Systematic variation

Inductive learning has been the major process of acquiring chemical knowledge from the very beginnings of chemistry - or, to make the point, alchemy. Chemists have done experiments, have made measurements on the properties of their compounds, have treated them with other compounds to study their reactions, and have run reactions to make new compounds. Systematic variations in the structure of compounds, or in reaction conditions, provided results that were ordered by developing models. These models then allowed predictions to be made. 

This is not E, i , of course you must find the minimum energy by systematic variation of ot. Alternatively, a QBASIC or TBASIC program can be written to integrate Eq. (6-28) by Simpson s rule. 

The emission yield, Ra, defined as the radiation of the spectral line, k, of an element, i, emitted per unit sputtered mass must be determined independently for each spectral line. The quantities g, and Ry are derived from a variety of different standard bulk samples with different sputtering rates. In practice, both sputtering rates and excitation probability are influenced by the working conditions of the discharge. Systematic variation of the discharge voltage, L/g, and current, I, leads to the empirical intensity expression [4.185] ... 

It is only in the context of the systematic variation of the properties of the adhesive and/or the adherend surface in a set of otherwise identical specimens subjected to a given mechanical testing procedure that it is reasonable to think of predicting relative interfacial strength. 

Since the rate of aliphatic acylation is higher than that of aromatic acylation, the olefin may possess aromatic substituents yields are lower, however, than with aliphatic olefins. Tlie types of olefins with aliphatic or aromatic substituents, undergoing diacylation, are shown in Table I. Systematic variation of the structure of the olefin... 

Systematic variation of the lowest-energy levels in a given configuration for An I plotted as a function of N, where N = Z - 88. 

A wide and systematic variation of structure, usually only possible with a high experimental effort, can be realized. 

The brute force method depends on a systematic variation of all involved coefficients over a reasonable parameter space. The combination yielding the lowest goodness-of-fit measure is picked as the center for a further round with a finer raster of coefficient variation. This sequence of events is repeated until further refinement will only infinitesimally improve the goodness-of-fit measure. This approach can be very time-consuming and produce reams of paper, but if carefully implemented, the global minimum will not be missed, cf. Figures 3.4 and 4.4. 

Systematic variation in the water temperature, (WW), will produce a profile reflecting this influence. Vary the / b(WW) and J(WW) values in Example 5.3 to simulate different water temperatures. Run the dynamics for these different water temperatures to observe its influence. Note whether this is a linear or nonlinear effect on the cluster size. The structures formed may be quantified by recording the average micelle cluster size. The typical pattern looks like the examples in Figure 5.5. 

A systematic variation of the rules governing the interactions of B and A can be made to reveal the influence of substrate concentration, Bq. Run... 

The order in oxidant is considered to result from attack of Cu(II) upon a chelate complex of the azo-compound and a second Cu(II) species. Systematic variations... 

We chose the number of PCs in the PCR calibration model rather casually. It is, however, one of the most consequential decisions to be made during modelling. One should take great care not to overfit, i.e. using too many PCs. When all PCs are used one can fit exactly all measured X-contents in the calibration set. Perfect as it may look, it is disastrous for future prediction. All random errors in the calibration set and all interfering phenomena have been described exactly for the calibration set and have become part of the predictive model. However, all one needs is a description of the systematic variation in the calibration data, not the... 

Since carbohydrates constitute an inexpensive and highly modular chiral source for preparing chiral ligands," Claver et al. have reported the use of a series of thioether-phosphite" and thioether-phosphinite furanoside ligands" in the test palladium-catalysed allylic substitution reaction. In the first type of ligand, a systematic variation of the donor group attached to the carbon atom C5 indicated that the presence of a bulky phosphite functionality had a positive effect on the enantioselectivity. Indeed, the enantioselectivity was controlled mainly by the phosphite moiety. This was confirmed by the use of a ligand... 

There may, however, be a number of other reasons to pursue a predictive first principles theory of Mossbauer spectroscopy. For example, one may want to elucidate structure/spectroscopy correlations in the cleanest way. To this end one may construct in the computer a number of models with systematic variations in oxidation states, spin states, coordination numbers, and identity of hgands to name only a few chemical degrees of freedom. In such studies it is immaterial whether these molecules have been made or could be made what matters is that one can find out which structural details the Mossbauer parameters are most sensitive to. This can provide insight into the effects of geometry or covalency that are very difficult to obtain by any other means. 

This work also shows that the time constants for the ionic surfactant micelle solutions are twice as fast as the TX solution time constant. Differences between the Stern layers of the micelles appear to be the charge of the surfactant polar headgroups and the presence of counterions. However, these differences do not account for the observed dynamics. Since the polar headgroups and counterions should interfact more strongly with the water molecules, the water motion at the interface should be slower. This view is supported by recent investigations where systematic variation of surfactant counter-... 

Quade J, Ceding TE, Bowman JR (1989) Systematic variations in the carbon and oxygen isotopic composition of pedogenic carbonate along elevation transects in the southern Great Basin. United States Geol Soc Am Bull 101 464-475... 

The objective of traditional multistep synthesis is the preparation of a single pure compound, but combinatorial synthesis is designed to make many related molecules.57 The purpose is often to have a large collection (library) of compounds for evaluation of biological activity. A goal of combinatorial synthesis is structural diversity, that is, systematic variation in subunits and substituents so as to explore the effect of a range of structural entities. In this section, we consider examples of the application of combinatorial methods to several kinds of compounds. 

The alternative N—N bond making route entails prior transformation of the attracto to repulso conformation. An approximate energy profile of this process (Figure 2.22) has been obtained by systematic variation of the appropriate reaction coordinate, that... 

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