Theoretical insights

After Hertz s death Helmholtz paid tribute to his former student as a consummate physicist, who uniquely combined mathematical ability, theoretical insight, and experimental skill. These qualities enabled Hertz to make many important contributions to physics, of which only those relating more directly to energy are outlined below. 

Taylor CD, Neurock M. 2005. Theoretical insights into the structure and reactivity of the aqueous/metal interface. Curr Opin Solid State Mater Sci 9 49-65. 

An approach that provides a general theoretical insight into the redox properties of a linearly combined multi-redox system has been presented by Aoki and Chen (75). The theory is constructed on the basis of interaction energies between neighboring redox sites, uqr,... 

Special theoretical insight into the internal relaxation behavior of polymers can also be provided on the basis of dynamic scaling laws [4,5]. The predictions are, however, limited since only general functional relations without the corresponding numerical prefactors are obtained. 

Theoretical insight into the interfacial charge transfer at ITIES and detection mechanism of this type of sensor were considered [61-63], In case of ionophore assisted transport for a cation I the formation of ion-ionophore complexes in the organic (membrane) phase is expected, which can be described with the appropriate complex formation constant, /3ILnI. 

It is hard to imagine a scientific discipline older than the study of dynamical systems. The remarkable history of the field testifies to nature s inexhaustible store of subtlety and ability to surprise. Ever since Galileo, remarkable experiments, deep theoretical insights, and powerful calculational tools have all contributed to creating the rich panorama that the field presents today. 

The COD fractions can also be determined by iterative simulation methodologies based on a model corresponding to the matrix formulation in Table 7.1 and with parameters determined from procedure number 1 (Section 7.2.1). Successful use of this methodology requires, however, not only theoretical insight into sewer processes but also experience in calibration techniques. 

Response-surface methodology has also been used to gain theoretical insight into a reacting system (B19) and to determine the order of a reaction (P3). 

The evaluation of matrix elements for exphcitly correlated Gaussians (46) and (49) can be done in a very elegant and relatively simple way using matrix differential calculus. A systematic description of this very powerful mathematical tool is given in the book by Magnus and Neudecker [105]. The use of matrix differential calculus allows one to obtain compact expressions for matrix elements in the matrix form, which is very suitable for numerical computations [116,118] and perhaps facilitates a new theoretical insight. The present section is written in the spirit of Refs. 116 and 118, following most of the notation conventions therein. Thus, the reader can look for information about some basic ideas presented in these references if needed. 

This system of metal and iodosobenzene has resulted in important theoretical insights but so far has not achieved preparative significance for the formation of oxiranes compared with the reaction shown in Eq. (3). 

This chapter is not intended to furnish a comprehensive review of the latest theoretical developments across all types of reaction and catalyst in heterogeneous catalysis. It will instead briefly survey two cross-cutting themes that have in recent years benefited substantially from theoretical insights, especially what first-principles DFT calculations have been able to explain and predict, and that are commanding substantial current interest the design of new catalysts aided by theoretical insights and the elucidation of the molecular level effects of reactive physiochemical environments on catalytic reactivity. The relatively simple and predictable structure of metals... 

In the context of practical, especially vacuum line, chemistry, it is my pleasure to express a warm appreciation of Fred Fairbrother, a big man in every way. He had a reputation of sequestering scarce apparatus in his laboratory through a non-return valve , but towards me he always showed the greatest generosity in sharing equipment and his incomparable store of practical experience and theoretical insight. 

The potential of the m-benziporphyrin skeleton to produce aromatic macrocycles, foreseeable in the above discussion of its hypothetical tautomers, was actually revealed by introduction of hydroxy groups on the phenylene ring. These functionalities serve as additional tautomerization sites, which become effective aromaticity switches in appropriately designed systems. Theoretical insight into the switching capabilities of hydroxybenziporphyrins was gained from a theoretical survey of relative stabilities and aromatic character of various hydroxybenziporphyrin tautomers [287, 288], which was concurrently verified by experimental work (Table 2) [250],... 

R.W. Gora, W. Bartkowiak, S. Roszak, J. Leszczynski, A new theoretical insight into the nature of intermolecular interactions in the molecular crystal of urea. J. Chem. Phys. 117, 1031-1039 (2002)... 

Marti S, M Roca, J Andres, V Moliner, E Silla, I Tuiion, J Bertran (2004) Theoretical insights in enzyme catalysis. Chem. Soc. Rev. 33 (2) 98—107... 

A theoretical insight into this part of the electrolysis of organic compounds is much less clear than in the case of cathodic processes. 

While these experiments, which were carried out without giving a theoretical insight into the nature of the electrochemical reaction, yielded almost all the possible oxidation products in the oxidation of methyl alcohol, Elbs and Brunner 2 have discovered a method which gives 80% of the current yield in formaldehyde. This is exactly the substance which could not be proven present up to that time among the electrolytic oxidation products of methyl alcohol. Elbs and Brunner electrolyzed an aqueous solution of 160 g. methyl alcohol and 49 to 98 g. sulphuric acid in a litre. They employed a bright platinum anode in an earthenware cylinder, using a current density of 3.75 amp.1 and a temperature of 30°. Only traces of formic acid and carbonic acid and a little carbon monoxide, aside from the 80 per cent, of formaldehyde, were formed. Plating the platinum anode with platinum decreased the yield of formaldehyde at the expense of the carbon dioxide. With an anode of lead peroxide the carbon dioxide exceeded the aldehyde. 

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