10 resultados para Caputo Fractional Derivatives

em Brock University, Canada


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The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

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The mass spectra of compounds of t he series (C6F5 )3-n MP~ (n = 1,2,3, M = P and As ), (C6F5>3Sb, Ph) Sb and (C6F5 )2SbPh have been studied in detail and the important modes of fragmentation were e1ucidated, a ided by metastable ions. Various trends attributed to the central atom and or the . substituent groups have been noted and, where applicable, compared to recent studies on related phenyl and pentafluorophenyl compounds of groups IV and V. The mass spectra of fluorine containing organometallic compounds exhibit characteristic migrations of fluorine to t he central atom, giving an increasing abundance of MF+, MF2+' and RMF+ (R = Ph or C6F5) ions on descending the group_ The mass spectra of pentafluorophenyl , antimony, and arsenic compounds show a greater fragmentation of the aromatic ring than those of phosphorus. The mixed phenyl pentafluorophenyl derivatives show a characteristic pattern depending on the number of phenyl grm.lps present but show t he general characteristics of both the tris(phenyl) and tris(pentafluorophenyl) compounds. The diphenyl pentafluorophenyl der ivatives show the loss of biphenyl ion as the most import ant step, the los s of phenyl t o give the i on PhMC6F5 + being of secondary importance. The ,bis(pentafluorophenyl) phenyl derivatives fragment primarily by loss of PhC6F5 to give C6F5M+ ions, the abundance of t hese increasing r apidly from phosphorus to arsenic. This species then, exhibits a characteristic fragmentation observed in the tris(penta- fluorophenyl ) compounds. However, the abundance of (C6F5)2M+ species in these compounds i s small. I ons of the type C6H4MC6F4 + and tetrafluorobiphenylene ions C6H4C6F4 + also are observed on substitution of a phenyl group for a penta- fluorophenyl group. The fully fluorinated species (C6F4)2M+ is not observed, although octafluorobiphenylene ions , (C6F4)2+' are evident in several spectra . The appearance potentials of the major ions were obtatned from the ionisation efficiency curves. Attempts were made to correlate these to the effect of the central atom in substituent groups, but the large errors involved prevented the reaching of quantitative conclusions, although it would appear that the electron is removed from the ligand in the ionisation of t he parent molecule .

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The work described in this thesis has been dtvided into six sections . The first section involves the reaction of 3,5-diphenyl-2-methyl-l,3,4-oxadiazolium perchlorate with acetic and benzoic anhydrides. The second section deals with the preparation and reactions of 1,3,4-thia diazolium salts. Some monomeric 1,3,4-thiadiazoline methine bases have also been prepared by reacting 1,3,4-thia d iaz ol ium s al t s with concen trated ammonium hydroxide solution. Variable temperature p.m.r. of 2-(3-acetylacetonylidene)-3,5-diphenyl-A4 -1,3,4-thiadiazoline has also been described. The third section deals with prepar a tion and reactions of some compounds in benzoxazole series. The fourth section deals with the prep a ration and reactions of N-alkyl-2-methylbenzothi azolium salts with base , a nd with some a cetylating and thioacetylating agents. Treatment of 2,3-dimethylbenzothiazolium iodide and of 3-ethyl-2-methylbenzothia zolium iodide with base wa s found to give the corresponding dimeric methine b a ses and evidence supporting their structure is also given. Thiol acetic acid was found to exchange 0 for S in its reactions with 2-acetonylidene-3-methylbenzothiazoline and 2-acetophenonylidene-3-methylbenzothi a zoline. (ii) In th e fifth section, the r eactions of 2,3-dimethylbenzselenazolium iodide with a variety of ac e tylating and thioacetylating agents has been described. The treatment of 2,3-dimethylbenzselenazolium iodide with base was found to give rise to a dimeric methine base and evidence supporting its structure is also given. The reactions of this dimeric methine b a se with benzoic anhydride and phenylisothiocyanate have also been described. The sixth section deals with the preparation and reactions of l-alkyl-2-methylquinolinium salts. Treatment of 1,2-dimethylquinolinium iodide and l-ethyl-2-methylquinolinium iodide was found to give the corresponding monomeric methine bases and evidence supporting their structure is also given. The E-type geometry of the olefinic bond in 2-acetonylidene-l-methylquinoline has been established on the basis of an N.O.E. experiment.

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Reactions of 5,6- and 4,5-epoxycholestane derivatives with strong bases were investigated. Epoxidation of 3a-acetoxycholest-5-ene also gave a new compound along with the anticipated epoxides. Interconversions of the latter were observed. Some possible mechanisms of its formation and rearrangements have been pIioposed. No reaction was observed with any of the 5,6- and 4,5-steroidal epoxides employed in the present study, using potassium tertiary butoxide under refluxing conditions. n-Butyllithium reacted only with 5,6-epoxycholestanes bearing a ketal moiety at the C3 carbon. Opening of the ketal group was observed with n-butyllithium in the case of a ~-epoxide. The reaction was also investigated in the absence of epoxide functionality. A possible mechanism for the opening of ketal group has been proposed. Lithium diethylamide (LDEA) was found effective in rearranging 5,6- and 4,5-epoxides to their ~orresponding allylic alcohols. These rearrangements presumably proceed via syn-eliminations, however the possibility of a corresponding anti-elimination has not been eliminated. A substituent effect of various functional groups (R = H, OH, OCH2CH20) at C3 has-been observed on product distribution in the LDEApromoted rearrangements of the corresponding epoxides. No reaction of these epoxides was observed with lithium diisopropylamide (LDA) • In the second part of the project, several attempts were made towards the sYRthesis of deoxycorticoste~one~17,2l,2l~d3' a compound desirable for the 2l-dehydroxylation studies of deoxycorticosterone. Several routes were investigated, and some deuterium labelled pregnane derivatives were prepared in this regard. Microbial 21-hydroxylation of progesteronel7,21,21,2l- d4 by ~ niger led to loss of deuterium from C21 of the product. An effort was made to hydroxylate progesterone microbially under neutral condtions.

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The mass spectra and fragmentation of a variety of fluoroaromatic compounds of Group V and some selected transition elements are discussed in some detail, aided by data from metastable defocussed experiments. Results of ,studies on the coupling reaction using unstable organotitanium chloride intermediate species are reported. The preparation of some 5-substituted octafluorodibenzophospho1es is also discussed. Rearrangements under electron bombardment resulting in the loss of heteroatom-fluoride fragments are discussed in the light of presently accepted mechanisms for these processes as are rearrangements observed in compounds involving thionophosphoryl bonds ( p=s ).

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Development of guanidine catalysts is explored through direct iminium chloride and amine coupling, alongside a 2-chloro-l,3-dimethyl-IH-imidazol-:-3-ium chloride (DMC) induced thiourea cyclization. Synthesized achiral catalyst N-(5Hdibenzo[ d,t][1,3]diazepin-6(7H)-ylidene)-3,5-bis(trifluoromethyl) aniline proved unsuccessful towards O-acyl migrations, however successfully catalyzed the vinylogous aldol reaction between dicbloro furanone and benzaldehyde. Incorporating chirality into the guanidine catalyst utilizing a (R)-phenylalaninol auxiliary, generating (R)-2-((5Hdibenzo[ d,t] [1,3 ]diazepin-6(7H)-ylidene ) amino )-3 -phenylpropan-l-ol, demonstrated enantioselectivity for a variety of adducts. Highest enantiomeric excess (ee) was afforded between dibromofuranone and p-chlorobenzaldehyde, affording the syn conformation in 96% ee and the anti in 54% ee, with an overall yield of30%. Attempts to increase asymmetric induction were focused on incorporation of axial chirality to the (R)phenylalaninol catalyst using binaphthyl diamine. Incorporation of (S)-binaphthyl exhibited destructive selectivity, whereas incorporation of (R)-binaphthyl demonstrated no effects on enantioselectivity. Current studies are being directed towards identifying the catalytic properties of asymmetric induction with further studies are being aimed towards increasing enantioselectivity by increasing backbone steric bulk.

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The use of theory to understand and facilitate catalytic enantioselective organic transformations involving copper and hydrobenzoin derivatives is reported. Section A details the use of theory to predict, facilitate, and understand a copper promoted amino oxygenation reaction reported by Chemler et al. Using Density Functional Theory (DFT), employing the hybrid B3LYP functional and a LanL2DZ/6-31G(d) basis set, the mechanistic details were studied on a N-tosyl-o-allylaniline and a [alpha]-methyl-[gamma]-alkenyl sulfonamide substrate. The results suggest the N-C bond formation proceeds via a cisaminocupration, and not through a radical-type mechanism. Additionally, the origin of diastereoselection observed with [alpha]-methyl-[gamma]-alkenyl sulfonamide arises from avoidance of unfavourable steric interactions between the methyl substituent and the N -protecting group. Section B details the computationally guided, experimental investigation of two hydrobenzoin derivatives as ligands/ catalysts, as well as the attempted synthesis of a third hydrobenzoin derivative. The bis-boronic acid derived from hydrobenzoin was successful as a Lewis acid catalyst in the Bignielli reaction and the Conia ene reaction, but provided only racemic products. The chiral diol derived from hydrobenzoin successfully increased the rate of the addition of diethyl zinc to benzaldehyde in the presence of titanium tetraisopropoxide, however poor enantioinduction was obseverved. Notably, the observed reactivity was successfully predicted by theoretical calculations.

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This thesis describes a method involving the preparation of an L-proline-derived imidazolone protected with an N-triethylsilyl group that undergoes diastereoselective lithiation followed by electrophile quench to give C5-substituted products with syn stereochemistry. The N-silylated derivatives may be more easily N-deprotected as compared to previous N-t-Bu analogues to give secondary ureas. These may serve as precursors to N-phenyl chiral bicyclic guanidines or as NHC precursors for synthesis of corresponding complexes.

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This thesis describes a method involving the preparation of an L-proline-derived imidazolone protected with an N-triethylsilyl group that undergoes diastereoselective lithiation followed by electrophile quench to give C5-substituted products with syn stereochemistry. The N-silylated derivatives may be more easily N-deprotected as compared to previous N-t-Bu analogues to give secondary ureas. These may serve as precursors to N-phenyl chiral bicyclic guanidines or as NHC precursors for synthesis of corresponding complexes.

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(A) Most azobenzene-based photoswitches require UV light for photoisomerization, which limit their applications in biological systems due to possible photodamage. Cyclic azobenzene derivatives, on the other hand, can undergo cis-trans isomerization when exposed to visible light. A shortened synthetic scheme was developed for the preparation of a building block containing cyclic azobenzene and D-threoninol (cAB-Thr). trans-Cyclic azobenzene was found to thermally isomerize back to the cis-form in a temperature-dependent manner. cAB-Thr was transformed into the corresponding phosphoramidite and subsequently incorporated into oligonucleotides by solid phase synthesis. Melting temperature measurement suggested that incorporation of cis-cAB into oligonucleotides destabilizes DNA duplexes, these findings corroborate with circular dichroism measurement. Finally, Fluorescent Energy Resonance Transfer experiments indicated that trans-cAB can be accommodated in DNA duplexes. (B) Inverse Electron Demand Diels-Alder reactions (IEDDA) between trans-olefins and tetrazines provide a powerful alternative to existing ligation chemistries due to its fast reaction rate, bioorthogonality and mutual orthogonality with other click reactions. In this project, an attempt was pursued to synthesize trans-cyclooctene building blocks for oligonucleotide labeling by reacting with BODIPY-tetrazine. Rel-(1R-4E-pR)-cyclooct-4-enol and rel-(1R,8S,9S,4E)-Bicyclo[6.1.0]non-4-ene-9-ylmethanol were synthesized and then transformed into the corresponding propargyl ether. Subsequent Sonogashira reactions between these propargylated compounds with DMT-protected 5-iododeoxyuridine failed to give the desired products. Finally a methodology was pursued for the synthesis of BODIPY-tetrazine conjugates that will be used in future IEDDA reactions with trans-cyclooctene modified oligonucleotides.