Difficulties in calculations

Because of difficulties in calculating the non-adiabatic conpling terms, this method did not become very popular. Nevertheless, this approach, was employed extensively in particular to simulate spectroscopic measurements, with a modification introduced by Macias and Riera [47,48]. They suggested looking for a symmetric operator that behaves violently at the vicinity of the conical intersection and use it, instead of the non-adiabatic coupling term, as the integrand to calculate the adiabatic-to-diabatic transformation. Consequently, a series of operators such as the electronic dipole moment operator, the transition dipole moment operator, the quadrupole moment operator, and so on, were employed for this purpose [49,52,53,105]. However, it has to be emphasized that immaterial to the success of this approach, it is still an ad hoc procedure. 

The well-known difficulties in calculating tliree-dimensional structures of macromolecules from NMR data mentioned above (sparseness of the data, imprecision of the restraints due to spin diffusion and internal dynamics) also make the validation of the structures a challenging task. The quality of the data [88] and the energy parameters used in the refinement [89] can be expected to influence the quality of structures. Several principles can be used to validate NMR structures. 

Selection should be made for minimum power input, which is also likely to be the quietest fan for the duty. Performance is usually quoted for a standard condition of 1.2 m /kg. Calculations of system resistance are best carried out at the same condition. The user may find only the static pressure quoted. If total or velocity pressure are also quoted or the outlet velocity can be calculated the designer can calculate how much pressure can be recovered after the exit. Any mismatch due to difficulty in calculating system resistance will cause the volume to rise or fall, to settle on the fan characteristic curve. 

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

In order to be appUed the models should be predictive. Unfortunately, the models frequently fail and demonstrate significantly lower prediction ability compared to the estimated one, when they are applied to new unseen data [100-103, 106]. One of the main reasons for such failures can be the lack of available experimental data and difficulties in calculating log D, as discussed in Section 16.4.2. Another problem of low prediction ability of log D models can be attributed to different chemical diversity of molecules in the in-house databases compared to the training sets used to develop the programs. 

The difficulty in calculating a small number as a difference of two large ones, both known with limited accuracy, is not new and arises in many other fields. It often justifies using perturbation theory, which is aimed at estimating the quantity of interest directly. We will attempt to follow the same approach here. To do so, we combine (2.60) with (2.11) from Sect.2.2, in which we substitute U for This yields... 

At the most negative potentials the gains at 1943 cm-1 and 1828 cm-1 were attributed to the formation of (Dmbpy")Re[CO]3, for which the calculated frequencies are 1967 cm 1836 cm"1 and 1821cm"1 the two lowest frequencies were taken as corresponding to the broad feature near 1828 cm". The large difference between the observed and calculated values for the remaining peak were attributed to the difficulty in calculating the effect of the Dmbpy -. 

However, due to the difficulties in calculating ion yields in SIMS, quantitation of the data is not very reliable, and their work was not conclusive. We have determined here that the reaction of chemisorbed ethylene to form ethylidyne is first order in ethylene coverage. A noticeable isotope effect was observed, with activation energies of 15.0 and 16.7 Kcal/mole for C H and 02 respectively. These values are smaller than those calculated from TDS, but the differences can be reconciled by including the recombination of hydrogen atoms on the surface in the interpretation of the thermal desorption experiments. 

Thus, the RQ value can be used to estimate the metabolic status in an aerobic bioreactor. In practice, the RQ value can be determined based on the analysis of CO2 and O2 in the off-gas from a bioreactor. There may be difficulty in calculating the RQ due to the noise of measured data when the COj content in the off-gas is relatively low compared with the O2 content in the supply of air (20.91%). 

Moreover, for atoms with open shells, the difficulties in calculating the angular parts of the PT expansion grow very rapidly with the increase in the order of expansion terms. Even the methods of their calculations are not developed sufficiently, unlike the usual mathematical apparatus of the theory of atomic spectra. Therefore, in order to successfully apply the PT to complex atoms, further development of the many-body theory... 

The contribution of fishing to the diet of Homo sapiens is determined by the ratio of the volume of products taken from the World Ocean to agricultural products. Numerous estimates of this contribution and prediction for the future differ widely, which is explained by the difficulties in calculating marine ecosystem productivity. In this connection we agree with Garcia and Grainger (2005) who state ... 

The difficulty in calculating coupling constants is much more than for calculating chemical shifts for the same requirements of accuracy. On the other hand, the structural information is equally relevant. Our contribution to this important topic can be... 

Clearly, a difficulty in calculation of volumes of activation is addressing correctly the calculation of the partial molar volumes of both the activated complex and the reactant... 

Ab initio (from first principles) calculations are difficult to do with reasonable accuracy, due to the difficulty in calculating the energy of liquids. 

There are no major difficulties in calculating the mean square normal coordinate when more general formulae (4.28) and (4.29) for the functions Mu(s) and /ij/(s) are used. In this case three sets (branches) of relaxation times... 

In terms of developing QSARs, water solubility is not a commonly used parameter in the development of quantitative models. When used it is usually in the form of the logarithm to the base 10 (log Saq). The reasons for its low usage are probably due to difficulty in calculation and colinearity with log Kow (which should be used in preference), rather than its lack of meaning or relevance. Despite this, the use of log Saq in QSAR should not be discounted either to describe the solubility cut-off, or as a parameter in it own right. 

A 20% difference in is observed between the values from the polish rate vs. velocity plots and the polish rate vs. pressure plot obtained on the Suba IV. The difference in values obtained from the polish rate vs. pressure and velocity plots is likely to be a result of difficulties in calculating the true pressure on the wafer during polishing. Assuming that obtained from the polish rate vs. velocity plot is accurate, the different values suggest that the pressure calculations are approximately 20% underestimated. Pressure is calculated by assuming that the down force is evenly distributed across the wafer and template assembly. Because the wafer protrudes approximately one-third of the wafer thickness out from Ae template, the pad will compress more under the wafer than under the template and there will be more pressure exerted on the wafer than the template. Not accounting for the fact that the wafer protrades from the template pocket is the likely source of the error in pressure calculation. 

The success of Wood s correlation, Eq. (4), led us to use it for estimating the P values for the adsorbates C3+, which are clearly vapors at ambient temperature on the other hand, the p values for the adsorbates C2-, which have critical temperatures close to or below ambient, had to be obtained experimentally by superposing the corresponding adsorption data onto the characteristic curve of the higher alkanes. We believe that the reason for this is the difficulty in calculating densities of condensed, adsorbed phases at temperatures approaching and exceeding critical temperatures. 

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