Charge distance-dependent

By using an effective, distance-dependent dielectric constant, the ability of bulk water to reduce electrostatic interactions can be mimicked without the presence of explicit solvent molecules. One disadvantage of aU vacuum simulations, corrected for shielding effects or not, is the fact that they cannot account for the ability of water molecules to form hydrogen bonds with charged and polar surface residues of a protein. As a result, adjacent polar side chains interact with each other and not with the solvent, thus introducing additional errors. 

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

The above poten tial describes the m onopole-m on opole interactions of atomic charges c. and q. a distance R.. apart. Normally th CSC eh arge in teractiori s arc corn pti ted on ly for non bon ded atom s and once again the I 4 in tcraetioti s m igti t be treated differen ily from the more normal nonborided interactions (I 5 relationship or rn ore). Th c dielectric con Stan t t used in th c calculation is sometimes scaled or made distance-dependent, as described in the next section. ... 

The presence of the q B term with its implied distance dependency means that the charges depend upon the molecular geometry. Thus, should the conformation of a molecule change the atomic charges will also change. Just three parameters are required for each atom in the system (the electronegativity, the idempotential and the covalent radius). 

Li) he so-called distance-dependent dielectric models. The simplest implementation of a dis-i.iiice-dependent dielectric is to make the relative permittivity proportional to the distance. Tine interaction energy between two charges qi and qj then becomes ... 

Another important factor to determine the charge separation efficiency is the distance between and the mutual orientation of the donor and the acceptor in the geminate ion-pair state. The rate of charge recombination depends on whether... 

Studies of base-base CT in B-form DNA duplexes versus A-form DNA R-NA hybrids also confirmed our fundamental tenet that the pathway of efficient charge transfer will be the well-stacked pathway. In A-form duplexes considerable intra- and interstrand stacking exists. Not surprisingly then, in DNA RNA hybrids we observed a similar distance dependence for the yields of intra- and interstrand CT [105]. So, the distinction between intra- and interstrand CT observed in B-DNA duplexes truly correlates with differences in base stacking. 

Fig. 5 Schematic representation of long distance radical cation migration in DNA. In AQ-DNA(3), irradiation of the anthraquinone group linked at the 5 -terminus leads to reaction at GG steps that are 10, 28, 46 and 55 base pairs from the charge injection site. The solid arrows indicate approximately the amount of reaction observed at each GG step. The plot shows the natural log of the normalized amount of reaction as a function of distance from the AQ. The results appear to give a linear distance dependence...

Notice that, with the current data, one cannot draw immediate parallels with the spectrochemical series (nor with the nephelauxetic series). At any rate, these comparisons are not trivial depending on the symmetry, CF parameters of orders 4 and 6 are more or less important compared with those of order 2. Thus, the ratio charge/distance cannot generally quantify the strength of the LF exerted by a kind of ligand, or at least not in a way that is totally independent of the geometry of the complex. 

The effective CF models, intended to include covalence effects via effective charges and shielding parameters [46] (superposition model [47], effective charge model [48], simple overlap model [49, 50]), keep the radial (M-L distance) dependence of the CF parameters as in the simple (point charge) electrostatic model. Dedicated studies have shown, however, that the radial dependence of these parameters deviates strongly from the latter for the whole series of lanthanide ions [51, 52]. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

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