Hueckel theory

T. Kennedy. Debye-Hueckel theory for charge symmetric Coulomb systems. Commun Math Phys 92 269-294, 1983. 

Calculations (Hacker and Kasai 1993) in the framework of extended Hueckel theory found the LUMO of o-diazobenzoquinone to be mainly (up to 60%) localized at the N—N sector. The electronegativity of the o-carbonyl oxygen enhances the acceptor properties of the diazo group. Charge-spin separation is an understandable consequence of the situation. 

Lee, B.P., and Fisher, M.E. Density fluctuations in an electrolyte from generalized Debye-Hueckel theory. Phys. Rev. Lett., 1996, 76, p. 2906-9. 

This mechanistic question is one of the examples of the success of density functional theory (DFT) methods for metal-organic chemistry. Earher work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on Extended Hueckel theory (EHT) calculations led to the conclusion that the (3+2) pathway is more likely, but the authors could not exclude the possibility of a (2+2) pathway [4] similar to the results of HE calculations in combination with Quadratic configuration interaction (QCISD(T)) single points [32]. 

My friend Leszek Stolarczyk remarked on still another kind of symmeby in chemistry (in an impublished paper). Namely, the alternant hydrocarbons, defined in the Hueckel theory, despite the fact that they often do not have any spatial sjfmmetry at aU, have a S)mimetric energy level pattern with respect to a reference energy. We meet the same feature in the Dirac theory, if the electronic and positmiic levels are considered. This suggests a underlying, not yet known, internal reason common to the alternant hydrocarbons as viewed in the Hueckel theory and the Dirac model, which seems to be related somehow to the notion of supersymmetry. 

Naphthalene undergoes electrophihc substitutions at the a rather than p position. The Hueckel molecular orbital calculations show that all the carbons have the same jt electron density 1.0. This is not in agreement with the theory of organic reactions based on the Coulombic interaction that electrophilic attack occurs on the most negatively charged atom. Fukui [7] proposed the frontier orbital theory for the discrepancy between the theory and the experimental observation. The importance of... 

The orbital phase theory includes the importance of orbital symmetry in chanical reactions pointed out by Fukui [11] in 1964 and estabhshed by Woodward and Holiimann [12,13] in 1965 as the stereoselection rule of the pericyclic reactions via cyclic transition states, and the 4n + 2n electron rule for the aromaticity by Hueckel. The pericyclic reactions and the cyclic conjugated molecules have a conunon feature or cychc geometries at the transition states and at the equihbrium structures, respectively. 

A part of the chemical consequences of the cyclic orbital interactions in the cyclic conjngation is well known as the Hueckel rule for aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions [14]. In this section, we describe the basis for the rnles very briefly and other rules derived from or related to the orbital phase theory. The rules include kinetic stability (electron-donating and accepting abilities) of cyclic conjugate molecules (Sect. 2.2.2) and discontinnity of cyclic conjngation or inapplicability of the Hueckel rule to a certain class of conjngate molecnles (Sect. 2.2.3). Further applications are described in Sect. 4. 

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

According to the theory of cyclic conjugation, the Hueckel rule is applicable only to a continuous cyclic conjugation, but not to a discontinuous one (Schemes 14 and 15). In the discontinuously conjugated molecules, electron donors and acceptors are alternately disposed along the cyclic chain [25].The thermodynamic stability depends neither on the number of n electrons nor the orbital phase properties, but on the number of neighboring donor-acceptor pairs. Chemical consequences of the continuity-discontinuity of cyclic conjugation are reviewed briefly here. 

Hoflmann in 1965. Ten years later, Fukni and Inagaki proposed an orbital phase theory for cyclic molecules and transition states, which includes the Woodward-Hofftnann rule and the Hueckel rule for aromaticity (Scheme 4). In 1982 Inagaki... 

Basic equations for almost every subfield of electrochemistry from first principles, referring at all times to the soundest and most recent theories and results unusually useful as text or as reference. Covers coulometers and Faraday s Law, electrolytic conductance, the Debye-Hueckel method for the theoretical calculation of activity coefficients, concentration cells, standard electrode potentials, thermodynamic ionization constants, pH, potentiometric titrations, irreversible phenomena. Planck s equation, and much more, a indices. Appendix. 585-item bibliography. 197 figures. 94 tables, ii 4. 478pp. 5-% x 8. ... 

Debye and Hueckel s work is historically important to soil chemistry because their derivation was similar to that of Guoy and Chapman, published independently about 1910, who tried to predict the ion distribution in the aqueous solution around a charged surface such as a soil particle. Although the Guoy-Chapman theory and its... 

Vela, A., Gfequez, J. L. (1988). Extended Hueckel parameters from density functional theory. J. Phys. Chem. 92(20), 5688-5693. 

While polyelectrolyte behavior is generally not within the remit of this work, Stellwagen, et a/. s use of capillary electrophoresis to examine a fundamental physico-chemical issue is worthy of note(49). Their interest was a vexing question, namely whether or not zwitterions contribute to the ionic strength / of a solution. Many would assert that the theoretical studies of Kirkwood are substantially definitive, but some doubts remain(50,51). Stellwagen, etal. noted that the Debye-Hueckel-Onsager electrophoretic theory requires pi [Pg.57]

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