Hiickel rule/approximation

It is well known that Hund s rule is applicable to atoms, but hardly so to the exchange coupling between two singly occupied molecular orbitals (SOMOs) of a diradical with small overlap integrals. Several MO-based approaches were then developed. Diradicals were featured by a pair of non-bonding molecular orbitals (NBMOs), which are occupied by two electrons [65-67]. Within the framework of Hiickel MO approximation, the relationship between the number of NBMOs,... 

All atoms are equivalent by translation a. Although this is only a simplified ideal situation, it is used as a first example in many introductory textbooks on physical chemistry and solid state physics, because it is a problem simple enough to be treated analytically, especially if an easy approximation such as Hiickel s model Flamiltonian is applied. Several important simplifications in Hiickel s model make the calculation very easy, while preserving the main topological characteristics of the system. In this simple model, only one pz AO is considered for each atom. The different orbitals will be identified by the g lattice vector of the cell in which they are centered and denoted as p. Hiickel s approximation prescribes simple rules for the determination of the overlap and the Hamiltonian matrices with two parameters, a and p ... 

Although the Hiickel An+ 2 rule is rigorously derived for monocyclic systems, it is also applied in an approximate way to fused-ring compounds. Since two fused rings must share a pair of ir electrons, the aromaticity and the delocalization energy per ring is less than that of benzene itself. Decreased aromaticity of polynuclear aromatics is also revealed by the different C—C bond lengths. 

To form Pj" s P, for example, we need only nse the valne of z at each vertex to obtain P Hiickel approximation (see Hiickel Theory), but this is simply to provide an idea of the bonding/antibonding character, and some more accurate calculations will be discussed below. (Note that the splitting obeys another center-of-gravity rule.) The normalization is simply 1 /s/l, as overlap between the two a orbitals has been neglected. ... 

Huckel s rule (in its original form) stated that monocyclic polyenic molecules are aromatic only if their re-systems contain An + 2) re-el ec-trons, where n is an integer 1>. There have been many advances in LCAO-MO theory since Hiickel s original contributions (although the simplest approximation still bears his name, i.e. HMO), and today a more precise statement of the rule might read as follows. 

Historically the extended Hiickel model (EHT, Extended Huckel Theory, as it was originally called) is one of the most important schemes developed. Even in its simplest form, orbitals with energies approximating ionization potentials and of the proper nodal structure and symmetries are obtained. The famous Woodward-Hoffmann rules were founded on these simple calculations, and frontier molecular orbital arguments are easily based on EHT orbitals. 

In this chapter we discuss some of the properties of electrolyte solutions. In Sec. 12-1, the chemical potential and activity coefficient of an electrolyte are expressed in terms of the chemical potentials and activity coefficients of its constituent ions. In addition, the zeroth-order approximation to the form of the chemical potential is discussed and the solubility product rule is derived. In Sec. 12-2, deviations from ideality in strong-electrolyte solutions are discussed and the results of the Debye-Hiickel theory are presented. In Sec. 12-3, the thermodynamic treatment of weak-electrolyte solutions is given and use of strong-electrolyte and nonelectrolyte conventions is discussed. 

The basic concepts of this theory were the mutual repulsion consequent upon the interaction of two electro-chemical double layers, and the attraction by the London—Van der Waals forces. The principal facts of stability could be explained by combining these two forces. Among other things, a quantitative explanation of the rule of Schulze and Hardy has been given. For this purpose it was essential to use the unapproximated G o u y—C h a p m a n equations for the double layer. The approximation of Debye and Hiickel, however useful in the theory of electrolytes, appears to have only a very limited applicability in colloid chemistry. 

The states in the gap and the associated optical transitions for P" are shown in Figure 22.3a. The polaron energy states in the gap are SOMO and LUMO, respectively, separated by 2wo(P) [52]. Then three optical transitions Pf, P2, and P3 are possible [52-54]. In oligomers, the parity of the HOMO, SOMO, LUMO, and LUMO + 1 levels alternates they are g, u, g, and u, respectively. Therefore, the transition vanishes in the dipole approximation, and the polaron excitation is then characterized by the appearance of two correlated optical transitions below Eg. Even for long chains in the Hiickel approximation, transition P3 is extremely weak, and therefore the existence of two optical transitions upon doping or photogeneration indicates that polarons were created [51,54]. Unfortunately, polaron transitions have not been calculated for an infinite correlated chain. This is a possible disorder-induced relaxation of the optical selection rules that may cause ambiguity as to the number of optical transitions associated with polarons in real polymer films. 

The critical coagulation concentrations (c.c.c.) determined turbidimetrically for latex A-2 with NaCl, CaCl2, AlCl3(pH 3), and AlCl3(pH 7) were 180, 18.5, 0.37, and 0.15 mM, respectively (the values for NaCl and CaCl2 were independent of pH). These results do not follow the inverse sixth-power Schulze-Hardy rule derived by Verwey and Overbeek (18, 22) for the dependence of c.c.c. on valence. Instead, the log c.c.c.-log valence plot has a slope of about 3.3. This could indicate a low C potential for this system, since, in the limiting case of low potentials where the Debye-Hiickel approximation applies, the derived dependence is second-power (22) However, more extensive data are required before it can be concluded that this case deviates from the "normal sixth-power Schulze-Hardy rule. 

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