Distance calculation

Interatomic distances calculated from the detailed analysis of rotational fine structure of the UV spectrum of pyrazine are in close agreement with those observed in (7) and (8), with the calculated bond lengths for C—C of 1.395, C—N 1.341 and C—H 1.085 A (60DIS(20)4291). Thermochemical data have provided a figure of 75 kJ moP for the delocalization energy of the pyrazine ring (B-67MI21400). 

Because the objective of the calculation is now to calculate the distance at which a specific pressure occurs, rather than to calculate pressure at a given distance, calculations must follow a different order. 

Fig. 8. A1—E bond distances [calculated, experimental and Zreov(AlE)] of EtaAl—ETms3 adducts...

Interproton distances of 0-ceIIobiose (see Ref. 49) error 0.01 A. Interproton distances of 1,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.01 A. Interproton distances of -cellobiose octaacetate (see Ref. 49) error 0.05 A. Interproton distances of 2,3,4-tri-0-acetyl-l,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.05 A. Error calculations based on the errors of the measured quantities in Eqs. 18 and 21. Interproton distances calculated from the relaxation parameters of the methylene protons. 

Figure 9.21 Specific activity and Pd-Pd bond distance calculated from XRD data against the concentration of Fe in Pd-Fe/C elecfrocatalysts treated at 500 °C. (Reproduced with permission from Shao et al. [2006c].)...

Calculate the positive duration of the blast at the endpoint distances. Using the combustion-scaled distance, calculated in Step 4 above, Equation 7.5b and Figure 7.2b (Reference 5), the blast durations can be calculated. Entering Figure 7.2b at the combustion-scaled distance for each endpoint overpressure, the dimensionless positive phase duration (t+) may be read from Curve 10. 

It is at this point that the bulk of the CPU time is utilized, since the number of distance calculations increases with the square of the number of chain segments. To reduce this time, an abbreviated check is made to determine if a given atomic cartesian coordinate is within a specified distance (e.g., 12 A) of the newly appended atom. Thus, the vast majority of existing segments are disposed of with one, or at most three, subtraction calculations rather than full calculations of the exact distance. Terms in the second moment from atoms outside this cubic volume are not included in the summation. This is valid because of the rapidity at which the magnitude of a term decreases with increasing separation. 

The estimate of the distance must now consider the estimate of the interstellar extinction Av, best estimated by the reddening Av can take several values and in calculations of molecular cloud chemistry typical values are of order 1 but may be as much as 5. The distance calculation in Equation 5.1 can be significantly perturbed so that an A v of 2.4 can reduce the apparent distance by a factor of 3. 

O-H stretching frequencies in cm-1. b Deviation (in cm 1) from the standard frequency for O-H stretching (3629 cm-1). c O- H distances calculated. " 0--H distances estimated from Dreiding stereomodels. 

As a consequence of the smaller covalence of Cu(TPP), the pyrrole proton tensors are nearly axially symmetric and the Cu-H distances calculated with the entire unpaired electron at the Cu(II) ion are in excellent agreement with X-ray data. The difference in covalency of Ag(TPP) and Cu(TPP) is also reflected by the s-spin densities on the pyrrole protons which amount to PH(Ag) = 0.15% and pH(Cu) = 0.093%, respectively. A comparison with the corresponding data of an Xa calculation on Cu(II)-porphine1725 (oh(Cu) = 0.071%) indicates that the state-of-the-art electronic structure calculation underestimates the amount of unpaired spin density on the porphyrin ring. 

Fig. 21. Ratio between the correct molecular weight (M) and that calculated from dissymmetry (Md), as a function of the root mean square end-to-end distance calculated from dissymmetry (< h2 >y2) for different values of e 30 ...

It may be seen that the bond distances calculated using H-73 basis set agree better with experiment than those obtained using aug-cc-pVQZ or aug-cc-pVTZ basis set, and are close to the highly accurate values computed using FVMO method. 

The multivariate tools typically used for the NIR-CI analysis of pharmaceutical products fall into two main categories pattern recognition techniques and factor-based chemometric analysis methods. Pattern recognition algorithms such as spectral correlation or Euclidian distance calculations basically determine the similarity of a sample spectrum to a reference spectrum. These tools are especially useful for images where the individual pixels yield relatively unmixed spectra. These techniques can be used to quickly define spatial distributions of known materials based on external reference spectra. Alternatively, they can be used with internal references, to locate and classify regions with similar spectral response. 

Fig. 3. This figure shows the total energy of the H2 molecule as a function of intemuclear distance, calculated from the electronic energies shown in Figure 2. For small values of R, the calculation using 15 atomic orbitals per atom agrees well with the values of Kolos and Wolniewicz but another configuration would be needed for agreement at large R.

Figure 8.4 Energies of formation versus H- -H distances calculated for C-H- -H-Li dihydrogen-bonded complexes 1, LiNCH+- -HLi 2, NaNCH+- -HLi 3, NCH- -HLi 4, NCCCH- HLi 5, CICCH- HLi 6, LCCH- HLi and 7, HCCH- HLi. (Reproduced with permission from ref. 13.)...

Fig. 2. Agreement between experimental distances of nuclei of lysozyme, from the bound Gd(III) (obtained from the sixth root of the observed nmr broadening in solution) and the distances calculated from the X-ray structure. The numbers in this and Figs. 3 and 4 refer to the residues in the sequence (see Ref. 5). 

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