Further Theoretical Studies

No single factor can be identified as determining the outcome of radical addition. Nonetheless, there is a requirement for a set of simple guidelines to allow qualitative prediction. This need was recognized by Tedder and Walton,2 17 Beckwith ei ah, Giese. and, most recently, Fischer and Radom.4 With the current state of knowledge, any such rules must be partly empirical and, therefore, it is to be expected that they may have to be revised from time to time as more results become available and further theoretical studies are carried out. 1 lowever, this does not diminish their usefulness. 

Further theoretical studies supported by in situ spectroscopy and high-resolution microscopy are needed to be able to understand this unusually strong bonding between Cu and Ce. To apply such first-principles quantum chemical MD approach, new computational methods accelerating computational time by several orders of magnitude must be developed. 

Further theoretical study of the mechanism of decomposition of /3-propiolactone and jS-butyrolactone, to form CO2 and ethene or propene, respectively, has concluded that the process can best be described as asynchronous and concerted. Calculations also suggest that concerted processes are preferred for both decarbonylation and decarboxylation of jj-thiobutyrolactone. ... 

In addition to the experimental investigations, the phenomenon of the gel collapse was intensively studied theoretically. Tanaka and coworkers from Massachusetts Institute of Technology gave the first theoretical description of the collapse of charged networks in the absence of salt [7]. Further theoretical studies in this field were made by M. Ilavsky at the Institute of Macro-molecular Chemistry in Prague [18] and also at the Moscow State University [19, 20]. 

The kinetics of defect accumulation requires further theoretical studies at temperatures at which they become mobile. The creation under the action of radiation of an ordered structure from the accumulation of radiation defects is an effect akin to those discussed in the theory of self-organization of structures - synergetics [14]. 

As the two sorbates methane and krypton on 5A appeared to have different mechanistic behaviour, further theoretical study appeared warranted. Two hypothetical gases P and Q whose properties are tabulated in Table 1 were used for comparison with the behaviour of methane and krypton. Hypothetical gas P was designed to have a Henry constant equal to methane, but to be a localized sorbate having entropy of sorption values decreasing incrementally as for krypton. Conversely, hypothetical gas Q had a Henry constant equal to that of krypton, but entropy of sorption values non-localized and decreasing incrementally as for methane. 

Nonetheless, participation of some other impurity is not excluded. Further theoretical studies in combination with other experimental techniques such as EPR, electron-nuclear double resonance (ENDOR), etc., are needed to establish microscopic structure of the H-I defect. 

Further theoretical studies by Floryconcerned the clarification of phase transitions for the systems with a definite distribution of macromolecules over the length and also the analysis of equilibrium for a model system composed of macromolecules in which rigid blocks are separated by flexible units. An example of such systems are copolyesters exhibiting the thermotropic transition into the liquid crystalline state in the absence of a solvent... 

It must be mentioned that C2 structures have been obtained using MP2/cc-pVDZ treatment which are not predicted by epikernel principle for the e type JT coordinate (these are possible for the e" one only). Nevertheless, further theoretical studies using larger basis sets and more exact methods are desirable. 

In further theoretical studies, Schleyer and coworkers found" that the nonclassical 2-norbornyl cation (126) is more stable by 13.6kcalmoE than the 127 classical structure, and 126 is the only stable form in the gas phase and in solution, and the classical form (127) is unlikely to be involved in solvolysis reactions [MP4(fc)SDQ/6-31G /MP2(full)/6-31G -p ZPVE level]. They also performed a rigorous ab initio calculation and defined the classical 127 structure as an artifact and found that it is a transition state in the rearrangement of 126 into the bridged 2-norpinyl cation. The computed MP2-GIAO 0 chemical shifts for 126 are close to the experimental values, whereas those calculated by Schindler (IGLO) for 127 deviate considerably. The comparison of the chemical shifts for the two structures with the experimental data proves once again the symmetrical nonclassical structure. 

The authors conclude that [2.2.3]cyclazine (219) is intermediate in aromaticity between the polynuclear aromatic hydrocarbons and peripheral conjugated aromatic compounds involving delocalized 10 tt or 14 tc electrons. They also state that the resulting [2.2.3]cyclazines and benzo[2.2.3]-cyclazines are strongly dlatropic and claim that further theoretical study is required before the details of these novel conjugated systems can be fully understood. 

Perhaps little did Ralph Pearson realize when he proposed the hardness concept that it would encompass such a multitude of physico-chemical problems and that it would spawn so many new concepts. The Maximum Hardness Principle and the HSAB Principle, if they prove out, should be cornerstones for understanding molecular structure and molecular reactivity. The complex of ideas related to hardness and softness deserve extensive further application and careful further theoretical study. 

In the following papers are presented further theoretical studies including used mathematical models of unsteady-state-operated TBRs [17-20]. Schubert [21] analyzed dynamic reactor models of recent years and presented a comparison of their useful applications for the simulation of periodically operated reactors. 

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