Shift, equation

It is obvious that the addition of HF will lead to a F Nb ratio that is greater than 6 and will shift Equation (47) to the left, leading in turn to the disappearance of NbOF52 ions from the solution. 

A(0) and A(t) are the total surface area before and after the parallel shift. Equation (115) is exactly the definition of the averaged mean, (//), and Gaussian, (K), curvatures. From Eq. (140), (//) and (K) can be deduced from the area variation of the parallel surfaces with the parallel displacement t as a variant. 

In the course of dolastane synthesis (the dolastanes are a group of marine diterpenes) interesting rearrangements catalyzed by Lewis acids were found. Treatment of the trienone 293 with excess (1.5 eq) ethylaluminum dichloride at low temperatures (—5°C, 48 h) gave the tetracyclic enone 295 in 53% yield while the tricyclic dienone 296 (50%) was formed at room temperature (equation 102)156. It was assumed that both products can be derived from the common zwitterion 294 which undergoes intramolecular alkylation at low temperatures (path a) whereas an alkyl shift takes place at elevated temperatures (path b), followed by a 1,2-hydride shift (equation 102). 

The Mossbauer effect involves the resonance fluorescence of nuclear gamma radiation and can be observed during recoilless emission and absorption of radiation in solids. It can be exploited as a spectroscopic method by observing chemically dependent hyperfine interactions. The recent determination of the nuclear radius term in the isomer shift equation for shows that the isomer shift becomes more positive with increasing s electron density at the nucleus. Detailed studies of the temperature dependence of the recoil-free fraction in and labeled Sn/ show that the characteristic Mossbauer temperatures Om, are different for the two atoms. These results are typical of the kind of chemical information which can be obtained from Mossbauer spectra. 

So far, only defocus and spherical aberration have been considered as aberrations affecting the image contrast. Both depend only on the magnitude of the spatial frequency g[ but not on the diffraction direction, thus resulting in rotationally symmetric phase shifts (Equation 11). However, the objective lens may exhibit further aberrations resulting in additional phase shifts, which are not necessarily rotational symmetric. The most important of these additional aberrations are astigmatism and coma. 

Since the microwave frequency and gyromagnetic ratio are constant, changes in the applied stress will result in a shift in the resonant magnetic field. Indeed, the shift equation is... 

The complexes [Ru(cod)py4]2+, [RuCl2(CO)2py2] and [RuCl2py4] catalyze the reduction of nitrobenzene by carbon monoxide and water (equation 74).397 The cationic complex gave the best results, and a number of substituted nitrobenzenes were reduced in good yields. Unlike some other catalysts for this reaction, it did not catalyze the water-gas shift (equation 70). 

Vacuum pyrolysis of 12 has been recently studied by high-resolution mass spectrometry200. The ionization potential (IP = 9.17 0.10 eV) for silole 2 was found to be in excellent agreement with the IP (9.26 eV) calculated by the semiempirical PM3 method. Thermodynamic calculations on possible decomposition mechanisms of 12 have shown that 2 is probably formed from the primary intermediate silylene 9 via two consecutive hydrogen shifts (equation 3). 

Over 7 days at room temperature, the anionic dimesityl-1,8-naphthalenediylborate 68 undergoes ring expansion to the tetracyclic borataalkene, via an apparent 1,3-aryl shift (Equation 25) <2004JCD1254>. 

Semipinacol rearrangement of a-haloalkyl aryl acetates has produced good yields of 2-aryl alkanoic esters. The acids formed on hydrolysis are important anti-inflammatory agents (such as Ibuprofen) and the reaction has been reviewed in some detail1010. In a similar process, oc-bromoalkyl aryl acetals thermally rearrange in protic solvents (under neutral or slightly basic conditions) via a 1,2-aryl shift (equation 193)1010,1011. 

The fused thiazines (84) have been shown to be photo-labile and they decompose in acetonitrile at 300 or 350 nm to yield fused pyrroles (90) (Table 2) suggesting that the RS group undergoes a very rapid [1,5] sigmatropic shift (Equation (27)) <86JCS(Pi)497>. 

Photolysis of ylidic thieno[3,2-c][l,2A4]thiazines, which are stable sulfinimides, gives thieno[3,2-6]pyrroles, suggesting that the methyl(and phenyl)thio group undergoes very rapid [l,5]-sigmatropic shifts (equation 66) (81CC927). 

In contrast to compounds 68, 70 and 72, the Li 1,3-sigmatropic shift in 74 is too fast to measure at all temperatures investigated, down to 150 K. The data indicated that while 74 describes the X-ray crystallographic structure, in solution the material consists of two stereoisomers 74 and 84 in roughly equal concentrations, rapidly interconverting by means of a very fast Li 1,3-sigmatropic shift (equation 109). 

The dihydropyridine derivative 236, a cyclic enamine, is formed from crotonaldehyde and the phosphonium salt 235 by a Wittig reaction, followed by electrocyclization of the resulting 1,3,5-triene. The dihydropyridine readily rearranges to the tetrahydropyr-idine 237 by a [1.5] hydrogen shift (equation 99)122. 

Benzeneselenenyl azide adds to alkenes readily. The addition of the selenenyl azide always occurs with trans stereochemistry. The yield of adducts is reliably high with several different alkenes. Unlike benzeneselenenyl chloride, mixtures of regioisomers are found with simple primary alkenes. No addition occurs between benzeneselenenyl azide and ethyl crotonate. The reagent adds to conjugated dienes in a trans 1,4-fashion which is thought to be due to an initial trans 1,2-addition, followed by a facile 1,3-allylic azide shift (equation 19). Unfortunately, this reagent must be prepared and used in situ ... 

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