Hiickel notation

The secular determinant can be further simplified by considering only interactions between first-nearest neighbors. In this case, aU the other matrix elements become equal to zero. Using the familiar Hiickel notation, Eq. 5.16 then looks hke ... 

Suppose two groups, R and X, unite to form RX. If the orbitals of R and X have the same symmetry and overlap spatially they will mix and the conjugated system can be represented by equation 10a which is identical to equation 10 but is written in Hiickel notation. 

We now introduce the Hiickel approximation, employing the a, /i notation, the convention that a is the zero of energy, and using ft itself as the unit of... 

The first assignment step was to detect planar rings that obey the Hiickel rule of 4n+2 p-electrons and flag them as aromatic, i.e. force all the atoms into an sp2 hybridization state. For planarity recognition, three arbitrarily chosen adjacent ring atoms form a base plane. Subsequently, for each atom of the ring, the distance to this base plane is computed, d being zero for the ideal case. In vector notation, the plane equation can be described as follows ... 

The Hiickel approximation has already been discussed in this scries (see references 27 and 29). The notation used here is the usual a and jS designate the Coulomb integral and resonance integral, respectively. 

Therefore, Hiickel theory of n electron systems distinguishes only between linear chains and rings. It is useful to introduce the notation ... 

It is often interesting and instructive to read the original papers describing important discoveries in your field of interest. Two Web sites. Selected Classic Papers from the History of Chemistry and Classic Papers from the History of Chemistry (and Some Physics too), present many original papers or their translations for those who wish to explore pioneering work in chemistry. To learn about early work on the subject of this chapter, use your Web browser to connect to http //cheniistry.brookscole.coni/ skoogfac/. From the Chapter Resources Menu, choose Web Works. Locate the Chapter 10 section. Click on the link to one of the Web sites just listed. Locate the link to the famous 1923 paper by Debye and Hiickel on the theory of electrolytic solutions and click on it. Read the paper and compare the notation in the paper to the notation in this chapter. What symbol do the authors use for the activity coefficient What important phenomena do the authors relate to their theory Note that the mathematical details are missing from the translation of the paper. 

We now revise our notation a little in order to bring it into line with what has become traditional in Hiickel theory it is called the a, -notation. 

Fig. 3.30 Porphyrin HOMOs b], >2 and LUMOs Cj and Cj showing their original (Hiickel) group theoretical notation and their modified notation as used on the four-orbital model. The original coefficients are proportional to the size of the circles. SoUd or dashed circles indicate sign. Symmetry nodes are drawn in heavy lines.

This is analogous to the simple Hiickel approximation in molecular orbital calculations (365). Since it is assumed that the electrons are constrained to a single chain, i.e., k is parallel to a, k-a is equal to ka. Vector notation is therefore discontinued. Because of the very small overlap assumed it is seen from Eq. 7 (with A = 0) that... 

Ion-selective electrodes offer an observable value for the biologically relevant parameter the ion s active molality in the aqueous phase of the biological specimen directly. This might be a challenge for elements that are associated by 30-50% to different anions, e.g., magnesium and calcium. For alkaline and alkaline-earth metal cations the Debye-Hiickel formalism allows a fair approximation of the mean activity coefficient ji+ as measured for an ion and its counterion in a calibration solution. The notation of... 

This section introduces the context and the notation of the Hiickel-Lewis (HL) methods. The notations that follow can be found in Table 13.1. 

The Pariser-Pople-Parr method is the simplest implementation of the self-consistent field method. Like the Hiickel method, it treats only the electrons in delocalized pi orbitals in planar molecules and represents these orbitals as linear combinations of basis functions that include only the unhybridized p orbitals. All overlap integrals are assumed to vanish, as in the Hiickel method, but not all of the integrals representing electron-electron repulsions are assumed to vanish. Two notations are used for these integrals ... 

In some publications the Debye-Hiickel equation is used only in reference to the spherically symmetric bulk electrolyte solution, with the term linear Poisson-Boltzmann (or LPB) equation referring to the result of linearizing the Poisson-Boltzmann equation, whatever its application. We follow more common usage and use the two terms interchangeably thus DH = LPB in our notation.]... 

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