Profile vibrational lines

Figure 7 Incident electron energy dependence of the X v = 0, 1, 2, 3 vibrational and the a Ag (v = 0) electronic loss scattered intensities from a 10-layer film of O2 condensed on Pt(lll). was set at 10° with 6 at 45° and the azimuth at 10°. Also shown is the energy dependence of the inelastic background intensity located just before the v = 1 loss peak onset at Aif = 0.16 eV along with that contributing to each energy-loss profile (dashed lines). (From Ref. 118.)...

A fascinating category of experiments can be found in Table IV. These are the use of lasers to determine thermodynamic parameters. These include calorimetry (43), enthalpies of vaporization and vaporization rates (44, 45), and heat capacities (46). Other laser experiments that can be found in Table IV include the use of CW laser spectroscopy to determine the iodine binding-energy curve (47), the study of vibrational line profiles to determine intermolecular interactions (48), two photon ionization spectrometry (49), a study of optical activity and optical rotatory dispersion (50) and the development of several experiments using blue diode lasers (57). 

Vibrational Line Profiles As a Proof of Molecular Interactions 48... 

Improved vibrational line profile. In some of the modeling attempts based on the X and Y functions introduced above, numerical problems have been encountered which required special attention. Although in all practical cases simple solutions to these problems could be found, an alternative approach is now preferred because it is easy to use [48],... 

B. P. Asthana and W. Kiefer, Vibrational line profiles and frequency shift studies by Raman spectroscopy, in Vibrational Spectra and Structure (J. R. Durig, ed.), Vol. 20. Elsevier, Amsterdam, 1992. 

Distortions along low-frequency modes and small frequency changes between the neutral and cation states, if present, contribute to the width of the vibrational lines in the photoelectron spectra after taking into account instrumental line broadening. Such band profiles can be treated semiclassi-cally using equation (8), where IE is the ionization energy and D is related to the transition moment. The Gaussian functions used to fit the experimental spectra can be described... 

VIBRATIONAL LINE PROFILE AND FREQUENCY SHIFT STUDIES BY RAMAN SPECTROSCOPY, B. P. Asthana and W. Kiefer... 

Figure 2-37. Efficiency of vibrational energy in a simple exchange reaction A + BC —> AB + C. (A) Solid curve - reaction profile dashed line represents a vibronic term, corresponding to an atom A interaction with a vibrationally excited molecule BC (Ey) (B) part of the reaction profile near the summit of the exchange reaction barrier.

JP Berger, R Saint-Loup, H Berger, J Bonamy, D Robert. Measurement of vibrational line profiles in H2-rare gas mixtures Determination of the speed dependence of the line shift. Phys Rev A49 3396-3406, 1994. 

Figure 7.6 Absorption line scan across a sharp edge in a polymer photoresist using the X, = 6 pm amide vibration spectral feature. Raw absorption signal as a function of distance (open circles) and the expected profile (solid line) assuming a perfectly sharp edge convolved with a calculated point spread function.

Eo is the difference between the minima of the upper and lower energy surfaces, and F is the mentioned arbitrary damping factor whose value determines the width of the vibrational lines. Values of F ranging between 10 cm and 200 cm are common. The full absorption or emission intensity profile is calculated as the superposition of the profiles of the individual electronic origins, with weight factors having die same ratios as the oscillator strengths of the individual absorptions. 

The French physicist and mathematician Jean Fourier determined that non-harmonic data functions such as the time-domain vibration profile are the mathematical sum of simple harmonic functions. The dashed-line curves in Figure 43.4 represent discrete harmonic components of the total, or summed, non-harmonic curve represented by the solid line. 

In most machinery, there are numerous sources of vibrations therefore, most time-domain vibration profiles are non-harmonic (represented by the solid line in Figure 43.10). While all harmonic motions are periodic, not every periodic motion is harmonic. In Figure 43.10, the dashed lines represent harmonic motions. 

Each process parameter directly affects both the machinery dynamics and the vibration profiles. For example, the line tension, strip width, and hardness of the incoming strip radically affect the vibration profile generated by a continuous process line in a steel mill. With few exceptions, process variations such as these must be considered in the vibration analysis. 

Theoretically, a perfectly balanced machine that has no friction in the bearings would experience no vibration and would have a perfect vibration profile - a perfectly flat, horizontal line. However, there are no perfectly balanced machines in existence. All machine-trains exhibit some level of imbalance, which has a dominant frequency component at the fundamental mnning speed (lx) of each shaft. 

Fig. 13 Isotopic line splitting of the V3 stretching vibration in single crystalline (see also Fig. 12(a)), after [108, 109], The origin of each absorption band is indicated by an isotopomer present in crystals of natural composition. While the absorption could be fitted by a Lorentzian band profile, the remaining peaks were dominated by the Gaussian contribution in the Voigt band shapes (solid lines below the spectrum). The sum result of fitting the isotopic absorption bands is inserted in the measured spectrum as a solid line...

The vibrational frequency of the special pair P and the bacteriochlorophyll monomer B have also been extracted from the analysis of the Raman profiles [39,40,42,44,51]. Small s group has extensively performed hole-burning (HB) measurements on mutant and chemically altered RCs of Rb. Sphaeroides [44,45,48-50]. Their results have revealed low-frequency modes that make important contribution to optical features such as the bandwidth of absorption line-shape, as well as to the rate constant of the ET of the RCs. 

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

Because of the large number of rotational levels in the upper and lower states, the overlap between the exciting laser line and the dopp-ler broadened absorption profile may be nonzero simultaneously for several transitions (u", / ) (v, f) with different vibrational quantum numbers v and rotational numbers J. This means, in other words, that the energy conservation law allows several upper levels to be populated by absorption of laser photons from different lower levels. 

The frequency of a single-mode laser inside the spectral gain profile of its active medium is mainly determined by the eigenfrequency of the active laser cavity mode. Therefore any instability of resonator parameters, such as variation of cavity length, mirror vibrations or thermal drifts of the refractive index will show up as frequency fluctuations and drifts of the laser line. 

Fig. 19. Experimental NMRD profiles and data calculated using classical vibration model for aqueous Ni(II). Thin line SBM thick line general theory. Reproduced with permission from Kruk, D. Kowalewski, J. J. Chem. Phys. 2002,116,4079-4086. Copyright 2002 American Institute of Physics.

As an example, Fig. 6.20 below compares the Ai AL = 0001 and 2023 line profiles at 195 K which were computed with and without (solid and dashed curves, respectively) accounting for the vibrational dependences of the interaction potential. The correct profiles (solid curves) are more intense in the blue wing, and less intense in the red wing by up to 25% relative to the approximation (dashed), over the range of frequencies shown. Whereas the dashed profiles satisfy the detailed balance relation, Eq. 6.59, if a> is taken to be the frequency shift relative to the line center, the exact profiles deviate by up to a factor of 2 from that equation over the range of frequencies shown. In a comparison of theory and measurement the different symmetries are quite striking use of the correct symmetry clearly improves the quality of the fits attainable. 

While for an accurate (+1%) treatment of the rototranslational spectra (v = v = 0) the matrix elements (vj (9 v f) of the lower rotational states do not much depend on the rotational transitions (j,f), for the vibrational bands (v > 0), for v f v, relatively strong j,f dependences are usually observed (9 designates the multipole and polarizability operator. Similar j dependences are also obtained for the dipole components Bc that are significant for line shape computations [63]. The accounting for the j dependences is relatively easy because the main effect of the j dependence is on the integrated intensity, but not so much on the shape of the profile. The main effect of neglecting the j dependence in the low-temperature spectra is an excess intensity of the Sj(l) lines. 

On pp. 31 Iff., a preliminary discussion of the symmetry of induced line profiles was given. The spectral lines encountered in collision-induced absorption show a striking asymmetry which is described roughly by a Boltzmann factor, Eq. 6.59. However, it is clear that at any fixed frequency shift, the intensity ratio of red and blue wings is not always given exactly by a Boltzmann factor, for example if dimer structures of like pairs shape the profile, or more generally in the vibrational bands. We will next consider the latter case in some detail. 

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