Dielectric constant, distance dependent

These ideas based on Bjerrum s picture of ion-pair formation have received considerable experimental support. Thus, in Fig. 3.46, the association constant is seen to inaease markedly with deaease of dielectric constant. The dependence ofion-pair formation on the distance of closest approach is seen in Fig. 3.47. 

Distance-dependent dielectric constant In computing the Coulomb interaction between two point charges, the dielectric constant is set to the value of the dielectric medium. In an attempt to implicitly simulate water, the dielectric constant should be 80 at long distances, but 1 at close range. Replacing the dielectric constant by r makes the dielectric effect distance-dependent at negligible computational cost. 

The Van der Waals force between the glass substrate and the sUica sphere is given by the superposition of the forces between (i) the glass substrate and the sUica sphere acting across an adsorbed layer of 8CB, (ii) the forces between the adsorbed layers and the prenematic 8CB, and (iii) the glass and prenematic 8CB acting across the adsorbed layer [8]. These different interactions are accounted for via the Hamaker constant Ah. A precise determination of the Hamaker constant is difficult, because it depends on the optical properties of the medium between the two surfaces, i.e. on the temperature and distance dependent anisotropic dielectric constants. To estimate Ah we ignored the anisotropy of the dielectric constant [8]. Dependent on the dielectric constant, the refractive index and the substrate, the Hamaker constant varies between 0.5 x 10-21 J < Ah < 10 X 10-21 J. 

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. 

Use a constant dielectric of 1.0 with TIP3P water molecules in a periodic box. Because of the parameterization of TIP3P molecules, using a distance-dependent dielectric or a value other than 1.0 gives unnatural results. 

A distance-dependent dielectric constant is commonly used to mimic the effect of solvent in molecular mechanics calculations, in the absence of explicit water molecules. 

You can use two types of dielectric functions a constant and a distance-dependent dielectric. Use constant dielectric for in vacuo systems and for molecular systems with explicit solvent molecules. 

Also use constant dielectric for MM+ and OPLS calculations. Use the distance-dependent dielectric for AMBER and BlO-t to mimic the screening effects of solvation when no explicit solvent molecules are present. The scale factor for the dielectric permittivity, 8, can vary from 1 to 80. HyperChem sets 8 to 1.5 for MM-t. Use 1.0 for AMBER and OPLS, and 1.0-2.5 for BlO-t. 

The above potential describes the monopole-monopole interactions of atomic charges Q and Qj a distance Ry apart. Normally these charge interactions are computed only for nonbonded atoms and once again the interactions might be treated differently from the more normal nonbonded interactions (1-5 relationship or more). The dielectric constant 8 used in the calculation is sometimes scaled or made distance-dependent, as described in the next section. 

As for the dielectric constant, when explicit solvent molecules are included in the calculations, a value of 1, as in vacuum, should be used because the solvent molecules themselves will perform the charge screening. The omission of explicit solvent molecules can be partially accounted for by the use of an / -dependent dielectric, where the dielectric constant increases as the distance between the atoms, increases (e.g., at a separation of 1 A the dielectric constant equals 1 at a 3 A separation the dielectric equals 3 and so on). Alternatives include sigmoidal dielectrics [80] however, their use has not been widespread. In any case, it is important that the dielectric constant used for a computation correspond to that for which the force field being used was designed use of alternative dielectric constants will lead to improper weighting of the different electrostatic interactions, which may lead to significant errors in the computations. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

Places the Langevin dipoles at grid points. I The (1 +r0) term is a distance dependent I dielectric constant for the non iterative LD I procedure ( See references 4). 

What is the relationship between a constant dielectric and a distance dependant dielectric for pseudo-vacuum simulations ... 

Following the concepts of H. Helmholtz (1853), the EDL has a rigid structnre, and all excess charges on the solntion side are packed against the interface. Thus, the EDL is likened to a capacitor with plates separated by a distance 5, which is that of the closest approach of an ion s center to the surface. The EDL capacitance depends on 5 and on the value of the dielectric constant s for the medium between the plates. Adopting a value of 5 of 10 to 20 nm and a value of s = 4.5 (the water molecules in the layer between the plates are oriented, and the value of e is much lower than that in the bulk solution), we obtain C = 20 to 40 jjE/cm, which corresponds to the values observed. However, this model has a defect, in that the values of capacitance calculated depend neither on concentration nor on potential, which is at variance with experience (the model disregards thermal motion of the ions). 

A subject not treated here is the use of distance-dependent effective dielectric constants as a way to take account of the structure in the dielectric medium when a solute is present. This subject has recently been reviewed [120], In the approaches covered in the present chapter, deviations of the effective dielectric constant from the bulk value may be included in terms of physical effects in the first solvation shell, as discussed in Section 2.2. 

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