Continuum ideal

In the reaction field method, the space surrounding a dipolar molecule is divided into two regions (i) a cavity, within which electrostatic interactions are sunnned explicitly, and (ii) a surrounding medium, which is assumed to act like a smooth continuum, and is assigned a dielectric constant e. Ideally, this quantity will be... 

The preceding discussion was limited mostly to VP processes occurring by direct coupling of the quasibound state of the complex to the dissociative continuum, which is the simplest and most commonly observed decay route for the complexes. However, these systems also serve as ideal venues for studying an array of more complicated dynamical processes, including IVR, and electronic predissociation. This brief section will focus on the former, underscoring some of the inherent dynamical differences between Rg XY complexes by discussing the IVR behavior of a few systems. 

An exhaustive statistical description of living copolymers is provided in the literature [25]. There, proceeding from kinetic equations of the ideal model, the type of stochastic process which describes the probability measure on the set of macromolecules has been rigorously established. To the state Sa(x) of this process monomeric unit Ma corresponds formed at the instant r by addition of monomer Ma to the macroradical. To the statistical ensemble of macromolecules marked by the label x there corresponds a Markovian stochastic process with discrete time but with the set of transient states Sa(x) constituting continuum. Here the fundamental distinction from the Markov chain (where the number of states is discrete) is quite evident. The role of the probability transition matrix in characterizing this chain is now played by the integral operator kernel ... 

Fig. 3.20. Idealized continuum and actual fluxes measured in 50-A-wide bands of A7 stars in the Hyades open cluster with Teff = 8000 K, plotted against inverse wavelength in turn-1. Horizontal lines above the spectrum show the locations of the Johnson U, B, V pass bands and the vertical boxes show schematically the corresponding properties of the Stromgren system with central wavelengths in A. (In that system, there are actually two H/3 pass bands, one narrow and one broad, so that comparison of the two gives a measure of the strength of the line.) Some prominent spectral features are marked.

This system is ideal for illustrating many issues associated with continuum solvation modeling, and we note several points that particularly merit discussion. Table IV provides the relevant details of the calculations. 

With the acceptance of the atomic view of the world - accompanied by the necessity to explain reactions in extremely dilute gases (where the continuum theory fails) - the kinetic gas theory was developed. Using this it is possible not only to derive the ideal gas law in another manner but also to calculate many other quantities involved with the kinetics of gases - such as collision rates, mean free path lengths, monolayer formation time. 

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. 

---