Theory accommodation

Apart from Poples model, few water theories accommodate the possibility that hydrogen bonds may not be linear or close to linear. Indeed, practically all major theories of water structure assume that highly bent hydrogen bonds were relatively unimportant. 

The scientific method works most rigorously when it identifies observations that are incompatible with current hypotheses. Faced with a new observation, scientists list all hypotheses that might explain it and then discard those that are incompatible with accepted physical law. Hypotheses that are not discarded as incompatible remain possibilities. If only one remains, it is promoted to theory. If disproving all hypotheses but one is not possible, we may retreat to demonstrating compatibility with theory, recognizing that compatibility is weaker than proof. In science, we use the phrases I think. . . and I believe. . . as synonyms, both implying .. . based on known physical law. In other words, This theory accommodates all the observations that we currently know. ... 

Of the five r/-orbitals, it is assumed that only 2.56 are capable of bonding, the remaining 2.44 being localised atomic d-orbitals, which are non-bonding, and capable of receiving electrons with parallel spins as long as is permitted by Hund s Rule. With chromium the sixth electron is divided as shown in Table 1.1. Now the r/ip-hybrid orbital should in theory accommodate 6.56 electrons... 

The other thermodynamic properties follow in standard fashion from the partition function. In particular, unlike the original lattice treatment, the theory accommodates a nonvanishing excess volume the volume change on mixing... 

In contrast to the Tsai-Hill theory, Equation 9.12 where different values for the strength terms have to be used for tension and compression, the Tsai-Wu theory accommodates tension and compression in the one equation. 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

HyperChem supplements the standard MM2 force field (see References on page 106) by providing additional parameters (force eon slants) using two alternative schemes (see the second part of th is book. Theory and Melhod.s). I h is exten ds th e ran ge of chem ical compounds that MM-t-can accommodate. MM-t-also providescut-offs for calcu latin g nonbonded in teraction s an d periodic bou n d-arv condition s. 

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules ia a gas at low pressure can be taken to be isolated for the short time between coUisions. Unimolecular reactions such as photodissociation or isomerization iaduced by photon absorption can sometimes be studied between coUisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity ia one direction and almost zero velocity ia perpendicular directions. Not only does this reduce coUisions, it also aUows bimolecular iateractions to be studied ia intersecting beams and iacreases the detail with which unimolecular processes that can be studied, because beams facUitate dozens of refined measurement techniques. (J) Means have been found to trap molecules, isolate them, and keep them motionless at a predetermined position ia space (11). Thus far, effort has been directed toward just manipulating the molecules, but the future is bright for exploiting the isolated molecules for kinetic and dynamic studies. 

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

The color and constitution of cyanine dyes may be understood through detailed consideration of their component parts, ie, chromophoric systems, terminal groups, and solvent sensitivity of the dyes. Resonance theories have been developed to accommodate significant trends very successfully. For an experienced dye chemist, these are useful in the design of dyes with a specified color, band shape, or solvent sensitivity. More recendy, quantitative values for reversible oxidation—reduction potentials have allowed more complete correlation of these dye properties with organic substituent constants. 

In his valence bond theory (VB), L. Pauling extended the idea of electron-pair donation by considering the orbitals of the metal which would be needed to accommodate them, and the stereochemical consequences of their hybridization (1931-3). He was thereby able to account for much that was known in the 1930s about the stereochemistry and kinetic behaviour of complexes, and demonstrated the diagnostic value of measuring their magnetic properties. Unfortunately the theory offers no satisfactory explanation of spectroscopic properties and so was... 

The oxygen vacancies then diffuse to the gas interface where they are annihilated by reaction with adsorbed oxygen. The important point, however, is that metal is consumed and oxide formed in the same reaction zone. The oxide drift has thus only to accommodate the net volume difference between the metal and its equivalent amount of oxide. In theory this net volume change could represent an increase or a decrease in the volume of the system, but in practice all metal oxides in which anionic diffusion predominates have a lower metal density than that of the original metal. There is thus a net expansion and the oxide drift is away from the metal. 

Theories of the oxidation of tantalum in the presence of suboxide have been developed by Stringer. By means of single-crystal studies he has been able to show that a rate anisotropy stems from the orientation of the suboxide which is precipitated in the form of thin plates. Their influence on the oxidation rate is least when they lie parallel to the metal interface, since the stresses set up by their oxidation to the pentoxide are most easily accommodated. By contrast, when the plates are at 45° to the surface, complex stresses are established which create characteristic chevron markings and cracks in the oxide. The cracks in this case follow lines of pores generated by oxidation of the plates. This behaviour is also found with niobium, but surprisingly, these pores are not formed when Ta-Nb alloys are oxidised, and the rate anisotropy disappears. However, the rate remains linear it seems that this is another case in which molecular oxygen travels by sub-microscopic routes. 

Solar Power With improved technology and production methods considerable use is being made of solar power in remote locations. The output of photovoltaic arrays is used to maintain conventional storage batteries in a state of charge. The cathodic protection system is in turn energised from the batteries. It is usual to incorporate sufficient battery storage to accommodate a number of no-sun days. Whilst in theory the capacity of equipment is unlimited, a practical maximum would be ca. SOO W. 

I was also familiar with the work of science historian Stephen Brush who had argued that in most important cases, such as relativity theory and quantum mechanics, and contrary to popular opinion, it was successful accommodations that had swayed scientists of the time rather than any dramatic predictions. 

Worrall had made similar claims regarding theories of light developed in the seventeenth century and in particular, the case of Fresnel whose dramatic and subsequently confirmed predictions had not been as influential as his accommodation of already known optical phenomena. Meanwhile, Stephen Brush had turned his attention to chemistry and the periodic table, given that this seemed to be a case for which successful predictions made by Mendeleev are widely held to have been the reason for the acceptance of the periodic... 

A scientific theory T (in conjunction with accepted auxiliary assumptions) deductively entails some empirical sentence e e is, moreover, true (or, rather, accepted as true on the basis of experiment or observation). Does the extent to which this success lends confirmation or support to T depend on whether e describes some state of affairs that was unknown at the time of Ts articulation or instead on whether it describes some already well known state of affairs The methodological issue of whether, roughly speaking, successful prediction counts more for a theory than successful accommodation formed a celebrated part of the debate between William Whewell and John Stuart Mill. The latter, while allowing that successful predictions were well calculated to impress the ignorant vulgar , expressed utter... 

Successful theories typically both accommodate and predict. Most people, however, are more impressed by predictions than by accommodations. When Mendeleev produced a theory of the periodic table that accounted for all sixty [really sixty-two] known elements, the scientific community was only mildly impressed. When he went on to use his theory to predict the existence of two unknown elements that were then independently detected, the Royal Society awarded him its Davy Medal, . , Sixty accommodations paled next to two predictions, (Lipton, 1991, p, 134)... 

The difference between the two types of case cannot, therefore, concern what was or was not known when theory was produced. Instead the crucial difference is the fact that, in the cases of little or no support, certain aspects of the theory concerned were fixed precisely to yield the phenomena at issue. The relative velocities around the deferent and epicyclic circles in Ptolemy s theory had to be read off the phenomena of stations and retrogressions in order for that theory to yield those phenomena. The details of the fossil-accommodating version of creationism had to be read off the already known fossil record—which particular pretty pictures God chose to draw and what particular features the bone-like structures have can only be determined by observation. 

There is no reason why a successful accommodation] should not count just as highly for a theory as a predictive success—nothing prevents the former being just as severe a test for the theory as the latter. So planetary stations and retrogressions and the precession of the equinoxes—which Copemican theory and Newtonian theory, respectively, accommodated —fully supported those theories. Or, to take another example, the precession of Mercury s perihelion, which had been known about for decades beforehand, fully supported the general theory of relativity. 

The accommodation of some piece of evidence e by some theory T undoubtedly tells us something positive about T—namely that it is at least consistent with e. When, as sometimes happens, it begins to seem as if there is no possible explanation for some evidence within some theory, then even finding an accommodation of that evidence may give scientists more confidence in the theory. Something like this happened, for example, with Darwinian evolutionary theory and the widespread phenomenon of apparently altruistic behaviour—the consistency proof in that case coming in the form of the theories of kin selection and reciprocal altruism. 

Something else should be said about the impact of accommodation- When the (general) theory concerned is strongly supported independently of the fact at issue, the accommodation of some fact, even in this ad hoc way, may well still supply the best explanation that science can currently supply for that fact. So, for example, the best explanation in, say, 1700 for the observation of no stellar parallax was surely the Copemican one—that there must in fact be an apparent parallactic motion but that even the nearest stars are so far away as to make the effect too small to be detected by even the best available telescopes. (Here, as before with Ptolemy and with scientific creationism, we use the phenomenon—no observed parallax—to fix (in this case in a rather loose way) an otherwise free parameter in the theory (distance to the nearest star).)... 

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