Subject theoretical studies

Whereas oxaziridine and diaziridine were partial subjects of comprehensive theoretical studies on cyclic compounds (73MI50800), diazirine and some of its simple derivatives were the special target of quantum chemical investigations. Since diazirine, the lowest molecular weight heterocycle, has only five atoms and is of high symmetry, there was a chance for ab initio calculations, which followed some semiempirical studies. 

Laminar Flow Normally, laminar flow occurs in closed ducts when Nrc < 2100 (based on equivalent diameter = 4 X free area -i-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundaiy conditions and geometrical configurations. However, true laminar-flow heat transfer veiy rarely occurs. Natural-convecdion effects are almost always present, so that the assumption that molecular conduction alone occurs is not vahd. Therefore, empirically derived equations are most rehable. 

In addition to various analytic or semi-analytic methods, which are based on the theory of the liquid state and which are not the subject of this chapter, almost the entire toolbox of molecular computer simulation methods has been applied to the theoretical study of aqueous interfaces. They have usually been adapted and modified from schemes developed in a different context. 

The stereochemical outcome of nucleophilic addition reactions to cyclic ketones is the subject of numerous experimental and theoretical studies, with substituted cyclohexanones and cy-clopcntanones having been intensively studied. In addition reactions to substituted cyclohexanones 1 the problem of simple diastereoselectivity is manifested in the predominance of cither axial attack of a nucleophile, leading to the equatorial alcohol 2 A. or equatorial attack of the nucleophile which leads to the axial alcohol 2B. 

NMP of S in heterogeneous media is discussed in reviews by Qiu et at.,205 Cunningham,206 207 and Schork et a/.208 There have been several theoretical studies dealing with NMP and other living radical procedures in emulsion and miniemulsion."09 213 Butte et nr/.210 214 concluded that NMP (and ATRP) should be subject to marked retardation as a consequence of the persistent radical effect. Charlcux209 predicted enhanced polymerization rates for minicmulsion with small... 

The choice of basis set in ab initio calculations has been the subject of numerous theoretical studies. Early SCF calculations utilized mainly spht-va-lence basis sets such as 3-21G and 4-31G. The importance of inclusion of d polarization functions on sulfur atoms has been stressed by several authors. For instance, Suleimenov and Ha found that the omission of d polarization functions leads to a substantially lower barrier for the internal rotation ( 16 kj mol for the central bond of H2S4) and produces an unreahstically large S-S bond length for the most stable rotamer [4]. In general, the use of... 

It is well estabhshed that sulfur compounds as well as elemental sulfur have the tendency to form long chain molecules. All of these substances can be regarded as derivatives of the hydrogen polysulfanes (or polysulfanes) H2S . Polysulfanes form a long series of homologous chain-like molecules since the number n can assume any value. S-S and S-H bonds are frequently found in chemical and biological systems. Thus, polysulfanes have been the subject of numerous experimental and theoretical studies (for a recent review, see [15]). 

Both benzene dimer ion radicals were a subject of a recent theoretical study (166). 

J(PQ) and J(PN)). Trends in J(P170) have been used to study the protonation of phosphoryl tribromide, phosphoryl trifluoride and dif1uorophosphoric acid. Nitric acid had a greater protonation power than Hammett acidity functions indicated.77 This coupling has been the subject of a semiempirical sum over states theoretical study.7 ... 

While excited-state properties of monomeric carotenoids in organic solvents have been the subject of numerous experimental and theoretical studies (Polfvka and Sundstrom 2004), considerably less is known about excited states of carotenoid aggregates. Most of the knowledge gathered so far stems from studies of aggregation-induced spectral shifts of absorption bands of carotenoid aggregates that are explained in terms of excitonic interaction between the molecules in the aggregate. 

Only limited number of neutral monocyclic 11,3,2 diazaphosphole representatives have been reported, which have mostly been prepared by [4+1] cyclocondensation of diaminomaleodinitrile (DAMN) with P(III) reagent and the alkylation of the initially formed 1,3,2-diazaphospholide [2, 4, 7], During recent times, 67t-aromatic [l,3,2]diazaphospholium ions of type 46 [45], more often represented as cyclic phosphenium cation 47 [46,47], have attracted more attention due to their isoelec-tronic nature with Arduengo carbenes . Nature of bonding and aromaticity of these cations have been the subject of several experimental and theoretical studies (Structure 2) [48-52],... 

We thus see that the electronic theory of heterogeneous photocatalytic reactions not only makes an attempt to explain, from the unified point of view, a large amount of experimental data, often contradictory at first glance, but also predicts new effects awaiting experimental verification. No doubt, the photocatalytic effect on semiconductors which has only recently become the subject matter of scientific research requires further experimental and theoretical study. 

Donor-free compounds RAu and R3Au are inherently unstable and no experimental data are available. However, model systems such as CH3Au and (CH3)3Au were the subjects of several early theoretical studies.2 8 More recent work has considered the stability of the [CH3Au]+ cations in a zAj state ( S atomic state). Depending on the... 

Waggoner, K. M. Hope, H. Power, P. P. Angew. Chem. Int. Ed. Engl. 1988, 27, 1699. Six-membered heterocycles [RMER ]3 have been subject to detailed preparative and theoretical studies since they are isoelectronic to borazine B3N3Hs. However, it was demonstrated that only B3P3-heterocycles exhibit a considerable delocalization of the 6 k-electrons, whereas the delocalization in other six-membered heterocycles of the desired type contributes very little to their stabilization. Power P. P. J. Organomet. Chem. 1990, 400, 49. 

The subject of liquid jet and sheet atomization has attracted considerable attention in theoretical studies and numerical modeling due to its practical importance.[527] The models and methods developed range from linear stability models to detailed nonlinear numerical models based on boundary-element methods 528 5291 and Volume-Of-Fluid (VOF) method. 530 ... 

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