Polarizability fluctuation

The polarizable fluctuating charge model in CHARMM results from the work of Patel, Brooks and co-workers [92, 214], The water model is based on the TIP4P-FQ model of Rick, Stuart and Berne [17], In the development of the force field the electronegativities and hardnesses were treated as empirical parameters and do not have any association with experimental or QM values, for example, from ionization energies and electron affinities of single atoms. 

Four different polarization directions are defined in Fig. 3.4.3. The specific components of the dielectric fluctuations or polarizability fluctuations that are responsible for each of these spectral components are ... 

The polarizability fluctuation given by Eq. (3.3.4) is now the sum over molecules in the state A with polarizability a and molecules in the state B with polarizability 2 so that... 

Biyce RA, Vincent MA, Malcolm NOJ, Hillier IH, Burton NA (1998) Cooperative effects in the stmcturing of fluoride water clusters ab initio hybrid quantum mechanical/molecular mechanical model incorporating polarizable fluctuating charge solvent. J Chem Phys 109(8) 3077-3085. doi 10.1063/1.476900... 

As described above (see section on Polarizability), fluctuating charges represent another type of model that can yield self-consistent results for the electrostatic moments of a molecule. Here the idea is to replace induction sites with some sort of movable or fluctuating charge distribution that responds to the field of the other molecules.Many variants of this approach have been reported, several of which we comment on. 

Most experimental techniques do not probe reorientational motions directly but measure the time-dependence of properties which themselves are sensitive to orientation. Thus in far infrared and Raman spectroscopy one measures dipole or polarizability fluctuations with respect to particular normal modes of vibration. Although the interpretation can be complicated, in cases where the fluctuations arise predominantly from rotational motions of localized groups correlation functions of the first and second Legendre polynomials, C t) and 2(1) respectively, can be retrieved from the data. 

Small Angle) Light Scattering 102- 10 Super molecular Structure Polarizability fluctuation correlations Orientation fluctuation correlations Spherulite properties Deformation effects... 

It is shown that the- angular dependence of the scattered light intensity can give information about correlations in density and orientation and at the same time permits conclusions about the type of orientational order present in the system under investigation. Absolute measurements, however, can add to these a quantitative estimation of the mean square of the polarizability fluctuation, which can be connected with phase separation and inhomogeneous cross-linking and the absolute value of the anisotropy which may be interpreted in terms of the kind of order and the relative parallelity of the chains on a microscale. 

For solutions, gels, or mixtures, the polarizability fluctuations arise mostly from concentration fluctuations 6C in a differential volume. By defining a number concentration fluctuation, 6c(r), we can write the scattered light intensity in the Rayleigh ratio Ra as... 

Between any two atoms or molecules, van der Waals (or dispersion) forces act because of interactions between the fluctuating electromagnetic fields resulting from their polarizabilities (see section Al. 5, and, for instance. 

In the next section we shall pursue the scattering by fluctuations in density. In the case of solutions of small molecules, it is the fluctuations in the solute concentration that plays the equivalent role, so we shall eventually replace 6p by 6c2. First, however, we must describe the polarizability of a density fluctuation and evaluate 6p itself. 

We define the concentration of fluctuation domains at any instant by the symbol N. In addition, we assume that the polarizability associated with one of these domains differs from the macroscopic average value for the substance... 

Molecule showing Charge Fluctuations and Inherent Polarizability... 

Dispersive forces are more difficult to describe. Although electric in nature, they result from charge fluctuations rather than permanent electrical charges on the molecule. Examples of purely dispersive interactions are the molecular forces that exist between saturated aliphatic hydrocarbon molecules. Saturated aliphatic hydrocarbons are not ionic, have no permanent dipoles and are not polarizable. Yet molecular forces between hydrocarbons are strong and consequently, n-heptane is not a gas, but a liquid that boils at 100°C. This is a result of the collective effect of all the dispersive interactions that hold the molecules together as a liquid. 

When an atom or molecule approaches a surface, the electrons in the particle - due to quantum fluctuations - set up a dipole, which induces an image dipole in the polarizable solid. Since this image dipole has the opposite sign and is correlated with fluctuations in the particle, the resulting force is attractive. In the following we construct a simple model to elucidate the phenomenon. 

Attractive forces arise from dipole interaction, a result of the fluctuations in the cloud of counterions. Although the mean distribution of counterions is uniform along the length of the polyion, there are fluctuations in the cloud of counterions which induce transient dipoles. When two polyions approach each other counterion fluctuations become coupled and enhance the attractive force. Since polyions have a high polarizability these attractive forces can be considerable. 

The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

Hoye JS, Stell G (1980) Dielectric theory for polar molecules with fluctuating polarizability. J Chem Phys 73(l) 461-468... 

Stern HA, Rittner F, Berne BJ, Friesner RA (2001) Combined fluctuating charge and polarizable dipole models application to a five-site water potential function. J Chem Phys 115(5) 2237-2251... 

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