Huckel model

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

The mean activity coefficient is the standard form of expressing electrolyte data either in compilations of evaluated experimental data such as Hamer and Wu (2) or in predictions based on extensions to the Debye-Huckel model of electrolyte behavior. Recently several advances in the prediction and correlation of mean activity coefficients have been presented in a series of papers starting in 1972 by Pitzer (3, Meissner 04), and Bromley (5) among others. 

As the basis for predicting ionic activity coefficients we chose to adopt an. empirical modification of Bromley s ( 5) extension of the Debye-Huckel model. The mean activity coefficient of a pure salt in water is given by... 

These equations do not reduce to the Debye-Huckel model for dilute solutions and are thus only justified for the treatment of very concentrated solutions. 

The discussion above is a description of problem that requires answers to the following (1) the determination of the distribution of ions around a reference ion, and (2) the determination of the thickness (radius) of the ionic atmosphere. Obviously this is a complex problem. To solve this problem Debye and Huckel used a rather general approach they suggested an oversimplified model in order to obtain an approximate solutions. The Debye-Huckel model has two basic assumptions. The first is continuous dielectric assumption. In this assumption water (or the solvent) is a continuous dielectric and is not considered to be composed of molecular species. The second, is a continuous charge distribution in the ionic atmosphere. Put differently, charges of the ions in the ionic surrounding atmosphere are smoothened out (continuously distributed). 

The Debye-Huckel model for ion-ion interaction yields the following equation for the activity coefficient of species i ... 

The particular approach described thus far forms the basis of the so-called Huckel model. Its implementation requires knowledge of the atomic OCp and values, which are eventually expressed in terms of experimental data, as well as a means of calculating the geometry dependence of the 3UiV s (e.g., some method for computing overlap matrices Sp,v ) ... 

The discussion of the stability of various electronic situations in these molecules and solids has focussed on the balance of one- and two-electron forces. One of the big problems of course is to actually calculate the magnitude of these, and then to decide how the structure of these materials determines the details of the overall electronic structure. In addition there is the other problem, which we mentioned in connection with the molecular Huckel model, of the frequent ambiguity in what the parameters of these models actually mean. The... 

In the Huckel model, the spin density p(, is taken as the square of the coefficient for the ith atom in the orbital to which the unpaired electron is assigned, Cto2. 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Huckel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be inmitive. One such model that continues to see extensive use today is the so-called extended Huckel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

Based on a Huckel model for the anthracene fragments of BA (which is an even alternant hydrocarbon) one can show that the delocalized LE state and the CT states should all have the same 7t bond order. This in turn implies that the vibrational modes and frequencies should be similar for LE, CT, and CT. Thus the vibrations of bianthryl can be ignored in the energy dependence on z (even for highly polar solvents). 

DCI. see Desorption chemical ionization Debye-Huckel model in interface studies, 625-626... 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

Table 5 Comparison of the critical radius Rc (in au), n (/cm3) and critical pressure Pc (in atm) between the results obtained by using a Debye-Huckel model and an Ion-Sphere (IS) model. Reprinted with permission from [203] Copyright 2006, John Wiley Sons, Inc.

Little is also known about photoelectron spectra of pteridines. The unsubstituted nucleus and its 4-methyl- and 2,4,6,7-tetramethyl derivative have been recorded and analyzed in terms of both a simple Huckel-model and semiempirical calculations <86CB1275>. The assignment of the n- and n-type PE bands of pteridine indicates that the low energy band is associated with an ionization process involving the nitrogen n electrons and followed by rc-bands. Furthermore, the pKa of free pteridine, which is masked in aqueous solution by partial covalent hydration, is suggested from the PE data to be in the order of —2. 

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