Homogeneous polarizable medium

It has beeome a quite common procedure to use relatively small models of enzyme active sites and apply quantum ehenueal methods to study their reaction mechatusms. According to this approach, the rest of the enzyme is usually treated using a homogeneous polarizable medium with some assumed dieleetrie eon-... 

To account for the polarization effects, the enzyme surrounding to a first approximation can he considered as a homogenous polarizable medium, which can he modeled using some dielectric cavity techniques. In addition, to model the steric effects that the enzyme surrounding imposes on the active site, it has been shown to be very useful to simply fix atoms at the edge of the active site model. The combination of continuum solvation and the coordinate-locking scheme represents a quite simple but yet powerful way to account for the parts of the enzyme that are not included in the model. 

The continuum model of solvation has evolved from these beginnings. The solvent is treated as a continuous polarizable medium, usually assumed to be homogeneous and isotropic, with a uniform dielectric constant e.11-16 The solute molecule creates and occupies a cavity within this medium. The free energy of solvation is usually considered to be composed of three primary components ... 

In more recent work, Johnston and co-workers (17,18,20,27,32) showed quantitatively that the local fluid density about the solute is greater than the bulk density. In these papers, results were presented for CQ2, C2H4, CF3H, and CF3C1. Local densities were recovered by comparison of the observed spectral shift (or position) to that expected for a homogeneous polarizable dielectric medium. Clustering manifests itself in deviation from the expected linear McRae continuum model (17,18,20,27,32,56,57). These data were subsequently interpreted using an expression derived from Kirkwood-Buff solution theory (20). Detailed theoretical... 

The OWB model describes the solute as a classical polarizable point dipole located in a spherical or ellipsoidal cavity in an isotropic and homogeneous dielectric medium representing the solvent. In the presence of a macroscopic Maxwell field E, the solute experiences an internal (or local) field E given by a superposition of a cavity field Ec and a reaction field ER. In terms of Fourier components E -n, Ec,n, ER,n of the fields we have... 

Light Scattering. A perfectly homogeneous medium will not scatter and that scattering results from fluctuations from uniformity. The fluctuation in polarizability is defined by... 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

Models to describe frequency shifts have mostly been based on continuum solvation models (see Rao et al. [13] for a brief review). The most important steps were made in the studies of West and Edwards [14], Bauer and Magat [15], Kirkwood [16], Buckingham [17,18], Pullin [19] and Linder [20], all based on the Onsager model [21], which describes the solvated solute as a polarizable point dipole in a spherical cavity immersed in a continuum, infinite, homogeneous and isotropic dielectric medium. In particular, in the study of Bauer and Magat [15] the solvent-induced shift in frequency Av is given as ... 

The valence bond method with polarizable continuum model (VBPCM) method (55) includes solute—solvent interactions in the VB calculations. It uses the same continuum solvation model as the standard PCM model implemented in current ab initio quantum chemistry packages, where the solvent is represented as a homogeneous medium, characterized by a dielectric constant, and is polarizable by the charge distribution of the solute. The interaction between the solute charges and the polarized electric field of the solvent is taken into account through an interaction potential that is embedded in the... 

Figure 3. Diagram showing the principle of dielectrophoresis (DEP), which only occurs in a non-homogeneous electric field, (a) Particle more polarizable than the medium positive dielectrophoresis (pDEP) (b) particle less polarizable than the medium negative dielectrophoresis (nDEP).

Although not rigorously correct, the approximation of water as a structureless homogeneous continuum dielectric medium is used by many simulative methodologies. Both Brownian dynamics (see the section entitled Implicit Solvation Brownian Dynamics) and electrodiffusive approaches (see the section on Flux-Based Simulation) include the water in the electrostatic picture as a continuous dielectric background with polarizability appropriately tuned... 

Now consider an absorbing molecule dissolved in the linear medium we have been discussing. If the molecular polarizability is different from the polarizability of the medium, the local electric field inside the molecule (Pfoc) will differ from the field in the medium (E j). The ratio of the two fields ( Eioc flE J), or local-field correction factor (/), depends on the shape and polarizability of the molecule and the refractive index of the medium. One model for this effect is an empty spherical cavity embedded in a homogeneous medium with dielectric constant e. For high-frequency fields (e = r ), the electric field in such a cavity is given by... 

Another class of polarizability formulations is based not on the integral equation in Eq. (2.5) but on the notion of a set of point dipoles. Draine and Goodman [100] found an optimal 0 ((W) ) correction to the CM polarizability in the sense that an infinite lattice of point dipoles with such polarizability would lead to the same propagation of a plane-wave as in a homogeneous medium with a given refractive index. This polarizability was called the lattice dispersion relation (LDR) ... 

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