Fractionation methods charge

The ground-state electronic diagrams of some thiazolo dyes have been calculated with the use of theoretical model of fractional core charge model applied to PPP method (659). 

As in the case of the free bases, the substitution of a nuclear hydrogen atom by a methyl group induces a bathochromic shift that decreases in the order of the position substituted 4->5->2- Ferre et al. (187) have proposed a theoretical model based on the PPP (tt) method using the fractional core charge approximation that reproduces quite correctly this Order of decreasing perturbation. 

With the use of the DV-Xa molecular orbital method, electronic structure calculations have been performed to investigate the impurity effect on material properties. Firstly, calculations were done for F atoms substituted for 0 (oxygen) atoms in copper oxide superconductors. It was found that the population of the atomic orbitals of F atoms is small in HOMO (highest occupied molecular orbital) and a small fraction of charge carriers enters the impurity sites. The F impurities are therefore expected to be effective for pinning magnetic flux lines in Cu oxide superconductors. 

Because the asphalt system is not a true solution, it can be fractionated into saturates, aromatics, resins, and asphaltenes by the solvent fraction method, SARA method, or TLC method. The polarity of these four fractions is increased in the order of saturates, aromatics, resins, asphaltenes. In crude oil, asphaltene micelles are present as discrete or dispersed particles in the oily phase. Although the asphaltenes themselves are insoluble in gas-oil (saturates and aromatics), they can exist as fine or coarse dispersions, depending on the resin content. The resins are part of the oily medium but have a polarity higher than gas-oil. This property enables the molecules to be easily adsorbed onto the asphaltene micelles and to act as a peptizing agent of the colloid stabilizer by charge neutralization. 

In collaboration with experimental groups, we have recently studied some chlorinated-benzene crystals, 1,2,4,5-tetrachlorobenzene (TCB) [59] and 1,4-dichlorobenzene (DCB) [60], as well as solid tetracyanoethene (TCNE) [58]. In these studies we have used empirical atom-atom potentials, of exp-6 type [see Eq. (6)], which we have supplemented with the Coulomb interactions between fractional atomic charges. Lattice dynamics calculations have been performed by the harmonic method, with inclusion of intramolecular vibrations [70], see Eqs. (17) to (24). The normal modes of the free molecules have been calculated from empirical Valence Force Fields, using the standard CF-matrix method [101, 102]. The results of these calculations are used here to illustrate some phenomena occurring in more complex molecular crystals. These phenomena are well known the numerical results show their quantitative importance, in some specific systems. 

It is shown how the eigenvalues and eigenfunctions of the hydrogen molecule can be obtained with a relatively simple method. FVom these solutions of the two-centre problem we construct the eigenfunctions of the molecule in first order and obtain the energy of the molecule by a perturbation calculation. If we introduce fractional nuclear charges for the outer electron, then the perturbation becomes very small in the excited states. Therefore the complicated perturbational calculations do not have to be performed very strictly it is sufficient to take some main terms of the eigenfunctions into account. 

Eq. (22-29) is suggested. The formulas (22-30) are aU normalized for 1 mol of monomer units. Another method is to use the novel method of Muthukumar [59] which allows also the adjustment of the fraction of charged monomers—see formulae in the strong PE section (43 7). 

A simple way to form necklaces in good solvents with the introduction of counterions was presented by Jeon and Dobrynin [136]. Such a counterion induced necklace formation was found to be possible by Jeon if the fraction of charged monomers in the simulation was reduced to 0.3 in good, theta and poor solvents [136]. The results of this method are summarized in Fig. 8, which is significantly different from Fig. 7a due to a different necklace forming mechanism and use of different PE. 

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