Theoretical Explanations

Cycloaddition reactions can be explained by using correlation diagrams. According to the orbital symmetry theory, the symmetry of the orbitals of the reactants must be conserved as they are transformed into the orbitals of the product. 

Consider a simple example of a cycloaddition reaction of two molecules of ethene to form cyclobutane. Let us classify all the MOs of reactants and the product as symmetric (S) or antisymmetric (A) with respect to symmetry planes m and C2. Once these symmetries are noted, correlations of reactants and product orbitals may be drawn so that orbitals of like symmetry are connected. It is assumed that ethene molecules attack each other in parallel planes (i.e. vertically). There are two symmetry planes (the mirror planes), one bisecting the TT-system of the molecules (plane 1, vertical) and the other between the interacting molecules (plane 2, horizontal), as shown in Fig. 8.20. 

There are two 77-MOs of each ethene molecule, tt and rr (bonding and antibonding, respectively). Orbitals of one ethene molecule can interact with orbitals of another ethene in four ways leading to cyclobutane. 

In the course of [2 + 2]-cycloaddition the four rr-orbitals of the two ethene molecules are transformed into four a-orbitals of cyclobutane (Fig. 8.20). 

Let us consider the orbitals of the cyclobutane (product) and analyze them with respect to the same planes used for the ethenes interaction. This is shown in Fig. 8.21. 

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The electronic spectrum of the radical has been recorded long before a satisfactory theoretical explanation could be provided. It was realized early on that the system should be Jahn-Teller distorted from the perfect pentagon symmetry (D5/, point group). Recently, an extensive experimental study of the high-resolution UV spectrum was reported [76], and analyzed using Jahn-Teller formalism [73],... 

Likewise, quantum mechanical calculation succeeds in giving a theoretical explanation of some facts that the resonance theory could not explain, for example, why bis(pyridine-2)monomethine cyanine and bis(pyridine-4)monomethine cyanine possess the same lowest energy transition contrary to the 2,2 - and 2,4 -quinoline monomethine dyes, together with a molecular coefficient extinction lower than that of the 4,4 -quinoline dye (11). Calculation shows also that there is no theoretical reason for observing a relationship between and pK in a large series of dyes with different nuclei as it has been postulated, even if limited observations and calculations in short homogeneous series could lead to this conclusion (105). 

The theoretical explanation of the butane reaction mechanism is as fully developed as is that of acetaldehyde oxidation (51). The theory of the naphtha oxidation reaction is more troublesome, however, and less well understood. This is largely because of a back-biting reaction which leads to cycHc products (52). 

Panel). Most of the basic processes were established almost a century and a half ago, but a coherent theoretical explanation was not available until the publication in 1938 of the classic paper by R, W. Gurney and N. F. Mott. (Pwc. Roy. Soc. A164, 151-67 (1938)). Since then the subject has stimulated a vast amount of fundamental research in wide areas of solid-state chemistry and physics. 

Efforts to establish a theoretical explanation of the reactivity of nucleophilic reagents have centered on correlations with intrinsic electron-donor properties which are the fundamental basis of nucleophilicity. According to Edwards and Pearson, in general, such properties include basicity, polarizability, and the presence of unshared electron pairs on the atom adjacent to the nucleophilic atom of the reagent. When only the first two of these properties are operative, Eq. (8), which was proposed by Edwards, has proved successful in... 

Fig. 3). There is not yet any convincing theoretical explanation for this exponent - but gratifyingly the simulation result is in excellent accord with experiments ... 

The hydrogen atom, containing a single electron, has played a major role in the development of models of electronic structure. In 1913 Niels Bohr (1885-1962), a Danish physicist, offered a theoretical explanation of the atomic spectrum of hydrogen. His model was based largely on classical mechanics. In 1922 this model earned him the Nobel Prize in physics. By that time, Bohr had become director of the Institute of Theoretical Physics at Copenhagen. There he helped develop the new discipline of quantum mechanics, used by other scientists to construct a more sophisticated model for the hydrogen atom. 

Of course, a more charitable interpretation of Bent and Weinhold s statement might be to emphasize that quantum mechanics provides an approximate explanation for the periodic table, whereas the periodic table itself was merely a successful classification awaiting a theoretical explanation. But one cannot help thinking that this interpretation is not what the authors had in mind. What they intended... 

Theoretical explanation of the trans-effect (and /rans-influence) has centred on two theories, one based on cr-bonding the other on 7r-bonding. The tr-bonding argument considers two frans-ligands sharing a metal p orbital (Figure 3.83). 

It certainly does not seem that these interactions continue in solution, so that their magnitude is weaker than solvation forces. Theoretical explanation has suggested that the unused, filled, 6s-5dz2 hybrid (section 4.1) interacts with vacant 6px,py orbitals at right angles to the digonal bonds (Figure 4.49). 

More detailed and theoretical explanations of the role of the catalyst, based on this scheme, have appeared (72, 74, 77-82). In order to obtain experimental evidence for this scheme, some investigators did experiments in which 1,2-dimethylcyclobutane or cyclobutane were brought into contact with an active metathesis catalyst. However, 1,2-dimethylcyclobutane was stable under conditions where propene gave a high conversion to ethene and 2-butene (63). The experiments with cyclobutane led to the same conclusion (83). From this, and from the fact that cyclobutanes are not reaction products, although this can be expected thermodynamically, it follows that cyclobutanes are not free intermediates. This prompted Lewandos and Pettit (83) to propose a tetramethylene complex as the key intermediate ... 

After more than two centuries had elapsed, a similar phenomenon was discovered.in electric circuits, and van der Pol was probably the first to give a theoretical explanation, which is substantially as follows ... 

Laser Cooling The 1997 Nobel Prize in physics was shared by Steven Chu of Stanford University, William D. Phillips of the National Institute of Science and Technology, and Claude N. Cohen-Tannoudje of the College de France for their development and theoretical explanation of laser cooling, a process that can lower the temperature of a gas to a very low value. 

Reference to the decomposition of KMn04 has already been made in the discussion of chain branching reactions (Chap. 3, Sect. 3.2) in which the participation of a highly reactive intermediate was postulated. This work provided a theoretical explanation of the Prout—Tompkins rate equation [eqn. (9)]. Isothermal decomposition in vacuum of freshly prepared crystals at 473—498 K gives symmetrical sigmoid a time curves which are described by the expression... 

A theoretical explanation for such an anomalous phenomenon in certain nonalternant hydrocarbons has first been attempted, in case of pentalene, by Boer-Veenendaal and Boer followed by Boer-Veenen-daal et Snyder and Nakajima and Katagiri for other related nonalternant hydrocarbons. By making allowance for the effects of <7-bond compression, these authors have shown that a distorted structure resembling either of the two Kekule-type structures is actually energetically favored as compared with the apparently-full symmetrical one. 

The works on super low friction coatings in the past decade brought a hope to approach the dream of eliminating friction by surface coating technology. However, no further important progress has been achieved recently. There are still great difficulties either in theoretical explanation, or in experimental. 

Exchange-transferred spectroscopy was introduced with the finding of the etNOE [97] and its theoretical explanation in terms of fast exchange several years later [98] laid the basis for the large variety of applications being present today. The core element of etNOE is the dependence of the cross-relaxation rate 0 ° on the correlation time T,-. The overall cross-relaxation rate is defined by ... 

Theoretical explanations for the effects of substituents on the hue of diphenylpyrazoline brighteners have been published by Glisten and co-workers [46,47]. In practice almost all commercially important diphenylpyrazoline FBAs have the general structure 11.30, in which S02R is a sulphone or sulphonamide grouping. 

More fundamentally, reductionism as a thesis about inter-theoretical explanation was undermined by the eclipse of the Deductive-Nomological model. Once philosophers of science began to doubt whether deduction from laws was sufficient or necessary for explanation, the conclusion that inter-theoretical explanation need take the form of reduction was weakened. 

We wish also to mention the discovery of an unusual magnetic field dependence of specific heat in some multicomponent glasses in the 0.3 tK range [46]. A theoretical explanation of the phenomenon can be found in ref. [[47] pp. 17-46]. 

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