Fragmentation equation

The most interesting feature in the spectra of the above compounds is the presence of an intense peak for [M — CH20]4 (except with 117 and 121), the identity of which was checked by means of accurate mass measurements and deuteriation of the central methylene group. The following mechanism was proposed to explain the loss of CHzO which governs very much also the consequent fragmentations (equation 38) ... 

The fragmentation equation can be scaled into the following time-invariant form for the case of homogeneous kernels ... 

Smoluchowski s equation, like the fragmentation equation, can be written in terms of the scaling distribution. Furthermore, general forms may be determined for the tails of the scaling distribution—limits of small mass, xls(t) < 1, and large mass, x/s(t) > 1. The details can be found in van Dongen and Ernst (1988). 

Hansen, S., and Ottino, J. M., Agglomerate erosion A nonscaling solution to the fragmentation equation. Phys. Rev. E S3, 4209-4212 (1996a). 

McGrady, E. D., and Ziff, R. M., Analytical solutions to fragmentation equations with flow. AlChE J. 34, 2073-2076 (1988). 

Charge-transfer activation of the EDA complex leads to the ion-radical pair, in which the bicumene cation radical undergoes a unimolecular fragmentation (equation 64). 

Intramolecular thermal [4+2] cycloaddition occurs smoothly, though at a high temperature, upon heating of the appropriately substituted electron-poor oxadiazole containing electron-rich alkene fragment (Equation 1) <2002JOC7361>. 

The dicyclopenta[a,characteristic element of some terpenoids was obtained in 100% yield by a very facile Cope rearrangement of the highly functionalized divinylcyclobutane derivative 533 on heating in benzene at 55 °C for 4 h. The mild conditions can be due to participation of the lone pair of the sulfur atom or to the strain energy of the divinylcyclobutane fragment (equation 206)259. 

BSSE arises from the intrinsic problem that finite basis sets do not describe the monomer and complex forms equally well. For instance, the energy of two monomers calculated in the full dimer basis is not the same as for the dimer. A simple evaluation of the interaction energy (AE) of the two fragments [Equation (1)] is incorrect. This problem is especially serious with small basis sets. Hence, the magnitude of the BSSE can be used as a measure of the basis set incompleteness. 

The key stage of the synthesis to prepare 100 g amounts of a novel anthelmintic drug 500 from the metabolite VM-44866 (499) was a Beckmann-type oxime fragmentation (equation 217). A two-step reassembly of the spiroketal moiety efficiently produced the target molecule (30% yield of complete sequence in a 0.5 kg scale). 

JHC297>. In a continuation of the above work, l,3,4-thiadiazolo[3,2-a][l,3,5]-triazines were also analyzed by electron impact mass spectrometry. A retro Diels-Alder process gave two fragments (Equation (1)) which in turn were further fragmented into smaller molecules. The mass spectral data for the 11 compounds analyzed has been tabulated in great detail <890MS(24)379>. 

A commonly used nucleophile has been water. Although initial attack affords a hydroxy-carbene derivative, ready cleavage of the Ca—Cp bond resulting from formal keto-enol tautomerism occurs to give either the acyl or the metal carbonyl (usually cationic) and the corresponding organic fragment (Equation 1.13) ... 

The cyclodextrin-supported cleavage of 1,3-oxathianes with IBX (cf Scheme 76, Section 8.11.6.4.6) <2006SC3771>, as well as the copper-catalyzed aminolysis of 1,3-dithianes <2006OL2547> has been published. l,3-Dioxane-2-ones readily undergo a Grob fragmentation (Equation 100) <2006CC4303>. This reaction is catalyzed by Ni- (24-99% yield) or by Pd-complexes (42-93% yield). 

Diallylpalladium complexes derived from the dimerization of butadienes have been isolated and found to contain both an V and an V-allyl unit- Although it is difficult to discern which allyl moiety is reacting, treatment of this complex with acetylenedicaiboxylate or DO Ac yields products consistent with nucleophilic participation by the V-fragment (equations 119 and 120).318-319... 

Reaction of pyruvic acid with H2NNHC(S)NHNH2 gave the cyclic Schiff bases possessing the 1,2,4,5-tetrazepine fragment (Equation 13) <1996MI67>. 

The thermolysis of the 1,2,3-dithiazole 138, containing an azide group in the ortho-position relative to the diazo group, produced in high yield the previously unknown benzotriazole 139 containing the 1,2,3-dithiazole fragment (Equation 30) <2004JHC37>. 

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