Root-mean-square method

Tentative heat of formation was defined by MOPAC. Calculation was started from initially defaulted value of inter-atomic distance in each sample Value of gradient by root-mean-square method Microwave spectroscopy cited in [13]... 

Step 3 The distribution of MCST is analyzed to obtain the value of crpp which is the maximum value among different cases and different bumups. The correlation uncertainty cc is also evaluated. The total uncertainty is evaluated by the root mean square method ... 

The results obtained by lineal regression (LR) and by pareial least square regression (PLS) methods have been eompared to quantify tlie 0-H signal in anhydrite samples. The PLS quality is eharaeterized by a eoirelation eoeffieient of 0.9942 (eross-validation) using four faetors and a root mean square eiTor of ealibration (RMSEC) of 0.058. Tlie eoirelation eoeffieient of LR metliod obtained was 0.9753. 

In order to examine whether this sequence gave a fold similar to the template, the corresponding peptide was synthesized and its structure experimentally determined by NMR methods. The result is shown in Figure 17.15 and compared to the design target whose main chain conformation is identical to that of the Zif 268 template. The folds are remarkably similar even though there are some differences in the loop region between the two p strands. The core of the molecule, which comprises seven hydrophobic side chains, is well-ordered whereas the termini are disordered. The root mean square deviation of the main chain atoms are 2.0 A for residues 3 to 26 and 1.0 A for residues 8 to 26. 

An alternative method of variance scaling is to scale each variable to a uniform variance that is not equal to unity. Instead we scale each data point by the root mean squared variance of all the variables in the data set This is, perhaps, the most commonly employed type of variance scaling because it is a bit simpler and faster to compute. A data set scaled in this way will have a total variance equal to the number of variables in the data set divided by the number of data points minus one. To use this method of variance scaling, we compute a scale factor, sr, over all of the variables in the data matrix, 8g,... 

Some alternative method had to be devised to quantify the TCDD measurements. The problem was solved with the observation, illustrated in Figure 9, that the response to TCDD is linear over a wide concentration range as long as the size and nature of the sample matrix remain the same. Thus, it is possible to divide a sample into two equal portions, run one, then add an appropriate known amount of TCDD to the other, run it, and by simply noting the increase in area caused by the added TCDD to calculate the amount of TCDD present in the first portion. Figure 9 illustrates the reproducibility of the system. Each point was obtained from four or five independent analyses with an error (root mean square) of 5-10%, as indicated by the error flags, which is acceptable for the present purposes. 

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Comparisons between optimized and X-ray structures were once again made by calculating root-mean-square (RMS) deviations. When comparing all heavy atoms in the protein, the total RMS deviation is approximately 1.7 A, irrespective of method for the model system or the ONIOM implementation (mechanical, ONIOM-ME, or electronic embedding, ONIOM-EE). The largest deviations occur for residues in the vicinity of the second monomer. Therefore, adding the second monomer to the model should improve the calculated geometries. 

The root-mean-square error in the kinetic fit was an acceptable 2.83% and was minimized by the SIMPLEX method discussed elsewhere (8). An... 

To compute the results shown in Tables 34-3 and 34-4, the precision of each set of replicates for each sample, method, and location are individually calculated using the root mean square deviation equation as shown (Equations 34-1 and 34-2) in standard symbolic and MathCad notation, respectively. Thus the standard deviation of each set of sample replicates yields an estimate of the precision for each sample, for each method, and for each location. The precision is calculated where each ytj is an individual replicate (/ ) measurement for the ith sample yt is the average of the replicate measurements for the ith sample, for each method, at each location and N is the number of replicates for each sample, method, and location. The results of these computations for these data... 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

It is known that ab initio methods are not accurate in reproducing or predicting molecular dipole moments. For example, a typical basis set minimization with no additional keywords was carried out, and the results show that the computed magnitude of the dipole moment is not particularly accurate when compared with experimental values. For alcohols, MP2 has a root mean squared deviation of 0.146 Debye, while HF had a deviation of 0.0734 Debye when measured against the experimental values. 

The differences between ab initio and molecular mechanics generated dipole moments were discussed. The MM3(2000) force field is better able to reproduce experimental dipole moments for a set of forty-four molecules with a root mean squared deviation (rmsd) of 0.145 Debye compared with Hartree-Fock (rmsd 0.236 Debye), M0ller-Plesset 2 (rmsd 0.263 Debye) or MM3(96) force field (rmsd 0.164 Debye). The orientation of the dipole moment shows that all methods give comparable angle measurements with only small differences for the most part. This consistency within methods is important information and encouraging since the direction of the dipole moment cannot be measured experimentally. 

Apart from fluorescence, several other methods may be used to obtain time-resolved information. In the case of proteins containing an iron atom, Mossbauer spectroscopy allows the determination, in the iron binding site, of not only root-mean-square shifts of atoms but also the times over which such shifts occur. Detailed investigations of myoglobin have yielded relaxation times on the order of 10 8 Proton NMR spectroscopy can be used to... 

Publication Date March 13, 2007 doi 10.1021/bk-2007-0958.ch009 Table 5. Mean Unsigned Errors (kcal/mol), Root-Mean-Square Errors, and Times for hybrid DFT and DPT Methods and AMI at QCISD/MG3 Geometries ... 

---