Heterogeneous dielectrics

Kucharski, A.A., 2000, Resonances in heterogeneous dielectric bodies with rotational symmetry-volume integral-equation formulation, IEEE Trans. Microwave Theory Tech. 48(5) 766-770. 

Heterogeneous dielectric media models have included the developments of Jprgensen et al. [7-9] (reviewed here) and Corni and Tomasi [52,53], Generally, the number of methods for determining frequency-dependent molecular electronic properties, such as the polarizability or first- and second hyperpolarizability tensors of heterogeneously solvated molecules, is very limited. 

This contribution contains a section on the energy functional and the response theory of a solvated molecule interacting with a solvent given by either a homogeneous or a heterogeneous dielectric media model. 

Continuum Solvation Models in Chemical Physics 2.10.4 Heterogeneous Dielectric Medium Model... 

The basic outline of the heterogeneous dielectric media method is to divide the total system into two subsystems. The solvated molecule is encapsulated in a cavity C which is given by the surfaces and 2 . The cavity is surrounded by a heterogeneous environment given by two part Sm and St. The two dielectric media are in contact with the cavity through the surfaces Xm and 2,. Each of the two dielectric media is taken to be a linear, homogeneous and isotropic dielectric medium and is characterized by a scalar, optical, inertial or static dielectric constant. As an illustration, we consider two dielectric media, Sm and Sh characterized by the dielectric constants em and eh respectively, with the following spatial positions ... 

The heterogeneous dielectric model presented is represented by a hemispherical cavity, C, having the radius R. The cavity is placed such that it is on the surface of Sm and embedded in S, and the volume is given by... 

Next, we present the fundamental equations for determining the time-dependent electromagnetic properties of a molecular system interacting with a heterogeneous dielectric medium. For the heterogeneous dielectric media model we utilize the representation that is given in Equation (2.234), which makes it possible to rewrite the contributions due to the two dielectric media as... 

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

We consider the effects of the heterogeneous dielectric media on the two-photon transition matrix elements by defining... 

The two-photon transition matrix element of the molecule in the heterogeneous dielectric media is rpo1... 

Additionally, we have observed that the relative magnitude of the shift of the transition moments increased as a function of the dielectric constant of the heterogeneous dielectric media. 

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. 

The inclusion of the environment effects for non-linear optical (NLO) properties is presented within the PCM (Cammi Mennucci) and the multipolar expansion (Agren Mikkelsen) solvation models. In the first contribution the attention is focused on the connection between microscopic effective properties and macroscopic NLO susceptibilities, whereas in the latter contribution the analysis is extended to treat heterogeneous dielectric media. 

A structured environment model based on the heterogeneous dielectric media method 359... 

A structured environment response approach the multiconfigurational self-consistent field response theory for the heterogeneous dielectric media model 373... 

We consider methods for investigating the interactions between aerosol particles and molecules and how to calculate properties of molecules interacting with aerosol particles. The basic models include a heterogeneous dielectric media approach and a quantum mechanical-classical mechanical approach. Both models describe the electronic structure of the molecule at the level of correlated electronic approaches or density functional theory approximations. 

Our next step concerns the mathematical background for calculating time-dependent electromagnetic properties of quantum mechanical subsystems that are interacting with a stmctured environment. In this section we let the stmctured environment, the aerosol particle, be represented as a heterogeneous dielectric media and we consider the modifications of the last term in Eq. (66). Based on these modifications we are able to determine the changes to the response function that... 

We observe that these contributions to the response equations have the same structure as the response equations for the molecule in vacuum [83]. We note that the implementation of these modifications to the vacuum MCSCF response equations gives us the possibility of investigating linear and nonlinear molecular properties of molecular systems interacting with heterogeneous dielectric media. 

We have presented response methods that provide procedures for calculating frequency-dependent molecular properties for a molecular subsystem coupled to a stmctured environment. We have shown that the molecular subsystem is treated on a quantum mechanical level and the stmctured environment as a classical subsystem. We have presented the stmctured environment, classical subsystem, as a heterogeneous dielectric media or a molecular mechanics force field. We have demonstrated that the interactions between the quantum mechanical and classical subsystems are part of the energy functional used for optimizing the MCSCF electronic wave function. 

Niedermeier, C. and K. Schulten. (1992). Molecular-dynamics simulations in Heterogeneous Dielectric and Debye-Huckel Media Application to the Protein Bovine Pancreatic Trypsin-inhibitor. Molecular Simulation. 8 361-387. 

If the dielectric material is not homogeneous but could be regarded as an association of several phases with different dielectric characteristic, new relaxation processes could be observed. This relaxation processes called Maxwell-Wagner processes occur within heterogeneous dielectric materials. An arrangement comprising a perfect dielectric without loss (organic solvent) and a lossy dielectric (aqueous... 

To allow for heterogeneous dielectric environments a local dielectric constant that varies at each charge site can be introduced into the standard GB formalism ... 

Tanizaki, S., Feig, M. A Generalized Bom formalism for heterogeneous dielectric environments Application to the implicit modeling of biological membranes. J. Ghem. Phys. 2005,122,12470-6. 

Heterogenous dielectric systems exhibit some special properties, among which most notable is interfacial polarization caused by hindered charge movement at the interfaces. This effect makes dielectric spectroscopy (AC and DC methods), in combination with other methods of structure determination, a usefol tool in studying the following phenomena in composite materials ... 

The thermally stimulated relaxation in heterogeneous dielectrics, consisting of relaxing components and exhibiting interfacial relaxation, presents a special problem, which has been solved exactly only for bilayer systems [2]. Here, the accumulation of space charge at the interfaces may cause anomalous depolarization effects (currents of reversed polarity). The same is true for samples measured with air gap or with one-sided electrodes (this latter is frequently used for corona charged samples). 

You now have two methods for deriving the electrostatic potential from a given distribution of fixed electrical charges. First, >ou can use Coulomb s law. But this becomes unwieldy for complex constellations of charges or for systems with tw-o or more different dielectric media. Second, you can solve Poisson s equation. The second method is more general, and it can also be used for heterogeneous dielectric media (see page 401). 

Spring Model for Piezoelectricity in Heterogeneous Dielectrics with Fixed... 

Fig. 3 Non-ajfine deformation of an elastically heterogeneous dielectric with kmatrix dipole leads to a dipole-density change (negative signal so-called secondary piezoelectricity)...

Cytochrome c -f cytochrome bs Ionic-strength dependence of electron transfer between wild-type proteins modeled well when heterogeneous dielectric modeled. Trends in rates of reduction on mutation of charged residues reproduced qualitatively. One binding orientation/domain consisting of many conformations. 77 b... 

The first protein associations to be studied by Brownian dynamics simulation with detailed protein models are those of cytochrome c with its electron transfer partner cytochrome c peroxidase. Simulations of the association of cytochrome c and cytochrome b have also been performed. From these simulations, electron transfer rates are computed by coupling descriptions of the electron transfer event to diffu-sional encounter trajectories of the proteins. Hiese simulations have shown that ionic-strength dependencies can be reasonably reproduced when a realistic model is employed with a heterogeneous dielectric function, that qualitative insights into the effects of mutations can be obtained, and that... 

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