Root-mean-square bond-length

Figure 2.9 Root-mean-square bond-length fluctuations 5 as a function of the total energy. The full and open symbols correspond to trajectories initialized from the and C2v, structures of the isomers I and II, III, respectively, of Li9 drawn with symmetry labels and energy sequence in eV [39]...

In previous work on Van der Waals clusters, it was established that the behaviour of a parameter characterizing the relative root mean square bond length fluctuations,... 

Fig. 4. Averaged relative root mean square bond length fluctuations for the Ar-Ar and Ar-SF distances for certain SF -(Ax) clusters. The shaded band identifies the 8 values chosen to define the Lindemann criterion for melting.

Fig. 1.8 (a) Log-log plot of the reduced mean square gyration radius, / g(0))/(.Rg(O)). vs. rescaled chain lenrth N - l)((/>f ) where f is the root mean-square bond length, and the theoretical value for the exponent i/(i/ = 0.59) is used. All data refer to a bead-spring model with stiff repulsive Lennard-Jones interaction, as described in Section 1.2.1 (Eq. [1.7]). (b) Same as (a) but for the bond fluctuation model. In both (a) and (b) the straight line indicates the asymptotic slope of the crossover scaling function, resulting from eq. (1.15). (From Gerroff et al.)... 

Root-mean-square end-to-end distance, which effectively takes account of the average distance between the first and the last segment in the macromolecule, and is always less that the so-called contour length of the polymer. This latter is the actual distance from the beginning to the end of the macromolecule travelling along the covalent bonds of the molecule s backbone. Radius of gyration, which is the root-mean-square distance of the ele-... 

Figure 3. Partition coefficient of freely jointed chains between the bulk solution and a cylindrical pore. The chains have different numbers of mass-points (n) and different bond lengths, and are characterized by the root-mean-square radius of gyration measured in units of the pore radius. See text for details.

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

The recently determined X-ray crystal structure of cyclopentacorannulene 25 provides an additional opportunity to test the performance of theory in predicting the minimum energy structures of nonplanar conjugated systems. Table 4 presents the C-C bond lengths in the crystal and a comparison with ab initio values calculated at HF/3-21G and HF/6-3IG levels. The agreement between experimental and theoretical bond lengths is very satisfactory with root mean square devia-... 

Bond Lengths and Their Root Mean Square Fluctuations for the Decaniobate Ion in Figure 4 as Predicted From Molecular Dynamics Calculations... 

Fig. 36 Definition of parameters a used in Tables 1 and 2. Each a value is a root mean square deviation calculated for the set of C-C bond lengths shown in bold. Low a values (<1.5 pm) are indicative of bond length averaging. The expected value for an alternating pattern of pure single and double bonds is ca. 6 pm [287]...

Macromolecular conformations describe the positions of the atoms that occur due to rotation about the single bonds in the main chain.2 Polymer chains in solution, melt, or amorphous state exist in what is termed a random coil. The chains may take up a number of different conformations, varying with time. Figure 15.4 shows one possible conformation for a single polymer chain. In order to describe the chain, polymer scientists utilize the root mean square end-to-end distance ((r2)m), which is the average over many conformations. This end-to-end distance is a function of the bond lengths, the number of bonds, and a characteristic ratio, C, for the specific polymer. 

Crystals of the seven-methionine variant were obtained using 2 M phosphate solutions, pH 6.7, and were found to be isomorphous with wild-type lysozyme (Weaver and Matthews, 1987). A data set to 1.9A resolution, 92% complete was measured. The structure was refined to a crystallographic residual of 15.2% with bond lengths and angles within O.ISA and 3.0° of ideal values and found to be similar to wild-type. The root-mean-square discrepancy of the main-chain atoms within the C-terminal domain was 0.20A. The Xi and Xi values of the mutant side-chains were similar to those in wild-type except at position 153 where Xi changed by 92° and avoided a steric clash (Table III). Thus, each of the substituted methionines essentially traces the path of... 

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