Intramolecular distance distribution function

Figure 2 A simulation of the autocorrelation function, AC(x), of the donor fluorescence calculated for different diffusion coefficients of one molecular end relative to the other end. The calculations were performed for a model oligopeptide whose end-to-end distance distribution function is given in Fig. 5, Ref. 15 (curve 8). R was assumed to be 25A. The time scale is given in units of 10 sec and each curve is marked by the value assumed for the intramolecular diffusion coefficients in units of 10 1( cm /sec. AC() is given in arbitrary units. (Reprinted with permission from Ref. 17).

In this equation g(r) is the equilibrium radial distribution function for a pair of reactants (14), g(r)4irr2dr is the probability that the centers of the pair of reactants are separated by a distance between r and r + dr, and (r) is the (first-order) rate constant for electron transfer at the separation distance r. Intramolecular electron transfer reactions involving "floppy" bridging groups can, of course, also occur over a range of separation distances in this case a different normalizing factor is used. 

Fig.9a-c. Scaled distribution function for the center-to-end distances of stars of f=3,10 and 50 arms (a is the repulsive distance range of the intramolecular potential) T=4 /kg corresponds to a good solvent T=3e/kg corresponds to a theta solvent T=2e/kg (lower temperatures correspond to the curves on the left). Solid curves Simulation data dashed lines Gaussian functions. Reprinted with permission from [131]. Copyright (1994) American Chemical Society... 

Figure 12-1. Radial distribution function for H-H separations, (a) Intramolecular distance, (b) Intermolecular distance...

Furthermore, the scattering profile can be written with the help of a distribution function p r) of intramolecular atomic distances ... 

The electron diffraction structure analysis can accordingly be characterized as if it were the determination of the frequencies and the damping of the components of a sum of sine functions. As the molecular intensity is Fourier-transformed, another important but more descriptive function is attained, which bears, somewhat unfortunately, the name of radial distribution function, and which is indeed connected with the probability distribution function of the intramolecular inter-nuclear distances. It is a Gaussian-like distribution that... 

The site-site intramolecular and intermolecular pair correlation functions play the same role in ISM fluids as the radial distribution function does in atomic fluids. The site-site intramolecular distribution function, coay(r), is the probability that two sites a and y are a distance r apart (normalized so that f dreoay(T) = 1). The site-site intermolecular pair distribution function, gay(r) is defined via... 

For simplicity, the polymer chain is assumed to have a Gaussian distribution of intramolecular intersite distances with a distribution function given by ... 

Fig. 19 Widths of the distribution functions of the largest intramolecular distances, Oe = e )-(e) )/ e), of a linear polymer and star polymers with up to 50 arms as a function of the Weis-senberg number. From [142]...

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