Distribution of charge

The unequal distribution of charge produced when elements of different electronegativities combine causes a polarity of the covalent bond joining them and, unless this polarity is balanced by an equal and opposite polarity, the molecule will be a dipole and have a dipole moment (for example, a hydrogen halide). Carbon tetrachloride is one of a relatively few examples in which a strong polarity does not result in a molecular dipole. It has a tetrahedral configuration... 

The quadrupole is the next electric moment. A molecule has a non-zero electric quadrupole moment when there is a non-spherically symmetrical distribution of charge. A quadrupole can be considered to arise from four charges that sum to zero which are arranged so that they do not lead to a net dipole. Three such arrangements are shown in Figure 2.8. Whereas the dipole moment has components in the x, y and z directions, the quadrupole has nine components from all pairwise combinations of x and y and is represented by a 3 x 3 matrix as follows ... 

The three moments higher than the quadrupole are the octopole, hexapole and decapoli. Methane is an example of a molecule whose lowest non-zero multipole moment is the octopole. The entire set of electric moments is required to completely and exactly describe the distribution of charge in a molecule. However, the series expansion is often truncated after the dipole or quadrupole as these are often the most significant. 

For a distribution of charges (one not restricted to lie along one of the Cartesian axes), th dipole moment is given by ... 

The charge density is simply the distribution of charge throughout the system and has 1 units of Cm . The Poisson equation is thus a second-order differential equation (V the usual abbreviation for (d /dr ) + (f /dx/) + (d /dz )). For a set of point charges in constant dielectric the Poisson equation reduces to Coulomb s law. However, if the dielectr... 

This involves a more uniform distribution of charge because of the identical substituents and thus lacks the stabilizing effect of the polar resonance form. The activation energy for this mode of addition is greater than that for alternation, at least when X and Y are sufficiently different. 

Several calculations of the electronic structure of isoindoles have Ijeen published, and the distribution of charge density around the isoindole nucleus calculated by these methods is summarized in X able I. A common prediction of the calculations, which are based on tlie LCAO-MO method or the frontier electron concept, is the relatively high electron density to bo found at position 1, and the expectation, thei efore, i.s that electrophilic substitution on carbon... 

In general, it is expected that AHS will differ from AHL, since the difference in volume between the liquid and solid alloy and the existence of a lattice periodicity will produce slight changes in the distribution of charge between the components, a small change in... 

Note that for the determination of molecular weight, the charge-state distribution is not of great importance as it does not affect the m/z value of the ion involved and thus the calculated molecular weight. If the conformational state of the biopolymer is of interest, however, the distribution of charged states is a fundamental consideration and any parameter likely to change this distribution must be carefully controlled. 

Nonhomogenous distribution of charge inside fully condensed DNA/polycation particles has been discussed earlier, in Section lll.F.l. Since it takes only 0.9 equivalents of positive charges to condense DNA in aqueous environment, there should be an excess of positive charge on the surface of completely condensed DNA/polycation particles. This fact opens the opportunity to form multilayered structures based on alternations of polyelectrolytes of opposite charge. Details of this approach of DNA/polyion self-assembly are discussed in Section III.F.9. 

The relation between the spatial distribution of the electrostatic potential /(jc) and the spatial distribution of charge density Qy(x) can be stated, generally, in terms of Poisson s differential equation. 

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