Cavity shape

If reliable quantum mechanical calcnlations of reactant and transition state stnictures in vacnnm are feasible, treating electrostatic solvent effects on the basis of SRCF-PCM rising cavity shapes derived from methods... 

A yet more realistic cavity shape is that obtained from the van der Waals radii of the atoms of the solute. This is the approach taken in the polarisable continuum method (PCM) [Miertus et al. 1981], which has been implemented in a variety of ab initio and semi-empirical quantu/rt mechanical programs. Due to the non-analytical nature of the cavity shapes in the PCM approach, it is necessary to calculate numerically. The cavity surface is divided... 

J. D. Honeycutt, D. Thirumalai. Influence of optimal cavity shapes on the size of polymer molecules in random media. J Chem Phys 92 6851-6858, 1990. 

The Isodensity PCM (IPCM) model defines the cavity as an isodensity surface of the molecule. This isodensity is determined by an iterative process in which an SCF cycle is performed and converged using the current isodensity cavity. The resultant wavefunction is then used to compute an updated isodensity surface, and the cycle is repeated until the cavity shape no longer changes upon completion of the SCF. 

J. B. Foresman, T. A. Keith, K. B. Wiberg, J. Snoonian and M. J. Frisch, Solvent Effects. 5. The Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on Ab Initio Reaction Field Calculations, J. Phys. Chem., submitted (1996). [Discusses the IPCM SCRF model.]... 

Over the years, many workers have addressed the problem of choice of cavity and the reaction field. Tomasi s polarized continuum model (PCM) defines the cavity as a series of interlocking spheres. The isodensity PCM (IPCM) defines the cavity as an isodensity surface of the molecule. This isodensity surface is determined iteratively. The self-consistent isodensity polarized continuum model (SQ-PCM) gives a further refinement in that it allows for a full coupling between the cavity shape and the electron density. 

Based on the gas adsorption behavior, Ko-zawa and Yamashita proposed a hypothesis [20, 21] that the cross—section of the fine pores of EMD is a cavity shape as shown in Fig. 16. The cross-section of the pore by computer calculation is a circle (Fig. 16A). Nobody knows the real shape of the cross-section as yet. Kozawa s belief in the cavity shape (Fig. 16B) is based on the results of experiments involving the oxygen adsorbed and desorbed from the pore walls [20]. 

Many injection molded products will influence the final product s performance, dimensions, and other characteristics. The mold includes the cavity shape, gating, parting line, vents, undercuts, ribs, hinges, and so on (Table 3-17). The mold designer must take all these factors into account to eliminate problems. At times, to provide the best design... 

As reviewed in other chapters, different plastics have different melt and flow characteristics. What is used in a mold design for a specific material may thus require a completely different type of mold for another material. These two materials might, for instance, be of the same plastic but use different proportions of additives and reinforcements. This situation is no different than that of other materials like steel, ceramics, and aluminum. Each material will require its own cavity shapes and possibly have its own runner system. 

Cavity Shapes Steric Fit of Host-Guest Compounds.103... 

Reaction Field the determination of the cavity shape, dielectric constant(s), the method to calculate the reaction field potential, presence of counterions (for finite... 

Various components of the interactions are calculated using different formalisms. In fact, the shape and size of the cavity are defined differently in various versions of the continuum models. It is generally accepted that the cavity shape should reproduce that of the molecule. The simplest cavity is spherical or ellipsoidal. Computations are simpler and faster when simple molecular shapes are used. In Bom model, with simplest spherical reaction held, the free energy of difference between vacuum and a medium with a dielectric constant is given as [16]... 

For certain ideal cavity shapes, the relevant PB equations have particularly simple analytic solutions. While such ideal cavities are not typically to be expected for arbitrary solute molecules, consideration of some examples is instructive in illustrating how more sophisticated modeling may be undertaken by generalization therefrom. 

So, while derivations of SCRF theory using ideal cavities are very useful for conceptual purposes, they are insufficiently accurate for all but the most crude analyses. Modem applications of continuum models almost invariably use arbitrary cavity shapes, typically constmeted from overlapping atomic spheres, and we turn to examples of these models next. 

A third possibility that has received extensive study in the SCRF regime is one that has seen less use at the classical level, at least within the context of general cavities, and that is representation of the reaction field by a multipole expansion. Rinaldi and Rivail (1973) presented this methodology in what is arguably the first paper to have clearly defined the SCRF procedure. While the original work focused on ideal cavities, this group later extended the method to cavities of arbitrary shape. In formalism, Eq. (11.17) is used for any choice of cavity shape, but the reaction field factors f must be evaluated numerically when the cavity is not a sphere or ellipsoid (Dillet et al. 1993). Analytic derivatives for this approach have been derived and implemented (Rinaldi et al. 2004). 

Many systems are described in which changing the cavity shape by allosteric effects allows the cation binding ability and the selectivity of the receptor to be modified and controlled. For instance a photo-responsive cis/trans isomerizable azobenzene unit has been introduced in macrocyclic structures in order to change the receptors cavity shape, leading to a photo-control of ion extraction. 

Cui and Weiss reported the photo-Fries rearrangements of 2-naphthyl myristate and 2-naphthyl acetate (Fig. 35) in unstretched and stretched low-density polyethylene films [116]. It was argued that the radical pair generated by irradiation is held in a cavity shaped like the starting ester and whose walls relax more slowly than the radicals recombine. The preferred solution product is too different in shape from the starting ester to be formed. 

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