Cavity fields model

Fig. 3.6 The effective electric field acting on a molecule in a polarizable medium (shaded rectangles) is Eiq fErtj d where is the field in the medium and / is the local-field correction factor, hi the cavity-field model (A) Ei c is the field that would be present if the molecule were replaced by an empty cavity (Ecav), in the Lorentz model (B) Ei c is the sum of E av and the reaction field (Ereaa) resulting from polarization of the medium by induced dipoles within the molecule (P)...

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

The simplest reaction field model is a spherical cavity, where only the net charge and dipole moment of the molecule are taken into account, and cavity/dispersion effects are neglected. For a net charge in a cavity of radius a, the difference in energy between vacuum and a medium with a dielectric constant of e is given by the Bom model. ... 

One-dimensional model Onsanger cavity field Onsanger equation Orbital polarization Ordered phase Ordered state... 

Exercise 2.1. Evaluate the ground-state potential surface for the CH3OCH3—> CH3 + CH30- reaction using the reaction field model, with a cavity radius a = R/2 + 1.5. 

In addition to packed catalyst bed, a fluidized bed irradiated by single and multi-mode microwave field, respectively, was also modeled by Roussy et al. [120]. It was proved that the equality of solid and gas temperatures could be accepted in the stationary state and during cooling in a single-mode system. The single-mode cavity eliminates the influence of particle movements on the electric field distribution. When the bed was irradiated in the multimode cavity, the model has failed. Never-... 

A related methodology that makes use of the calculated surface charges at the cavity surface to estimate the interaction with the solvent has been described in Ref. [54] in addition, the reaction field model can be extended to include the effects of higher order multipoles [55], In the present implementation, only dipole effects are considered. 

Results for improved by introducing the surrounding 4 water molecules into the cavity, but still only leads to 45% of the gas-to-liquid shift for the 170 nucleus (97). Likewise, this method fails to account for all of the gas-to-liquid shift of 19F in fluoromethanes (99) and of 77Se in H2Se (100). Clearly, medium effects can not be treated accurately by using a reaction field model. The major problem with the above two approaches is that only the electric polarization effects are included in the model. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

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... 

The IEF methodology, combined with an effective mean-field modelling of short-range orienting interactions, can also provide good predictions of the permittivity of nematics and its temperature dependence. Indeed, a realistic account of the cavity shape allows us to calculate the permittivity purely on the basis of the structure of the constituting... 

This is a generalization of the Onsager reaction field model for a point dipole inside a spherical cavity. For charged solutes, one should also include an ionic Born term, derived by... 

In the reaction field model (Onsager, 1936), a solute molecule is considered as a polarizable point dipole located in a spherical or ellipsoidal cavity in the solvent. The solvent itself is considered as an isotropic and homogeneous dielectric continuum. The local field E at the location of the solute molecule is represented by (78) as a superposition of a cavity field E and a reaction field (Boettcher, 1973). 

Onsager derived an improved formula by adopting a better model for the calculation of the local field at a molecule. His model consists of a spherical cavity which is excised in the dielectric material and which is just large enough to accommodate one molecule. The molecular dipole is supposed to be a point dipole fj, at the centre of the sphere, radius a. Onsager then said that the local field operating on the dipole at the centre of the cavity could be resolved into two components, a cavity field G and a reaction field R ... 

M. J. Frisch, in Abstracts of Papers, 205th National Meeting of the American Chemical Society, Denver, CO, American Chemical Society, Washington, DC, 1993. Paper COMP 3 A Reaction Field Model Which Includes an Ab Initio Definition of the Reaction Cavity and a Comparison of All Current Reaction Field Models. 

The simplest reaction field model is a spherical cavity, where only the net charge and... 

Canonical momentum operator, 248 Car and Parrinello (CP) method, 388 CASMP2, CASPT2 methods, 132 CASVB method, 202 Cavity, in reaction field models, 393 CBS-4, CBS-q, CBS-Q and CBS-APNO methods, 167... 

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... 

Another model is the reaction field model [83], Here, the solute is placed inside a cavity surrounded by a medium with a dielectric constant that is appropriate for the desired solvent and the effects on the energy of the... 

This model may describe, for example, a spin -particle confined to move in a one-dimensional harmonic potential whose spin is subject to a harmonic magnetic field or a two-level atomic system interacting with a single mode of a cavity field. It is of interest here as example of an interaction between a discrete- and a continuous-variable system. 

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... 

In addition, the molecules properties are changed due to the interaction with the surrounding medium. Several computational schemes have been proposed to address these effects. Tliey are essentially based on the extension of the Onsager reaction field cavity model and give effective hyperpolarizabilities, i.e. molecular hyperpolarizabilities induced by the external fields that include the modifications due to the surrounding molecules as well as local (cavity) field effects [40 2]. These condensed-phase effects have, however, not yet been included in the SFG hyperpolarizability calculations, which are therefore strictly gas-phase calculations. 

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