Electric polarization reaction field model

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 Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

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] ... 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

A polar molecule in solution can polarize the surrounding medium giving rise to an electric field, the reaction field (i ) at the solute. In a definitive paper, Buckingham" has developed a theory of the effect of the reaction field on chemical shifts based on the Onsager model. ... 

Equation (11.7) can be used to eliminate the exterior derivative of (p from Eq. (11.6). Then, given some initial approximation for rp (perhaps just tpf, which is known once the solute s wave function has been computed), one could compute the surface charge, and thus the reaction-field potential, without the need to perform any calculations outside of the solute cavity. For a QM solute, this procedure must then be iterated to self-consistency. The original PCM of Miertus, Scrocco, and Tomasi [60, 61] used precisely this approach this model is now known as D-PCM. It is less desirable than more modern PC Ms, owing to the need to compute the normal electric field, which may be subject to increased numerical noise relative to later formulations that involve only electrostatic potentials [77]. Perhaps more significantly, the formulation of this model has conflated the apparent and actual surface charge distributions, and corresponds to a neglect of volume polarization [13]. 

To integrate our continuum model with standard DFT algorithms, Wei and co-workers introduce the reaction field potential RF = — 0 with 4>o being the solution of the Poisson equation in homogeneous media [132]. The reaction field potential is the electric potential induced by the polarized solvent and its incorporation leads to the following effective energy function ... 

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)...

SRF (solvent reaction field) is the acronym introduced to denote the model proposed by Onsager in order to describe electric polarization effects produced by a solvent, represented as a continuum dielectric, on the charge distribution of a solute. 

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 ... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

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