Hiickel parameters

Table 7.1 Debye-Hiickel parameters for the activity coefficient, volume, enthalpy, and...

A simple qualitative model of the three-electron hemibond in [X.. X], based on the Hiickel approximation, has been proposed by Gill and Radom [122]. This qualitative model predicts that the strength of the hemibond should vary in proportion to the Hiickel parameter a, which can be replaced by the HOMO energy in X because a good correlation is found between Eho-Mo(X) and De(X-X ). This model readily rationahzes the marked substituent effect on the strength of the hemibond. In particular, electron-withdrawing substituents are found to have a strengthening effect. 

Here = 2.303T/3, where A is the Debye-Hiickel parameter. 

Helgeson, H. C. and D. H. Kirkham, 1974, Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures, II. Debye-Hiickel parameters for activity coefficients and relative partial molal properties. American Journal of Science 274, 1199-1261. 

A is a Debye-Hiickel parameter (cf. Appendix II) and I is the ionic strength. Pitzer found that binary interaction parameter Xdepends on ionic strength and may conveniently be expressed as ... 

Plotting ixbase VS. pH gives a sigmoidal curve, whose inflection point reflects the apparent base-pAi, which may be corrected for ionic strength, I, using Equation 6.11 in order to obtain the thermodynamic pATa value in the respective solvent composition. Parameters A and B are Debye-Hiickel parameters, which are functions of temperature (T) and dielectric constant (e) of the solvent medium. For the buffers used, z = 1 for all ions ao expresses the distance of closest approach of the ions, that is, the sum of their effective radii in solution (solvated radii). Examples of the plots are shown in Figure 6.12. 

Under mild conditions nitration and acetylation of hexahelicene give the 5-nitro-and 5-acetyl substitution product as the main product in about 50% yield. In both cases another monosubstitution product is formed, which was identified tentatively by NMR as the corresponding 8-substituted hexahelicene. From the relative rates of detritiation (krel) or the partial rate factors (f) given in Table 27, it seems more probable, however, that the 7-isomers are formed as the side product, as the positional reactivity order of detritiation is C(5) >C(7) >C(8) >C(1) >C-(4) >C(6) >C(2) > C-(3). The preferred reactivity at C(5), found in electrophilic substitutions, is predicted by all the simple Hiickel parameters, whereas the next two positions are correctly predicted by Nr and Lr. Judging from Nr-, Fr- and Lr-values the C-(l) position does not experience much steric hindrance in the H-exchange. Relative to some other positions (C(4), C(6)) its reactivity is higher than expected. The Mulliken overlap population predicts, however, the highest reactivity for C(l) and leaves room for the supposition that this position is considerably masked. 

The thickness of the diffuse-charge region is given by K 1,i.e., the Debye-Hiickel parameter (Section 6.6.4). Thus, if the fluid velocity is v at the distance k" then the velocity gradient is given by... 

Dependence of Debye-Hiickel parameter on temperature and type of... 

The Hiickel parameters for the neutral forms were chosen as a0 = ac + /3, /8C 0 = 1.40/SC C for the protonated forms, aQ = ac + 3/3, /3C 0 = O.8O0C C. These values were in reasonable agreement with those found from the subsequent Pariser-Parr-Pople treatment, taking the benzenoid values ac = —5.95 and /3C0 = —4.815 eV. 

Table 2.2 Some Hiickel parameters for heteroatoms, after Streitwieser15...

When Hiickel parameters are not available or reliable (e.g. for silicon or sulfur compounds), SCF calculations are used instead. In these cases, only pertinent MOs are given. Energies are then given in eV. Do not forget that FO is an approximate theory, to be used only for preliminary studies. Spending too much time calculating the frontier orbitals would be futile. Avoid sophisticated methods and use only simple ones (Hiickel, MNDO, AMI, PM3, STO-3G or 3-21G). 

Hiickel parameters for sulfur are not very reliable, so AMI calculations have been used for this exercise. All values in eV. 

Debye-Hiickel parameter, estimated here as k = y/ c/3 A. 1 (assuming the dielectric constant of the solvent medium inside the double layer is 80). valence of charges (= 1) electronic charge... 

Debye-Huckel parameter — The Debye-Hiickel parameter k of an electrolyte solution is calculated as... 

Debye-Hiickel parameter k (the Debye length), which has the dimension of length, serves as a measure for the thickness of the electrical double layer. Figure 1.5 plots the... 

Consider a charged plate with arbitrary surface potential ij/o in a symmetrical electrolyte solution of valence z and Debye-Hiickel parameter k. We take an x-axis perpendicular to the plate surface with its origin at the plate surface so that the region x > 0 corresponds to the solution phase while the region x < 0 to the plate interior. Equation (1.37) (or Eq. (1.38)) for the potential distribution ij/(x) around the surface in the region far from the surface, that is, at large kx, takes the form... 

The asymptotic expression for the potential of a spherical particle of radius a in a symmetrical electrolyte solution of valence z and Debye-Hiickel parameter k at a large distance r from the center of the sphere may be expressed as... 

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