Results Obtained by Calculation

This systematic experimental study provided data for the calculation of the free energies of activation (AG p) at standardized conditions from experimental rate constants against which the results obtained by calculation (AG lc) were compared. Two different basis sets have been employed in the DFT calculations the split valence double- (DZ) basis set 6-31G(d) with a triple- (TZ)55,56 valence basis set for manganese (this combination is named basis set I (BS1)) and the triple- basis set 6-311 + G(d,p), which will be denoted basis set II (BS2). The results for transition states and intermediates on the BSl-level of theory are shown in Table 3, a graphical comparison of the free activation energies is shown in Fig. 10. xyz-Coordinates of all geometries are given in the supplementary material of Ref. 57. 

In this section, two illustrative numerical results, obtained by means of the described reconstruction algorithm, are presented. Input data are calculated in the frequency range of 26 to 38 GHz using matrix formulas [8], describing the reflection of a normally incident plane wave from the multilayered half-space. 

The ordinary BO approximate equations failed to predict the proper symmetry allowed transitions in the quasi-JT model whereas the extended BO equation either by including a vector potential in the system Hamiltonian or by multiplying a phase factor onto the basis set can reproduce the so-called exact results obtained by the two-surface diabatic calculation. Thus, the calculated hansition probabilities in the quasi-JT model using the extended BO equations clearly demonshate the GP effect. The multiplication of a phase factor with the adiabatic nuclear wave function is an approximate treatment when the position of the conical intersection does not coincide with the origin of the coordinate axis, as shown by the results of [60]. Moreover, even if the total energy of the system is far below the conical intersection point, transition probabilities in the JT model clearly indicate the importance of the extended BO equation and its necessity. 

Figure 4. Spin-orbit splitting in AT — 1 and 2 vibronic levels of the state of NCN. Solid lines connect the results of calculations thar employ ab initio computed potential curves [28], For comparison the results obtained by employing experimentally derived potential curves (dashed lines) [30,31] are also given. Full points represent energy differences between P — K — and P — K spin levels, and crosses are differences between P — K + I and P — K levels.

For translational, rotational and vibrational motion the partition function Ccin be calculated using standard results obtained by solving the Schrodinger equation ... 

It is pertinent here to consider some of the results obtained by Greenwood and McWeeny using both q and tt,. as criteria of reactivity ( 7.2.2). They have calculated for quinoline the exact charges in the... 

Let s use a simple example to develop the rationale behind a one-way ANOVA calculation. The data in Table 14.7 show the results obtained by several analysts in determining the purity of a single pharmaceutical preparation of sulfanilamide. Each column in this table lists the results obtained by an individual analyst. For convenience, entries in the table are represented by the symbol where i identifies the analyst and j indicates the replicate number thus 3 5 is the fifth replicate for the third analyst (and is equal to 94.24%). The variability in the results shown in Table 14.7 arises from two sources indeterminate errors associated with the analytical procedure that are experienced equally by all analysts, and systematic or determinate errors introduced by the analysts. 

Interaction effects between variables 1 and 2 are obtained by calculating the difference between the results obtained with the high and lowvalue of 1 at the lowvalue of 2 compared with the results obtained with the high and low value 1 at the high value of 2. The 12-inter-action is... 

Comparison of Models Only scattered and inconclusive results have been obtained by calculation of the relative performances of the different models as converiers. Both the RTD and the dispersion coefficient require tracer tests for their accurate determination, so neither method can be said to be easier to apply The exception is when one of the cited correlations of Peclet numbers in terms of other groups can be used, although they are rough. The tanks-in-series model, however, provides a mechanism that is readily visualized and is therefore popular. 

We observe that for the Fe-Co system a sim le spin polarized canonical model is able to reproduce qualitatively the results obtained by LMTO-CPA calculations. Despite the simplicity of this model the structural properties of the Fe-Co alloy are explained from simple band-filling arguments. 

To more easily determine the effective tube lengths for U-tubes, the correction chart shown in Figure 10-27B is convenient. The chart is based on many actual U-tube bundle layouts. Values read from the chart are not more than 1 % lower than those obtained by calculations, except where the curve is extrapolated to lower tube counts. Such extrapolations result in errors of 3%, 4%, and higher, giving larger values than those calculated. This does not apply to higher tube count extrapolations. The chart is limited to -in. and... 

Calculate the amount of boron present by reference to a calibration graph of absorbance against boron concentration (mg L 1). Multiply the result obtained by the appropriate volume correction factor arising from neutralisation of the sample. 

Figure 3.2.1 shows flame kernels of the schlieren photograph taken by a high-speed camera. These photographs can be compared with the calculated temperature distribution in Figure 3.2.4. As can be seen, both of them bear a close resemblance. From this result, the authors firmly believe that the numerical simulation is a significant tool for grasping the mechanism of spark ignition. Of course, the experimental work should also be of importance to verify the results obtained by numerical simulations. In this work, the authors mainly introduce the results of numerical simulations that have been obtained xmtil then in their laboratory.

The experimental results obtained by measuring ions activity after equilibration with pectins are plotted as binding isotherms [Me +Jb/Cp vs [Me +Jt/Cp where [Me2+]b is the bound cation concentration at equilibrium (equiv.l-i) calculated from measured activity using previously calculated activity coefficients. 

Several methods exist that can be used to measure changes of ESE for solid electrodes as a function of potential or other factors, but the accuracy of such measurements is much lower than that for Uquid electrodes. A plot of ESE vs. potential is called the electrocapillaty cutye (ECC). Typical ECCs measured at a mercury electrode in NaF solutions of different concentration are shown in Fig. 10.6. Also shown in this figure is a plot of values vs. potential calculated via Eq. (10.27). This plot almost coincides with that obtained from capacitance measurements (Fig. lO.lfc). This is evidence for the mutual compatibility of results obtained by these two methods of measurement. 

FIG. 3 The calculated surface tension of an argon-methane mixture as function of composition (mole fraction of argon) is shown as open circles in comparison with corresponding simulation results obtained by Mecke, Winkelmann, and Fischer [J. Chem. Phys. //0 1188 (1999)]. The GvdW(HS-B2) functional was used with tanh(w, x) profiles. 

Figures 18.13, through 18.17 show the experimental data and the calculations based on model I for the low temperature oxidation at 50, 75, 100, 125 and 150TZ of a North Bodo oil sands bitumen with a 5% oxygen gas. As seen, there is generally good agreement between the experimental data and the results obtained by the simple three pseudo-component model at all temperatures except the run at 125 TT. The only drawback of the model is that it cannot calculate the HO/LO split. The estimated parameter values for model I and N are shown in Table 18.2. The observed large standard deviations in the parameter estimates is rather typical for Arrhenius type expressions.

---