Onsager model, polar molecule dielectric

In order to formulate a theory for the evaluation of vibrational intensities within the framework of continuum solvation models, it is necessary to consider that formally the radiation electric field (static, Eloc and optical E[jc) acting on the molecule in the cavity differ from the corresponding Maxwell fields in the medium, E and Em. However, the response of the molecule to the external perturbation depends on the field locally acting on it. This problem, usually referred to as the local field effect, is normally solved by resorting to the Onsager-Lorentz theory of dielectric polarization [21,44], In such an approach the macroscopic quantities are related to the microscopic electric response of... 

Within the dielectric continuum model, the electrostatic interactions between a probe and the surrounding molecules are described in terms of the interaction between the charges contained in the molecular cavity, and the electrostatic potential these changes experience, as a result of the polarization of the environment (the so-called reaction field). A simple expression is obtained for the case of an electric dipole, /a0, homogeneously distributed within a spherical cavity of radius a embedded in an anisotropic medium [10-12], by generalizing the Onsager model [13]. For the dipole parallel (perpendicular) to the director, the reaction field is parallel (perpendicular) to the dipole, and can be calculated as [10] ... 

In view of the approximations inherent in the derivation of the reaction field theory, it is not surprising that some instances are known in which a non-linear relationship exists between the solvent shift and dielectric constant in polar solvents. As pointed out by Buckingham, the reaction field model is only valid for a solute that reacts in no way with the solvent or with other solute molecules but simply presents a continuum of certain dielectric properties. Protons are normally on the surface of the molecule and are therefore exposed to direct contact with the surrounding molecules, so that the Onsager model is a poor approximation of the actual reaction field acting on a molecule. 

The chemical shifts of polar molecules are frequently found to be solvent dependent. Becconsall and Hampson have studied the solvent effects on the shifts of methyl iodide and acetonitrile. The results obtained from dilution studies in various solvents may be explained as arising from a reaction field around the solute molecules. The spherical cavity model due to Onsager was used to describe this effect, and this model was completely consistent with the experimental data when a modified value for the dielectric constant, s, of the particular solvent was used. 

FIGURE 2.2 Different computational treatments of solute-solvent interactions, (a) Solvent treated as an ensemble of discrete molecules. In this case, solvent molecules (in tube representation) can be treated at MM level, whereas the solute (in ball-and-stick representation) is treated at QM level, (h) Treatment of the solvent as a dielectric continuum. The solute is modeled as a sphere of radius ao and dipole moment /a according to the Onsager model, (c) Same as (b) but the solute is in an ellipsoidal cavity defined by axes a, b, and c. (d) Treatment of the solute solvent interactions according to the polarization continuum model (PCM). 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

On the basis of an Onsager cavity (23) model of dielectrics applied to a polar solute with an intrinsic dipole movement /xr° in its rth electronic state, Mazurenko gives an equation for the orientational free energy of the solute molecule in a pure polar solvent environment, which can be identified as equivalent to u/jlpe chem, thus 2... 

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). 

To address the problem of finite system size, the EFP method has also been combined with continuum models in order to model the effects of the neglected bulk solvent [125], The Onsager equation was used to obtain the dipole polarization of the solute molecule (modeled quantum mechanically) and explicit water molecules (modeled by effective fragment potentials) due to the dielectric continuum. Thus the energy becomes... 

For reactions in solution, one may implement explicit or implicit hydration schemes. In explicit hydration, water molecules are included in the system. These additional water molecules have a significant effect on the reaction coordinates of a reaction (e g., Felipe et al. 2001). Implicit hydration schemes, or dielectric continuum solvation models (see Cramer and Truhlar 1994), refer to one of several available methods. One may choose between an Onsager-type model (Wong et al. 1991), a Tomasi-type model (Miertus et al. 1981 Cances et al. 1997), a static isodensity surface polarized continuum model or a self consistent isodensity polarized continuum model (see Frisch et al. 1998). 

During the last 40 years it has been possible to witness an important evolution on the way the environment around a solute molecule is described. The reaction field approach, the effect a continuous dielectric medium has on the charge distribution of a molecule that polarizes back the dielectric and generates a reaction potential, is a standard scheme to consider the solvent effects on many molecular properties. Most modem continuum models obtain through a self-consistent cycle the wave function of the molecule affected by the reaction potential thus the self-consistent reaction field acronym (SCRF). Solvatochromic effects have been more or less successfully explained using from Onsager s to more refined models like Nancy SCRF [44], Tomasi s polarizable continuum model (PCM) [45], Cramer and Tmhlar s SMx models [46]. 

In relation to general interactions, the solvent is assumed to be a dielectric continuum. The earliest models for this type of interaction were developed by Kirkwood and Onsager, and were later modified with corrections for the effect of electrostatic saturation. " The intrinsic difficulty of these models in accurately determining the dimensions of the cybotactic region (viz. the solvent region where solvent molecules are directly per-tmbed by the presence of solute molecule) that surrounds each solute molecule in the solvent bulk, have usually raised a need for empirical approximations to the determination of a parameter encompassing solvent polarity and polarizability. An alternative approach to... 

A dipole in a cavity in a polarizable solvent will polarize the medium and create an electric field at its own position. The simplest model is that of a dipole ]1 at the center of a spherical cavity of radius a embedded in a dielectric. We already encountered its results in Section 9.5. The way Nee and Zwanzig [16] came to their results is as follows Outside the cavity there is a dielectric with dielectric constant c (o)), and inside the cavity we assume only electronic polarization C or vacuum (fj = 1). The frequency dependence of the outside dielectric constant derives from the fact that the molecules in the solvent can rotate to change the polarization. This rotation is diffusional, so the dipoles need time to adjust to a new situation. This does not have an effect on the solution of the boundary value problem. At the boundary, the usual boundary conditions apply the transverse component of the electric field is continuous, as is the normal component of the displacement field. Using these boundary conditions, it is possible to find the fields inside and outside the cavity. Solving this problem gives the electric and displacement fields inside and outside the cavity. The important field is the field created by the outside polarization inside the cavity, the so-called Onsager reaction field [23] E ... 

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