Semi-quantitative calculations

A semi-quantitative calculation of these frequency shifts as a... 

From a comparison of the optical absorption and excitation data for the oxides (Table V), it is clear that the energy decreases with increasing cation size along the series Mg to Ba. The bulk exciton transitions of these oxides also decrease in a similar manner (Table VI). It is possible to make a semi-quantitative calculation of the intrinsic surface energy states using the approach of Levine and Mark (151) where the ions in an ideal surface are considered to be equivalent to bulk ions except for their reduced Madelung... 

Compared with published data the concentrations are in the moderate to high level relative to the Berlin area (Fromme et al. 2001) far below the maximum concentrations measured by Heberer et al. (1999) higher than the concentrations reported from the Lippe river and the first results presented by Osemwengie and Steinberg (2001). Furthermore the HHCB concentrations in this study were a factor of 4-10 lower compared to data reported by Paxeus (1996). These differences may be due to the semi-quantitative calculation by Paxeus. 

Calculation procedures Semi-quantitative calculations ofthe relative abundances of the major clay mineral groups are made using the weighted peak area method of Johns et al. (1954) ... 

The bivalent metals possess two valency electrons for each atom, and since these should fill the lowest zone entirely, the conductivity might have been expected to show a very sharp fall. While it is quite true that group 1 contains the best conductors known, the power of other metals to carry current is also quite considerable. What has to be postulated, and what can be supported by semi-quantitative calculations, is that with certain atoms the three-dimensional Brillouin zones for the p electrons partially overlap with those of the s electrons, so that there can be a response to an accelerating field by a passage from the one tsrpe of zone to the other. The... 

The cc-pVDZ basis set contains too few functions to be useful for accurate molecular calculations, although it may be useful for qualitative and semi-quantitative calculations. At the next... 

Semi-empirical and ab initio methods differ in the trade-off made between computational cost and accuracy of result. Semi-empirical calculations are relatively inexpensive and provide reasonable qualitative descriptions of molecular systems and fairly accurate quantitative predictions of energies and structures for systems where good parameter sets exist. 

This technique provides quantitative information about tautomeric equilibria in the gas phase. The results are often complementary to those obtained by mass spectrometry (Section VII,E). In principle, gas-phase proton affinities, as determined by ICR, should provide quantitative data on tautomeric equilibria. The problem is the need to correct the measured values for the model compounds, generally methyl derivatives, by the so-called N-, 0-, or S-methylation effect. Since the difference in stability between tautomers is generally not too large (otherwise determination of the most stable tautomer is trivial) and since the methylation effects are difficult to calculate, the result is that proton affinity measurements allow only semi-quantitative estimates of individual tautomer stabilities. This is a problem similar to but more severe than that encountered in the method using solution basicities (76AHCS1, p. 20). 

These equations allow either to predict the swelling degree (w = l/(p) as a function of external conditions or to calculate the network parameters from the correlation between the theoretical and experimental dependencies w(q) or w(p) [22, 102], An example of such a correlation is given in Fig. 2 and 5. As can be seen, theoretical predictions are in good agreement with experimental data. However, when the outer solution contains multivalent cations, only a semi-quantitative agreement is attained. 

Then appeared the time of computers. Quantum chemists developed semi-empirical codes that rapidly evolved into ab-initio complex systems of programs. According to their optimistic or pessimistic views, colleagues have seen this period either as that of semi -quantitative or of semi-qualitative theoretical chemistry. Very recently came the age of super computers, and a generation of quantum chemists have seen their dream come true at last, the quality of the calculation is in harmony with the quality of the concepts. 

The goal in this chapter has been to show that it is possible to perform simulations relevant to electrochemistry-based ab initio surface calculations, without including all known physical effects. Focusing on trends and differences rather than absolute values, the approach in some cases yields not only qualitative results, but also (semi)-quantitative predictions. 

A classic pharmaceutical science textbook might have defined poor solubility as anything below a solubility of 1 g mL-1 (2 mol L-1 solution for a molecular weight of 500 Da) at pH 6.5 (or pH 7). This classic view is reflected in the Chemical Abstracts SciFinder 2001 solubility range definitions for solubility calculated using Advanced Chemistry Development (ACD) Software Solaris V4.67. These semi-quantitative ranges for molar solubility are very soluble, 1 mol L 1 < solubility soluble, 0.1 mol L 1 < solubility < 1 mol L 1 slightly soluble, 0.01 mol L 1 <... 

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

The discussions of actual reactions will be qualitative, with numerical calculations giving way to semi-quantitative correlations obtainable without excessive numerical computations. The actual numerical results of quantum-mechanical calculations on large molecular systems are always obtained after many, sometimes drastic approximations. This problem is magnified when photochemical processes are involved,... 

The test is primarily a screening tool relative to reactivity of substances and reaction mixtures and is highly useful for that purpose. The determined initiation temperature is approximate. The energy calculations based on temperature increase and heat capacities are semi-quantitative because of the quasi-adiabatic mode of the system operation. The method of insulating the test cell results in moderate reproducibility of temperature rise and related pressure rise. Another disadvantage is the relatively small sample quantity with respect to full scale quantities thus, there could be a problem in that the sample may not be truly representative. 

In all other cases the calculated values of a and p refer only to the given type of interactions, nomogram of which is not yet existing, and all the comparisons are merely assumptions of qualitative or semi-quantitative character. 

Model calculations for the Cs suboxides in comparison with elemental Cs have shown that the decrease in the work function that corresponds to an increase in the Fermi level with respect to the vacuum level can be explained semi-quantitatively with the assumption of a void metal [65], The Coulomb repulsion of the conduction electrons by the cluster centers results in an electronic confinement and a raising of the Fermi energy due to a quantum size effect. 

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