5 resultados para LORENTZIAN MANIFOLDS

em Brock University, Canada


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The near ultraviolet absorption of phosgene has been assigned to a * 1 1 ~.--n, A;-- Al electronic transition from vapour phase spectra recorded under conditions of high resolution and low_t~mperature. Progressions in Vi, v2' V3' V4 and V4 ha\1e been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground and a nonplanar excited state. A ba~rier height of 3170 cm~l:and a nona planar equilibrium angle of 32.5 were calculated for the upper state from a fit of the energy levels of a Lorentzian-guadratic potential func- ~ion to the observed levels of V 4 . ' ~he false ori- 3in, 41 0 , of the spectrum has been assigned to the band at 33,631 cm -1 . An oscillator strength of -3 1 . 1 f = 1. a x 10 has been obtained for the A - A 2 1 transition.

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Using the Physical Vapor Transport method, single crystals of Cd2Re207 have been grown, and crystals of dimensions up to 8x6x2 mm have been achieved. X-ray diffraction from a single crystal of Cd2Re207 has showed the crystal growth in the (111) plane. Powder X-ray diffraction measurements were performed on ^^O and ^^O samples, however no difference was observed. Assigning the space group Fd3m to Cd2Re207 at room temperature and using structure factor analysis, the powder X-ray diffraction pattern of the sample was explained through systematic reflection absences. The temperatiure dependence of the resistivity measurement of ^^O has revealed two structural phase transitions at 120 and 200 K, and the superconducting transition at 1.0 K. Using Factor Group Analysis on three different structiures of Cd2Re207, the number of IR and Raman active phonon modes close to the Brillouin zone centre have been determined and the results have been compared to the temperature-dependence of the Raman shifts of ^^O and ^*0 samples. After scaling (via removing Bose-Einstein and Rayleigh scattering factors from the scattered light) all spectra, each spectrum was fitted with a number of Lorentzian peaks. The temperature-dependence of the FWHM and Raman shift of mode Eg, shows the effects of the two structurjil phase transitions above Tc. The absolute reflectance of Cd2Re207 - '^O single crystals in the far-infrared spectral region (7-700 cm~^) has been measured in the superconducting state (0.5 K), right above the superconducting state (1.5 K), and in the normal state (4.2 K). Thermal reflectance of the sample at 0.5 K and 1.5 K indicates a strong absorption feature close to 10 cm~^ in the superconducting state with a reference temperature of 4.2 K. By means of Kramers-Kronig analysis, the absolute reflectance was used to calculate the optical conductivity and dielectric function. The real part of optical conductivity shows five distinct active phonon modes at 44, 200, 300, 375, and 575 cm~' at all temperatures including a Drude-like behavior at low frequencies. The imaginary part of the calculated dielectric function indicates a mode softening of the mode 44 cm~' below Tc.

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Raman scattering in the region 20 to 100 cm -1 for fused quartz, "pyrex" boro-silicate glass, and soft soda-lime silicate glass was investigated. The Raman spectra for the fused quartz and the pyrex glass were obtained at room temperature using the 488 nm exciting line of a Coherent Radiation argon-ion laser at powers up to 550 mW. For the soft soda-lime glass the 514.5 nm exciting line at powers up to 660 mW was used because of a weak fluorescence which masked the Stokes Raman spectrum. In addition it is demonstrated that the low-frequency Raman coupling constant can be described by a model proposed by Martin and Brenig (MB). By fitting the predicted spectra based on the model with a Gaussian, Poisson, and Lorentzian forms of the correlation function, the structural correlation radius (SCR) was determined for each glass. It was found that to achieve the best possible fit· from each of the three correlation functions a value of the SCR between 0.80 and 0.90 nm was required for both quartz and pyrex glass but for the soft soda-lime silicate glass the required value of the SCR. was between 0.50 and 0.60 nm .. Our results support the claim of Malinovsky and Sokolov (1986) that the MB model based on a Poisson correlation function provides a universal fit to the experimental VH (vertical and horizontal polarizations) spectrum for any glass regardless of its chemical composition. The only deficiency of the MB model is its failure to fit the experimental depolarization spectra.

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Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

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The absorption spectrum of F2CSe in the 18800-21900 cm-1 region has been recorded at -770 C and 220 C under the conditions of medium resolution. The responsible electronic promotion is TI* + n excitation which leads to 3A2 and lA2 excited states. Progressions in vI', v2', v3" v4' and v4" have been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground state and a nQnplanar excited state. The - 3 - 1 - 1 - 1 origins of the a A2 + X Al and A A2 + X Al systems were assigned to the bands at 19018 cm-l and 19689 cm-l . This has given a singlet-triplet splittl. n g lA2 - 3A2 P f 671 cm -1 The out-of-plane wagging levels were found to be anharmonic. 1 -1 Barrier heights of 2483 cm- and 2923 cm were obtained for the lA2 and 3A2 upper states from a fitting of the energy levels of a Lorentzian-quadratic function to the observed levels in the out-of-plane wagging modes. 1 3 For the A2 and A2 states nonplanar equilibrium angles of 30.10 and 31.40 have been evaluated respectively. i