Reaction cavity shape

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. 

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]... 

In the second class of systems the reaction is such that it involves little or no change of the molecular geometry in the vicinity of the reacting sites, nor of the external shape of the crystal. The concept of the reaction cavity is useful in this context (184). This cavity is the space in the crystal containing the reactive molecule(s), and its surface defines the area of contact between this molecule and its immediate surroundings. Only if the shape of this cavity is little altered as reaction proceeds will the activation energy for the process be reasonably small and the rate of reaction nonzero. 

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). 

A. Reaction cavity defined by boundary, size, and shape 91... 

B. Reaction cavities with very stiff walls and preformed shapes... 

This description is elaborated below with an idealized model shown in Figure 17. Imagine a molecule tightly enclosed within a cube (model 10). Under such conditions, its translational mobility is restricted in all three dimensions. The extent of restrictions experienced by the molecule will decrease as the walls of the enclosure are removed one at a time, eventually reaching a situation where there is no restriction to motion in any direction (i.e., the gas phase model 1). However, other cases can be conceived for a reaction cavity which do not enforce spatial restrictions upon the shape changes suffered by a guest molecule as it proceeds to products. These correspond to various situations in isotropic solutions with low viscosities. We term all models in Figure 17 except the first as reaction cavities even... 

Can we extend the reaction cavity concept, which emphasizes the shape... 

A. Reaction Cavity Defined by Boundary, Size, and Shape... 

It is very important to note that the exact size and shape of a reaction cavity (initial, effective, and final) that control the excited state behavior of guest reactants will depend on the particular reaction as well as on the guest and intermediate s) themselves. Whether the information regarding the space explored (effective reaction cavity) by the excited molecule will be registered in the distribution or stereochemistry of the products will depend on the nature of the mechanism involved in the product formation. In some cases, explorations over a larger space by excited state species and their intermediates may not be germane to the distribution and types of products formed. In certain cases, especially those that involve the probability of encounters, all of the space excited molecules and their intermediates explore before they yield final products may be important. In cases for which the distribution of specific product types is being probed, only the site in which... 

Consider reactant molecules or intermediates being caged within a reaction cavity with limited free volume. A preference might be envisioned in the reactions these reactant molecules or intermediates undergo, if the competing reactions require different amounts of free volume for shape changes that take... 

The influence of these various effects may be manifested in measurable parameters of the reaction like the overall quantum yields (On) and the photoproduct ratios for fragmentation to cyclization (E/C) and for trans to cis cyclobutanol formation (t/c) as shown in Scheme 41. The values of these quantities and their variations as the media are changed can provide comparative information concerning the relative importance of solvent anisotropy on Norrish II reactions, also. Specifically, they reveal characteristics of the activity of the walls and the size, shape, and rigidity of the reaction cavities occupied by electronically excited ketones and their BR intermediates. 

Another factor which should influence only minimally Norrish II reactions in fluid isotropic media is the size and shape of the photoproducts relative to each other and to the reactant ketone. However, in media that provide reaction cavities with stiff walls, this factor may be of paramount importance. 

As shown in Figure 42 for the Norrish II reactions of a simple ketone, 2-nonanone, not only do the shapes of the products differ from those of the reactant, but so do their molecular volumes [265]. Interestingly, the volume of the fragmentation products, 1-hexene and 2-hydroxypropene (which ketonizes to acetone), are closer in volume to 2-nonanone than is either of the cyclization products. They are also capable of occupying more efficiently the shape allocated by a stiff solvent matrix to a molecule of 2-nonanone in its extended conformation the cross-sectional diameter of either of the cyclobutanols is much larger than that of extended 2-nonanone or the fragmentation products when spaced end-on. Both of these considerations should favor fragmentation processes if isomorphous substitution for the precursor ketone in the reaction cavity is an important requirement for efficient conversion to photoproducts. 

The solid phases of 81 are also well ordered macroscopically and their higher E/C ratios require that the hydroxy-1,4-biradical be in rather inflexible reaction cages with little excess free volume. Hydrogen bonding to neighboring ketone molecules may be partially responsible for the high photoproduct ratios found upon collapse of the biradicals in the solid phases, but the size, shape, and flexibility of the reaction cavity are clearly the more important factors. The highest E/C ratios observed in the second solid phase of 81a... 

What is as noteworthy as the excess of 88a from the solid-state irradiation of 86a is the presence of any 87a at all. Its formation requires either that one of the more distant -/-hydrogen atoms be abstracted also or that the reaction cavity suffer some dramatic changes in shape and size while the hydroxy-1,4-biradical is present. Based upon the lattice properties of 86a, the latter seems the more probable scenario without the movement of groups on adjacent... 

Rather phase-insensitive Norrish II photoproduct ratios are reported from irradiation of p-chloroacetophenones with a-cyclobutyl, a-cyclopentyl, a-cycloheptyl, a-cyclooctyl, and a-norbonyl groups [282], In each case, the E/C and cyclobutanol photoproduct ratios are nearly the same in neat crystals as measured in benzene or acetonitrile solutions. On this basis, we conclude that the reaction cavity plays a passive role in directing the shape changes of these hydroxy-1,4-biradicals. As long as the initial ketone conformation within the cavity permits -/-hydrogen abstraction (and these ketones may be able to explore many conformations even within their triplet excited state lifetime), the cavity free volume and flexibility allow intramolecular constraints to mandate product yields. 

B. Reaction Cavities with Very Stiff Walls and Preformed Shapes and Sizes Silica Gel and Zeolites... 

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