Homogeneous dielectric medium

If one is interested in changes of the solute molecule, or if the structure of the surrounding solvent can be neglected, it may be sufficient to regard the solvent as a homogeneous dielectric medium, as was done in the older continuum theories, and to perform a quantum mechanical calculation on the molecule with a modified Hamiltonian which accounts for the influence of the solvent as has been done by Hylton et al. 18 5>. Similarly Yamabe et al. 186> substituted dipole-moment operators for the solvent in their perturbational treatment of solvent effects on the activation energy in the NH3 + HF reaction. 

In studying systems in an electrostatic field, we must consider two systems because of the dependence of the field on matter within the field. One system is a parallel-plate condenser in empty space. The area of the plates is designated by A, and the distance between the plates by /. The other is an identical condenser immersed in an isotropic, homogenous, dielectric medium. The conductivity of the medium is zero, so no free charges are present in the medium. Edge effects are neglected and rational units are used throughout. 

The propagation of light in a nonlinear medium is governed by the wave equation, which was derived from Maxwell s equations for an arbitrary homogeneous dielectric medium,... 

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... 

Homogeneous Dielectric Medium Response for Two-photon Absorption... 

The required modifications of the response equations follow closely those that occur for the homogeneous dielectric medium and heterogeneous dielectric media methods [10— 14,82-84,91], The different methods differ only by the representation of the effective operators. Furthermore, the mathematical structure of the WQM/CM-induced modifications to the response equations is similar to those for response equations for the molecule in vacuum [90], For the actual implementation of the contributions to the response equations due to the interactions between the molecular subsystem and the structured environment, it is easily observed that one needs to define, formulate and calculate the effective QM/CM operators and to insert these into an existing response program. 

For a homogeneous dielectric medium, in the absence of interface effects (see Sect. 3.2), the experimental quantities sx and e" are equal to the bulk properties e and e", and the experimental loss tangent becomes... 

The effect of the solvent can be modelled at various levels of sophistication. The simplest is to consider the molecule studied as surrounded by an infinite, homogeneous dielectric medium (the solvent) and interacting only via its total dipole moment. To avoid infinities in the numerical calculations, this also involves invoking a void (cavity) aroxmd the molecule studied, so that the distance between a point in the solvent and a point belonging to the... 

In the classical reaction-field model, the solute molecule is considered embedded in a cavity inside a homogeneous dielectric medium. From the Onsager theory (Onsager, 1936) the electronic reaction field at the center of the solute molecule is given by... 

For a homogeneous solid dielectric sphere (a particle with a radius of R) in a homogeneous dielectric medium, charges will accumulate at the interface between the particle and the medium. This results in an effective or induced dipole moment across the particle. The potential of the effective dipole moment Pg can be considered as an increment to the potential distribution of the applied field, which is given by ... 

The first step in Eq. 3.32 is the result of substituting Eq. 3.26 into Eq.3. 30 the second step is an integration by parts the third step makes use of Eqs. 3.27 and 3.29a and invokes the assumption that the mobile liquid phase is a homogeneous dielectric medium the fourth step is another integration by parts the fifth step is the result of Eqs. 3.27 and 3.28 along with the assumption that the mobile liquid phase has a uniform viscosity coefficient the sixth step involves the identity... 

The topic of this chapter is the solution of a simple and well-defined model problem, namely, the molecular electrostatics problem for one or more molecules immersed in a homogeneous dielectric medium characterized by a dielectric constant, e. The interface between the atomistic region (the solute) and the continuum solvent is defined by a molecule-shaped cavity such as the ones depicted in Figs. 11.1(a) and 11.1(b). In practice, this cavity is often constructed from atom-centered spheres, although more... 

When applying EA-VTST to enzyme reactions, another kind of system/ environment separation is made. Here the reactive system is considered to be the substrate and perhaps part of the enzyme or coenzyme (and perhaps including one or two closely coupled water molecules), and the environment is the rest of the substrate-coenzyme-enzyme complex plus the (rest of the) surrounding water. In what follows we will sometimes call the reactive system the primary subsystem and the environment as the secondary subsystem. For the treatment of reactions in liquids that was presented earlier, the solvent was replaced by a homogeneous dielectric medium, which greatly simplifies the calculation. For enzyme-catalyzed reactions, we treat the environment explicitly at the atomic level of detail. 

Here, A represents integral over the closed surface. If the closed surface is distorted such that the volume swept in distorting the surface is in a homogeneous dielectric medium, then owing to the divergenceless property, the integrals /, I, h, and /c remain invariant. 

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