Dielectric screening model

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin-orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius Rs which is embedded into an infinite medium with dielectric constant e. This leads to a reduction AFk of the Slater parameters (Newman, 1973) ... 

Experimental results for the Slater parameter reductions of Nd3+, Pr34-, and U3+ (Troster et al 1995) in LaCl under pressure up to 8 GPa in comparison with results from the dielectric screening model. All values in cm 1 3... 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

A. Schiiurmann, G. COSMO a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc., Perkins Trans. 1993, 799-805. (c) Klamt, A. Jonas, V. Burger, T. Lohrenz, J. C. W. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A 1998, 102, 5074—5085. (d) For a more comprehensive treatment of solvation models, see Cramer, C. J. Truhlar, D. G. Implicit solvation models equilibria, structure, spectra, and dynamics. Chem. Rev. 1999, 99, 2161— 2200. 

Some models carry the surface tension approach to extreme, and attempt to include even the electrostatic contributions in the surface tensions. These pure SASA models are obviously limited in their ability to account for such phenomenon as dielectric screening, but they have the virtue of being very easy to compute. Thus, they can be used to augment molecular mechanics calculations on very large molecules with a qualitative accounting for solvation. 

In addition to these external electric or magnetic field as a perturbation parameter, solvents can be another option. Solvents having different dielectric constants would mimic different field strengths. In the recent past, several solvent models have been used to understand the reactivity of chemical species [55,56]. The well-acclaimed review article on solvent effects can be exploited in this regard [57]. Different solvent models such as conductor-like screening model (COSMO), polarizable continuum model (PCM), effective fragment potential (EFP) model with mostly water as a solvent have been used in the above studies. 

Conductor-like screening model (COSMO) is one of variants of PCM method [29]. In this method, the cavity is considered to be embedded in a conductor with an infinite dielectric constant [29]. An extension to this method, called COSMO-RS... 

Here, r denotes the position vector of the charges qt with respect to the center of the sphere, and r, the distance from the center. By applying the dielectric scaling function for dipoles (Eq. (2.3)), which—as we have seen in Fig. 2.1—is also a good approximation for most other multipole orders, it was immediately clear that the idea of using a scaled conductor instead of the EDBC leads to a considerable simplification of the mathematics of dielectric continuum solvation models, with very small loss of accuracy. It may also help the finding of closed analytic solutions where at present only multipole expansions are available, as in the case of the spherical cavity. Thus the Conductor-like Screening Model (COSMO) was bom. 

There are currently three different approaches for carrying out ASC-PCM calculations [1,3]. In the original method, called dielectric D-PCM [18], the magnitude of the point charges is determined on the basis of the dielectric constant of the solvent. The second approach is C-PCM by Cossi and Barone [24], in which the surrounding medium is modelled as a conductor instead of a dielectric. The third, IEF-PCM method (Integral Equation Formalism) by Cances et al the most recently developed [16], uses a molecular-shaped cavity to define the boundary between solute and dielectric solvent. We have to mention also the COSMO method (COnductorlike Screening MOdel), a modification of the C-PCM method by Klamt and coworkers [26-28], In the latter part of the review we will restrict our discussion to the methods that actually are used to model solute-solvent interactions in NMR spectroscopy. 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

The conductor-like screening model (COSMO) approach replaces the dielectric medium with a conducting medium (basically a medium that effectively has an infinite dielectric constant). Interlocking spheres are used to generate the cavity. The conductor-like screening has been implemented as a PCM version, called CPCM.128,129... 

The elementary rate constant for proton activation is weakly dependent on the micropore size as long as steric constraints do not affect the transition state. Because of the zwitterionic nature of the transition state, dielectric screening by the oxygen atoms of the micropore tends to decrease the cluster-calculated transition state energies to 10 to 30% of the activation energies. Steric constraints on the transition state may substantially increase the cluster-computed activation energies by similar amounts. These steric constraints can be computed from periodical DFT calculations or from transition-state model structures using Monte Carlo adsorbate-zeolite pore interaction calculations. 

On the other hand, layer dependent screening contributions can be estimated for metal-dielectric interfaces applying a dielectric continuum model according to Aliis(d) A/ 7i(co) = -e2 /(1 (me(f dj [4, 8], where d is the distance from the mirror plane, AEB(d) and AEB(oo) is referred to the distance d and the infinitely thick film, respectively. Here, we assume e 3 and 0.34 nm for the molecule-molecule-distance. The distance of the first layer to the mirror plane of the metal di could be different on a microscopic scale. We apply the van der Waals radius of carbon in organic compounds (analogously to [8]) di = 0.17 nm and for comparison a distinct larger value (0.23 nm). The results are summarized in Table 1 ... 

Table 1. Layer dependent screening contributions estimated by dielectric continuum model. For the distance of the first layer to the mirror plane of the metal 1.7 A (left) and 2.3 A are chosen.

---