Calculated results, comparison

It was, therefore, clear in 1974 that electronic-structure methods were not sufficiently advanced to reproduce experimental data accurately for even a simple ionic oxide such as MgO. The emphasis at the time was on the determination of the effects of different approximations upon the calculated results. Comparison was usually made between one calculation and another rather than between calculation and experiment. The theoretical papers reported the quantities arising directly from the calculations, such as orbital eigenvalues and atomic-orbital charge decompositions, and spectral properties were interpreted primarily in terms of orbital energies. No attempt was made to evaluate equilibrium structural or energetic properties. 

Figure 2.54. Bethe lattice calculation result. Comparison of adatom bond energy according to Eq.(2.229), the value it calculated with the aid of Eq.(2.247). For parameters see insert Fig.(2.55).

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Results of rigorous calculations and comparison to plant data, when possible, are shown in Figs. 13-95, 13-96, and 13-97. Plant temperatures are in good... 

L.N. Kmetyk and P. Yarrington, Cavity Dimensions for High Velocity Penetration Events—A Comparison of Calculational Results with Data, SAND88-2693, Sandia National Laboratories, Albuquerque, NM, 1989. 

Presenting the results graphically completes the simulation. Before a simulation tool is handed to the design engineer, it must be thoroughly validated by computation of cases for which measurements have been performed and by comparison of the calculated results with the measured data. A basic rule ... 

Since a considerable amount of review articles on both theoretical frameworks and calculated results have been reported[15-25], the main objective of the present study is placed on the comparisons with experimental results. The organization of the present report is as follows In the next section, for the sake of completeness, a brief theoretical description of the PPM is summarized from the previous articles. In the third section, disorder-LIq transition is focused and visualized atomic (spin) configuration is compared with recent high resolution electron micrograph. In the fourth section, ordering relaxation... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

It will be shown, however, that the effectiveness factor does not critically depend on the shape of the particles, provided that their characteristic length is defined in an appropriate way. Some comparison is made be made between calculated results and experimental measurements with particles of frequently ill-defined shapes. 

The values of the half-widths of the components of the rotational absorption spectrum of HC1, dissolved in various noble gases, are borrowed from [291]. In order to make this example obvious, a continuous curve is drawn through the calculated points. Comparison between experimental data and calculated results demonstrates, in line with the qualitative agreement, a good numerical coincidence of the observed. /-dependence of the half-widths of the rotational lines with the theoretical one in the case of HC1 dissolved in Kr and Xe. This allows one to estimate the model parameters for these systems dispersion of the potential... 

An alternative to the traditional approach is to generate the electronic states as needed during the dynamics. This has been done for atomic collisions, where detailed calculations and comparisons with experimental results are possi-ble.(4-8) General treatments of the coupling of electronic and nuclear motions in molecular systems can be done in a variety of formulations. In particular, Ohrn, Deumens and collaborators have implemented a general variational treatment in... 

Figure 29 shows a comparison of experimental results with calculation results obtained for cyclohexane. The discretization of film thickness is again observed as in the OMCTS results, and the interval is 0.5-0.6 nm, which is roughly the same as the molecular diameter of cyclohexane. 

TABLE 5—Comparison of calculation results with and without rarefaction effect. ... 

Particle size distribution calculations (19,27) have illustrated that modifications in the more standard methods for evaluating the integral dispersion equation are necessary in order to achieve good comparison between measured and calculated results. 

A comparison of the calculated results (Figs. 1.53 and 1.54) with the mode of occurrences of quartz and barite in the submarine hydrothermal ore deposits indicates... 

In the ONIOM(QM MM) scheme as described in Section 2.2, the protein is divided into two subsystems. The QM region (or model system ) contains the active-site selection and is treated by quantum mechanics (here most commonly the density functional B3LYP [31-34]). The MM region (referred to as the real system ) is treated with an empirical force field (here most commonly Amber 96 [35]). The real system contains the surrounding protein (or selected parts of it) and some solvent molecules. To analyze the effects of the protein on the catalytic reactions, we have in general compared the results from ONIOM QM MM models with active-site QM-only calculations. Such comparisons make it possible to isolate catalytic effects originating from e.g. the metal center itself from effects of the surrounding protein matrix. 

Figure 26 Comparison of temperature dependence of experimental data (a) and calculated results from MD (b). The figure is reproduced from Tashiro and Yoshioka [132], Figure 11. Reproduced with permission from Elsevier. Copyright (2004).

Fig. 6.10. Comparison of overlap sampling and FEP calculation results for the free energy change along the mutation of an adenosine in aqueous solution (between A = 0.05 and 0.45) in a molecular dynamics simulation. The results represent the average behavior of 14 independent runs. (MD time step.) The sampling interval is 0.75 ps. The upper half of the plot presents the standard deviation of the mean (with gives statistical error) for AA as a function of sample size N the lower half of the plot gives the estimate of A A - for comparison of the accuracy, the correct value of AA is indicated by the bold horizontal line...

The accuracy of the measurement of radon concentrations with bare track detectors was found to be unsatisfactory due mainly to the changes of the deposition rate of radon progeny onto the detector as a result of air turbulence. In this work, therefore, a method was developed which can correct the contributions of the deposition to the track densities by classifying the etched tracks according to their appearance, i.e. round or wedge shaped. Using this method, about 30% improvement in the error of measurements was achieved. The calibration coefficient ob tained by experiment was 0.00424 tracks/cm /h/(Bq/m ), which agreed well with the calculated value. Comparison was also made of the present method with other passive methods, charcoal and Terradex, as to their performance under the same atmosphere. 

Assumption A is the principal matter considered in this paper. Results of Calculation and Comparison with Data... 

The random A1 siting method of reference (7) was used to compute 29Si NMR intensities for comparison with experimental results reported in reference (2). The results in Table II show clearly some discrepancy between the experimental and calculated results. The variance a2 ranges from 35 to 329. The discrepancy is greatest at higher Si/Al ratios where the experimental distribution is much sharper than is expected of the maximum probability distribution of silicon and aluminum atoms. These results imply some ordering of the aluminum atoms in the lattice. 

The comparison between measured and calculated results for vapor-liquid equilibria in aqueous systems of weak electrolytes confirms the applicability of van Krevelen 1s method for moderate temperatures and concentrations. The comparison also indicates that the procedure of Edwards, Maurer, Newman and Prausnitz yields reliable results also at temperatures around 100 °C therefore, it may be expected that it is also useful at higher temperatures where experimental material, necessary for checking that procedure, is not available... 

The comparison of predicted calculated results with the experimental ones in kinetics of the eross-linkina /when the latter will be available./ will allow also to choose one or another pathway of cross-linking processes during chemical modification of polymers. 

Although simple, a model system containing one solvent molecule together with one ion already provides valuable insight into the nature of the ion-solvent interaction. There is also convincing evidence that this two body potential dominates in much more complicated situations like in the liquid state 88,89,162). Molecular data for one to one complexes can be calculated with sufficient accuracy within reasonable time limits. Gas-phase data reported in Chapter III provide a direct basis for comparison of the calculated results. 

That result is included in Fig. 4.4. For precise comparison with experiment harmonic oscillator rigid rotor results should be corrected for the effects of nonclassical rotation and anharmonicity. In the region of the maximum (Fig. 4.4) these corrections (see Appendix 4.2), which are temperature dependent, lower the calculated results by several percent. The spectroscopic data employed for the calculation reported in Fig.4.4 are shown in Table4.2. 

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