemical bonding Mihai V. Putz * Laboratory of Computational and Structural Physical Chemistry, Chemistry Department, West University of Timis ßoara, Str. Pestalozzi No. 16, Timis ßoara, RO-300115, Romania article info Article history: Received 22 November 2008 Received in revised form 18 December 2008 Accepted 18 December 2008 Available online 30 December 2008 Keywords: Variational principle Electronegativity Density functional softness Density functional hardness Electronic response function abstract New chemical bonding paradigm in terms of chemical action functional and of its reformulations by means of electronegativity, linear response and density softness kernels is advanced; it makes no use of traditional molecular orbital bonding analysis while providing reliability in identifying the bonding regions through appropriate specialization of the chemical action variational (conservation) principle along the bond length. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Chemical bonding stands perhaps as the central issue of chem- ical interactions being in last century analyzed through many con- ceptual and computational tools: from single to many electronic wavefunction [1], to configuration interaction [2], to variational treatment of eigenstates [3], to orthogonal orbitals and hybridiza- tion [4], to pseudopotentials and localization functions [5], to reac- tivity indices and frontier (Fukui) orbitals [6], to electronegativity and chemical hardness principles [7], and finally to electronic den- sity description and of related functionals [8]. Actually, it turns out that variational principles make more accurate description of reac- tivity when associated with recording of the chemical events across reaction coordinate through the most probable path in spe- cific configurationally, phase, or electronegativity-hardness space [9]. Such path integral description of chemical bonding is fully compatible with the established density functional quantum para- digm of matter [10]; it practically leads with minimization of the total energy functional E[q] of an N-electronic system in isolate and interaction states (through its chemical potential l) [10,11], dðE½q NlÞ¼ 0; ð1Þ while its analytical specialization goes until the so-called chemical action C A [q] limit [12], since it is the only exact functional known as the applied potential expectation C A ½q¼ Z qðrÞV ðrÞdr ð2Þ along the unknown exchange, correlation and kinetic components in the established overall Hohenberg–Kohn density functional F HK [q] [10,13]. Fortunately, it can be proved that the above total energy varia- tional principle, Eq. (1), is formally equivalent with the chemical action principle [12,14] dC A ¼ 0 ð3Þ thus allowing the complete description of reactivity in terms of con- voluted electronic density with applied potential in accordance with the Hohenberg–Kohn theorems while univocally fixing the correspondence between these quantities for, in principle any, elec- tronic states. The chemical action concept and its variational Eq. (3) lays on the foreground of the present ‘‘functional” picture of chem- ical bonding and both will be closely analyzed firstly in this study. This way there will be conceptually be proved that chemical bond may be described as a quantum–classical interaction [15] leading with associated combined functional–geometrical way in thinking the bonding, anti-bonding and no-bonding regions in chemical encountering. The work may eventually step forward in achieving a unified view of chemical bonding by means of chemical action character and of its relationship with equalized electronegativity of atoms-in-molecules. 2. The chemical action concept Be an N-electronic system with mono-electronic orbitals u i ; i ¼ 1; N and the total density [8,10a] 0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.12.026 * Tel.: +40 256 592633; fax: +40 256 592620. E-mail addresses: mvputz@cbg.uvt.ro, mv_putz@yahoo.com URL: http://www.cbg.uvt.ro/mvputz. Journal of Molecular Structure: THEOCHEM 900 (2009) 64–70 Contents lists available at ScienceDirect Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem