Distance-dependent dielectric approximation

Distance-Dependent Dielectric Approximation Dependence on the Interim Dielectric Constant... 

For AMBER, BIO +, or OPLS (energy calculation of biomacromolecules) Choose Constant (for systems in a gas phase or in an explicit solvent) or Distance dependent (to approximate solvent effects in the absence of an explicit solvent) and set Scale factor for Dielectric permittivity ( 1.0 with the default of 1.0 being applicable to most systems). Select either Switched or Shifted for Cutoffs and set Electrostatic (the range is 0 to 1 use 0.5 for... 

The simplest continuum solvent model simply adju.sts the dielectric constant to equal the medium dielectric. An approximation widely used in MD simulations is known as the distance-dependent dielectric constant. In this approach, the dielectric con.stant is set equal to the distance r,/. as shown in Equation 28-38. The electrostatic energy is now proportional to Mr rather than l/r. When this was first proposed, the idea was to help reduce CPU lime. The rationalization is that the chtirges on two nonbonded atoms in a macromolecule are separated hy the protein, which should reduce the interaction terms. Thus, the interaction energy should fall off faster than l/r because the charges arc masked. 

Again, one can use the harmonic or quasiharmonic approximation to estimate the entropy term, although a more realistic implicit solvent model can be used here. Most of the previous MM/PBSA calculations employed more approximate distance-dependent dielectric models. 

If all of the atoms and charges in the system of interest are explicitly represented and atomic polarization is included, the use of a dielectric constant other than unity would be inappropriate. A variety of models has been used, however, to approximate the dielectric behavior of a macromolecular system where the solvent was not explicitly included. Dielectric constants for the protein interior between 2 and 10 have been employed, as has a distance-dependent dielectric response equal to the distance in angstroms.78 Also, simple forms of the Kirkwood-Westheimer-Tanford model79 have been used to approximate the effect of the aqueous solvent. An approach that may improve our understanding in this area employs linear response theory to evaluate the spatially dependent dielectric response.80 In any such model it is necessary to consider the frequency dependence of the dielectric constant relative to the time scale of the dynamic process under consideration. 

The simple distance-dependent dielectric has no physical basis and so it is not generally recommended, except when no alternative is possible. More sophisticated distance-dependent functions can also be employed. Many of these have an approximately sigmoidal shape in which the relative permittivity is low at short distances and then rises towards the bulk value at long distances. One example of such a function is [Smith and Pettit 1994] ... 

An alternative to the simple screened Coulomb interaction in protein modeling is the distance-dependent dielectric function [51]. In this approximation the effective electrostatic interaction between two partial charges q at distance r is written as... 

The dispersion interaction between an atom and a metal surface was first calculated by Lennard-Jones in 1932, who considered the metal as a perfect conductor for static and time-dependent fields, using a point dipole for the molecule [44], Although these results overestimate the dispersion energy, the correct l/d3 dependence was recovered (d is the metal-molecule distance). Later studies [45 17] extended the work of Lennard-Jones to dielectrics with a frequency-dependent dielectric constant [48] (real metals may be approximated in this way) and took into account electromagnetic retardation effects. Limiting ourselves to small molecule-metal distances, the dispersion interaction of a molecule characterized by a frequency-dependent isotropic polarizability a embedded in a dielectric medium with permittivity esol (note that no cavity is built around the molecule) reads ... 

This model is appropriate for a homogeneous system with only one dielectric constant and no ionic strength. By making e a distance-dependent function e(r), the model can be adapted to account for thef variation in dielectric to approximately represent a systerfi with low dielectric solutes immersed in high dielectric solvent. However, to properly account for dielectric discontinuities and ionic strength effects, other models, such as a continuum solvent Poisson-Boltzmann (PB) model must be used to compute electrostatic forces. 

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. 

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