Closest approach distance

Clebsch-Gordon coefficients, 404 Clifford algebra, 520 Closed trajectory, 328 Closest approach, distance of, 6 Code... 

A second source of error encountered with high area powders, is the annulus volume which exists between the powder surface and the closest approach distance of a gas molecule. Assuming that the closest approach of the helium atom to the powder surface is 0.5 A or 5 x 10" meter and that the specific area of the powder is lOOOm g", there will exist an annulus volume of 5 x 10" m g" or 5 x 10" cm g" This represents a density error of 5 % on materials with densities near unity. The use of gases with molecules larger than helium will exacerbate this error, again indicating the use of helium as the preferred gas. 

Detailed crystallographic structures are available for ccp, and c, and a detailed st ctural proposal exists for the noncovalent ccp/cytc complex, as shown in figure 9. In this complex, the hemes are roughly parallel with a closest approach distance of ca 16 A, (24 A Fe-Fe). A wide variety of physical evidence, including.chemical cross linking studies, supports this proposed structure. 

As shown above, for potentials with a repulsive part, a closest approach distance r = rc will exist, and this distance corresponds, according to the expression above, to an angle 9 = 9C (see Fig. 4.1.7). When the collision is over, we have t —> oo and r —> oo. It is easily verified that the same angle, 9C, is found if we had started the integration in Eq. (4.34) from this limit.5 Thus, the trajectory is symmetric around a line at 9 = 9C. A (straight) trajectory that is not deflected corresponds to 9 = it. The deflection angle is, accordingly, defined as... 

In the contact Smoluchowskii model refined by Collins and Kimball, the reaction takes place only at the closest approach distance a and the non-Markovian rate constant is a product of the contact rate constant kc and the pair density of reactants n r, t) at r = ct [2] ... 

If the ion-dipole center distance is 2.75 A and the overall packing corresponds to the closest approach distance for water (taken as 2.76 A), then the second set of dipoles are 15% further away than the first, whereas if it is 2.5 A, the second group are 31% further away. The concept of a tightly bound inner shell and a more loosely bound second shell offers a good explanation for the coordination number (c) and hydration number (n). 154,155... 

Using the same MD simulations, Pavel et al.66 designed monomers for MIPs specific for chemical warfare agents. They showed successful prediction of interaction energies, the closest approach, distances and the active site groups. 

The osmotic coefficient of [Ru(phen)3]S04 has been measured at 298 K and the closest approach distance of the ions calculated to be 11.5 A. ... 

Here c is the ion concentration in ions/cm, a is the closest approach distance between the cation and the anion, D is the mean self-diffusion coefficient of anion and cation, a is the thickness of the ionic charge cloud around the ions and... 

To simulate the habit of solution-grown crystals, the interactions of solvent molecnles at the crystal-solution interface conld be considered. In most cases, it is assnmed that the solvent affects crystal habit through preferential adsorption of solvent molecnles on specific faces and that removal of solvent molecules before the deposition of oncoming solnte molecules causes retardation of crystal growth. The extent of solvation of a crystal face could be qualitatively understood from the relative polarities of the varions crystal faces, which can be obtained from electrostatic potential maps calculated at closest approach distances (Berkovitch-Yellin 1985). 

The Born-Green-Yvon (BGY) integral equation approach was used [16] for dilute electrolyte solution, with a modification which ensures electroneutrality (BGY-i-EN). Ions were taken as hard charged spheres of the same diameter, corresponding to the closest ionic approach distance and to twice the closest approach distance to the interface (restricted pritive model, see Figure 2.5). 

Figure 2.5 Restricted primitive model closest approach distance to the interface (dashed line).

This quantity is experimentally known with high precision. The closest-approach distance o is calculated hy fitting to the expression for the equivalent conductivity the conductance data of a given salt. The fitted o is, in all studied cases, slightly larger than the sum of the anion s and the cation s crystallographic radii a - At low concentrations < 10 mol/L), theoretical results converge asymptotically to the ideal behaviour. 

Eq.(5.97) contains three imknowns the closest-approach distance tr, the mass of the solvated anion, and that of the solvated cation. 

We can see in eq.(5.97) that in the denominator of the main contribution is the specific conductance, as in the Debye s treatment. This quantity is known with a very good precision. In order to have a model consistent with this quantity, the closest-approach distance a is calculated by fitting the conductance data of a given salt by the expression for the equivalent conductivity... 

Two types of distance criterion can be used in options 1 and 3. The first of these is used when the pattern is known to contain secondary structural elements that are separated by large distances, i.e., greater than 10 A in this case, the user can specify a distance error for the distance between the mid-points of the axes fines. Alternatively, if the distances between the elements are small, i.e., less than 10 A, the distance error can be specified for the closest approach distance. The tolerances can be expressed as absolute quantities, e.g., a certain number of A, or as a proportion of the the distance concerned, e.g., 10%. In practice, the closest approach distance has been found to be more effective for retrieving secondary structures that interact with each other in some sense, e.g., neighbouring pairs of P-strands in a sheet, or helices in van der Waals contact with each other. However, the mid-point distance appears more appropriate for the case where the secondary structure elements are more remote from one another in the structure. The user can also specify whether or not the order that the secondary structure elements occur along the protein chain is important in the search for a particular query motif... 

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