Field reaction

Whether CT is possible depends on the polarity of the solvent, as measured by the dielectric constant. There are essentially two important dielectric constants one for slow processes or the static dielectric constant (Cj) and the other for very fast processes (faster than any reorganization process), referred to as or the dielectric constant at infinite frequency. of a compound can be obtained by measuring the capacitance of a condensator where the compound is used as a dielectricum. is obtained by measuring molecular polarizability. The higher the frequency of the applied electric field, the slower are the motions in the medium to follow the variations in the field. For example, a water molecule has a certain rotation time and when the field frequency is too fast, the water molecule no longer moves with the field. When the frequencies applied correspond to UV frequencies, (for all practical purposes) is measured. One may show that = n, where n is the refractive index. 

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TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

Integral terms extending on R are reduced to iJc using Boundary Integral Elements on the boundaries of the FEM domain (especially the influence of the source field hs). Inside the FEM domain, edge elements are used to compute the reaction field. 

Onsager s reaction field model in its original fonn offers a description of major aspects of equilibrium solvation effects on reaction rates in solution that includes the basic physical ideas, but the inlierent simplifications seriously limit its practical use for quantitative predictions. It smce has been extended along several lines, some of which are briefly sunnnarized in the next section. 

Onsager s original reaction field method imposes some serious lunitations the description of the solute as a point dipole located at the centre of a cavity, the spherical fonn of the cavity and the assumption that cavity size and solute dipole moment are independent of the solvent dielectric constant. 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

In the reaction field method, the space surrounding a dipolar molecule is divided into two regions (i) a cavity, within which electrostatic interactions are sunnned explicitly, and (ii) a surrounding medium, which is assumed to act like a smooth continuum, and is assigned a dielectric constant e. Ideally, this quantity will be... 

When carried out properly, the results of the reaction field method and the Ewald sum are consistent [67]. Recently, the reaction field method has been reconnnended on grounds of elTiciency and ease of progrannning [68, 69]. The... 

Gray C G, Sainger Y S, Joslin C G, Cummings P T and Goldman S 1986 Computer simulation of dipolar fluids. Dependence of the dielectric constant on system size a comparative study of Ewald sum and reaction field approaches J. Chem. Phys. 85 1502-4... 

Gil-Villegas A, McGrother S C and Jackson G 1997 Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals Mol. Phys. 92 723-34... 

The discrepancy is not large and the last term is zero for a system without net charge. Thus we see that the use of a shifted Coulomb force is equivalent to a tin-foil reaction field and almost equivalent to a tin-foil Born condition. 

The same idea was actually exploited by Neumann in several papers on dielectric properties [52, 69, 70]. Using a tin-foil reaction field the relation between the (frequency-dependent) relative dielectric constant e(tj) and the autocorrelation function of the total dipole moment M t] becomes particularly simple ... 

In the reaction field method, a sphere is constructed around the molecule with a radius equal to the cutoff distance. The interaction with molecules that are within the sphere is calculated explicitly. To this is added the energy of interaction with the medium beyond the sphere, which is rnodelled as a homogeneous medium of dielectric constant g (Figure 6.23). The electrostatic field due to the surrounding dielectric is given by ... 

The reaction field method. The shaded arrow represents the mm of the dipoles of the other molecules within sphere. 

IS added to the short-range molecule-molecule interaction. Problems with the reaction ethod may arise from discontinuities in the energy and/or force when the number of les j rvithin the cavity of the molecule i changes. These problems can be avoided by dng a switching function for molecules that are near the reaction field boundary. 

Friedman H L 1975. Image Approximation to the Reaction Field. Molecular Physics 29 1533-1543. 

If the species is charged then an appropriate Born term must also be added. The react field model can be incorporated into quantum mechanics, where it is commonly refer to as the self-consistent reaction field (SCRF) method, by considering the reaction field to a perturbation of the Hamiltonian for an isolated molecule. The modified Hamiltoniar the system is then given by ... 

The Poisson equation has been used for both molecular mechanics and quantum mechanical descriptions of solvation. It can be solved directly using numerical differential equation methods, such as the finite element or finite difference methods, but these calculations can be CPU-intensive. A more efficient quantum mechanical formulation is referred to as a self-consistent reaction field calculation (SCRF) as described below. 

SCRF (self-consistent reaction field) method for including solvation effects in ah initio calculations... 

The electrostatic free energy of a macromolecule embedded in a membrane in the presence of a membrane potential V can be expressed as the sum of three separate terms involving the capacitance C of the system, the reaction field Orffr), and the membrane potential field p(r) [73],... 

Another variant that may mrn out to be the method of choice performs the alchemical free energy simulation with a spherical model surrounded by continuum solvent, neglecting portions of the macromolecule that lie outside the spherical region. The reaction field due to the outer continuum is easily included, because the model is spherical. Additional steps are used to change the dielectric constant of that portion of the macromolecule that lies in the outer region from its usual low value to the bulk solvent value (before the alchemical simulation) and back to its usual low value (after the alchemical simulation) the free energy for these steps can be obtained from continuum electrostatics [58]. 

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