When the rules fail

Exercise 2.8. The structure of GaioR6 is shown below. Consider the cluster as made up of edge-fused octahedra and compare the observed eve with the calculated one. Now apply the mno rule to this fused cluster system and calculate the number of cluster electrons required from each of the bare Ga atoms in order to satisfy the rule. 

Answer. For two octahedral clusters fused on an edge, the eve count is (2 x 26 — 14) = 38 whereas the observed count is (10 Ga + 6 R) = 30 -I- 6 = 36. Thus, we cannot assume non-cluster bonding lone pairs on the bare Ga atoms. With the mno rule, m = 2, n = 10 and o = 0 giving m + n = 12 sep. Each of the two Ga atoms shared between the clusters contributes all three valence electrons. Hence, we have 6 RGa + 2 Ga(shared) + 2 Ga(unshared) = (12 + 6 + 2x)/2 = 12 sep, where x is the contribution of the unshared cluster Ga atoms. Clearly x = 3 in this cluster, which suggests there are no formal lone pairs on these two Ga vertices. Indeed, the structure shows the Ga-Ga distances between the apical RGa and Ga centers (broken lines in the drawing) are about 0.2 A shorter than the other Ga-Ga distances. Electron counting identifies the cluster bonding problem but does not solve it. We will have more to say about this cluster type below. 

Exercise 2.9. The cluster [Ali ]2-, with two bare A1 atoms, exhibits the unusual shape shown below and has been called a nano-wheel. In light of the discussion above of rule-breakers, consider its electronic structure at the level of electron counting and suggest a reasonable analysis. 

The reactivity of C6o with metal fragments appears to correlate more closely with that of dienes than aromatics, however. This suggests that localization to form, e.g., organometallic complexes does not involve large destabilization energies due to loss of aromaticity. We will come back to the interesting properties of C6o in Chapter 7. 

Despite these difficulties, the success of this simple analysis suggests that complex cluster species can be built up utilizing partially delocalized (a aromatic) building blocks. The approach of Section 2.9, that probably seemed extraneous to 

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Because chemical structure representation in diagrammatic form has inconsistencies and contradictions built into it, it is impossible to anticipate every case. Most of the problem areas can be dealt with by a few general rules, but to cover all eventualities would require a huge system of regulations, with many provisos. Therefore, the aim of our rules is to cover the commonest problems and to ensure that only one representation will need to be assigned in most cases. Even when the rules fail to resolve a choice of structure completely, at least the number of possible structures should be reduced. In cases not covered by our rules, the structures given in the document will be indexed. 

Under the earlier ISA guidelines and in the new lEC 61511 standard, there are permitted exceptions to the separation rules for sensors and actuators. If you can show that the safety integrity requirements can still be met it is permissible to share sensors in an SIL 1 application. This would only be possible if the sensor was used in the BPCS for a control function that was not related to the task required in the SIS i.e. if when the sensor failed it did not contribute to the hazard demand placed on the SIS. In practice this is unlikely to be true unless the sensor is working as a recording device. 

At present, this rule fails only when functional neighboring substituents, capable of anchimeric assistance and in a convenient position with respect to the developing positive charge, can compete with bromine in the charge stabilization of the cationic intermediate (ref. 15). For example, the reaction of some unsaturated alcohols (ref. 16) goes through five- or six-membered cyclic oxonium ions, rather than through bromonium ions. 

Biochemical reactions are interesting but they are not magic . Individual chemical reactions that comprise a metabolic pathway obey, obviously, the rules of organic chemistry. All too often students make fundamental errors such as showing carbon with a valency of 3 or 5, or failing properly to balance an equation when writing reactions. Furthermore, overall chemical conversions occur in relatively small steps, that is there are usually only small structural changes or differences between consecutive compounds in a pathway. 

As in any classification problem, there is a tradeoff between the rate of recall, or proportion of correct substructures detected, and the reliability, or avoidance of false positive assertions. It is rather the exception than the rule for an observation to have a single, unequivocal explanation. When reasonable alternative interpretations are possible, a decision must be made about what to report. At one extreme, all possibilities could be asserted, ensuring 100% recall (i.e. no substructure which is actually present will fail to be detected) at the cost of a high rate of false positives. 

The rule of the K nearest objects, KNN, has been used in classification problems, in connection and comparison with other methods. Usually KNN requires a preliminary standardization and, when the number of objects is large, the computing time becomes very long. So, it appears to be useful in confirmatory/exploratory analysis (to give information about the environment of objects) or when other classification methods fail. This can happen when the distribution of objects is very far from linear, so that the space of one category can penetrate into that of another, as in the two-dimensional example shown in Fig. 28, where the category spares, computed by bayesian analysis or SIMCA, widely overlap. 

The photocyclodehydrogenation of thienyl ethylenes is well-defined when both thiophene rings are bound via a C(2) atom to the ethylenic bond as in (70). In other cases, however, more cyclization products are possible. To predict the photocyclization mode for heterohelicenes the F s rule fails in many cases, because correction factors for the hetero atoms in the Huckel MO calculation have to be introduced and the systems are not well comparable with carbocyclic diaryl ethylenes. A better reaction parameter in these cases is the Mulliken overlap population (nrs)51), introduced by Muszkat52) for these cases. The overlap populations of the atoms r and s in ground and excited state (nIiS and n s), are calculated using the extended Huckel method. Cyclizations should not occur when nr>s and An s (= nr>s — n s) have negative values. (This method can also be used for diaryl olefins, but in these cases calculation of F s is more simple.). 

Combination treatment with two or more psychotropic medications is the rule rather than the exception for bipolar disorders (bipolar combos in Fig. 7—35). First-line treatment is with either lithium or valproic acid. When patients fail to stabilize in the acute manic phase on one of these first-line treatments, the preferred second-... 

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