Average deviation with calculator

The A (K) energies were derived ftom Eq. (12.2) by means of bond-by-bond calculations [Eq. (10.37)] and Del Re s approximation [Eq. (10.3)] for the nonbonded contributions [234,235]. Atomization energies of the host molecules, calculated in precisely the same manner, agree within 0.2 kcal/mol (average deviation) with their experimental counterparts. 

This equation was verified by application of the p-D-T-data of the melts of 23 polymers of very different structure, adapting the reducing parameters Ba/ vQ and T0 to the closest fit with the experiments. The obtained values are shown in the left part of Table 4.15. The average deviation between calculated and experimental v(P, T) data is the same as obtained with the Tait relation. The advantage of Hartmann s equation is that it contains only three constants, whereas the Tait equation involves 4. 

The suggested phenomenological model describes the retention of PFe ions on different reversed-phase columns very well. Average deviation of calculated values from experimentally measured values is on the level of 1%, which confirms that indeed a superposition of several processes govern the retention of liophilic ions in acetonitrile/water systems. Experimental values along with the theoretical curves are shown in Figure 4-53. 

Table 3 Mean average deviation between calculated (AV5Z basis) and experimental dipole and quadrupole moment values (in au). The quadrupole moments were calculated with respect to the center of mass, with the molecules aligned along the z-axis. For non-linear molecules, the z-axis coincides with the axis of highest symmetry. The experimental values for the dipole moments were taken from [38], whereas those for the quadrupole moments were taken from [39]. Ab initio values were taken from references [40] (MRSDCI) and [41] (HF, MP2 and BD).

Table III. Average deviations of calculated from experimental frequencies in the vibrationally excited Rano n bands of the N2 molecule, as obtained with the CCSD, 4R- and 8R-RMR CCSD methods and cc-pVTZ basis set The last column gives the range of experimentally available rotational / values, /min /inax9 d the difference between the maximum and minimum deviations for this range of rotational sublevels is enclosed in parentheses.

Fig. 7.2. Numerical estimates of the overall average elastic constants. The error-bars were calculated as cr-N°5, where N is the number of individual estimates for each of the two overall elastic constants obtained with a given number of spheres in the unit cell and a is the standard deviation. The two horizontal dashed lines drawn through the averages obtained with 64 spheres are meant to facilitate the convergence analysis...

In general, data are fit quite well with the model. For example, with only two binary parameters, the average standard deviation of calculated lny versus measured InY of the 50 uni-univalent aqueous single electrolyte systems listed in Table 1 is only 0.009. Although the fit is not as good as the Pitzer equation, which applies only to aqueous electrolyte systems, with two binary parameters and one ternary parameter (Pitzer, (5)), it is quite satisfactory and better than that of Bromley s equation (J). 

One very important use of E and C numbers is the calculation of heats of interaction for systems which have not been examined experimentally. From our knowledge of the standard deviations of the parameters and their correlation coefficients, we have calculated the expected standard deviations for calculated heats for all possible combinations of all but a few of the acids and bases listed in Tables 3 and 4. For the hydrogen bonding acids and sulfur dioxide, these predicted standard deviations nearly all lie between 0.1 and 0.3 kcal/mole. For other systems with much larger heats, the errors are somewhat worse than this averaging around 0.7 kcal mole-i. 

These data were obtained by mixing the SOx additive with a low alumina cracking catalyst and steaming at 1400°F in 100% steam in a fixed bed for 5 hours. The concentration of additive was adjusted so that the initial activity was approximately the same for all materials. (The amounts were the same as those used for the regenerability test.) The SO2 removal ability was then measured before and after steaming and the % loss calculated. The average deviation was 7%. 

Starting with a dimensional response metric, ES is the a measure of the average response in standard deviation units calculated as MC — ME/SD, j, where ME represents the mean of the experimental treatment, MC represents the mean of the control treatment, and represents pooling of the stan-... 

Fig. 35. Analysis of the 3-D standard deviation maps calculated from data acquired with the bed operating at a constant gas velocity of (a) 25 and (b) 3l ll l iiiin s as a function of liquid velocity. The number of independent liquid pulses identified at each liquid velocity ( ), and the standard deviation in the pressure drop measurements made over the length of the bed, recorded at 0.5 s intervals over a 10-min period (x), are shown. All data derived from the 3-D MRI standard deviation maps are averaged over six maps acquired for each set of operating conditions.

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