Linewidth experimental

Time-dependent quantum mechanical calcnlations have also been perfomied to study the HCO resonance states [90,91]. The resonance energies, linewidths and quantum number assigmnents detemiined from these calcnlations are in excellent agreement with the experimental results. 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

Experimental Linewidths of the NMR Signals Arising from Cysteine H/3 Protons... 

Optimum values for the probabilities may not be obtained in the case that experimental llnewidths in the spectrum are very different since only a single linewidth is used for the simulated spectra. The calculated probabilities may be stored in the database and hard copy reports may be printed-... 

Simulated spectra can be created by another option in the main menu of the program. Probabilities (P1-P4) are prompted from the user, depending on the model, if vaiues other than those stored with the data base are desired and a single linewidth is entered. Equation 1 and 2 are then used to simulate a spectrum which can be saved, compared to the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or plotted. 

Once creation of the PV A database is complete, optimized probabilities may be calculated for the experimental spectrum at hand. Since the iterative procedure is restricted to a 2048 data point region, zoom cursors are displayed and set by the user until this condition is satisfied. In this case, the methylene region was selected and an initial guess for the Bernoullian probability (Pr=0.5) and linewidth (13.0Hz) were given. Optimized values for the probability and linewidth were Pr=0.52 and 12.8Hz, respectively. 

Figure 4 shows zoomed regions of the experimental and simulated spectra. The methine region was simulated separately using the same optimized probability but with a linewidth of 8.0 Hz. At this point the user may wish to use the spectral manipulation options (overlay, subtraction, etc.), repeat the calculation, or do further simulations. 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

FIGURE 9.5 CW ENDOR spectrum of 1-carotene radicals, (a) Experimental spectrum of Figure 9.4. (Reported in Wu, Y. et al., Chem. Phys. Lett., 180, 573, 1991.) (b) Simulated ENDOR powder pattern (using linewidth of 0.6MHz) for the sum of radical cation and neutral radicals in 5 3 1 1 ratio. (Reported in Gao, Y. et al., J. Phys. Chem. B, 110, 24750, 2006. With permission.)... 

FIGURE 9.8 HF-EPR spectra of canthaxanthin radical cation adsorbed on silica-alumina (solid line)—experimental spectrarecorded at5 K (dotted line)—simu lated spectra using g-tensor values g = 2.0032 and g =gyy = 2.0023 and linewidth of 13.6G. (From Konovalova, T.A., J. Phys. Chem. B, 103, 5782, 1999. With permission.)... 

When one of the Fe-coordinating Ns of the porphyrin is made inequivalent to the others, for example, by pulling on it, or by putting a protein structure around the cofactor, then the molecular x axis and y axis become inequivalent, and the axial EPR spectrum turns into the rhombic spectrum in trace d with derivative trace e (see also Table 5.4). There are now three features in the spectrum a peak, a zero crossing, and a negative peak, and their field positions closely (exactly for zero linewidth) correspond to those of the g-values, gx, gy, and gz. Finally, in trace f of Figure 5.4, which is the experimental X-band spectrum of cytochrome c, it can be seen that not only the g-value (peak position) but also the linewidth is frequently found to be anisotropic. This extra complication will be discussed extensively in Chapter 9. 

Fig. 6 (a) SQ and (b) DQ rotor-synchronized 2H MAS NMR spectra of sodium tetrathionate dihydrate-d4 (solid lines). The dashed line in (a) represents the exact numerical simulation of the SQ spectrum for random molecular motion with the rate constant k given in the figure, (c) The corresponding experimental and simulated static 2H quadrupolar-echo spectra, (d) Simulated SQ (solid line) and DQ (dashed line) linewidths as functions of k. (Reproduced with permission from [88])... 

As for the width of NMR resonance lines, it is inversely proportional to mobility of resonating nuclei. The width calculated from the experimental NMR lines of the three samples is of the highest value for the sample CT ODA 5 and there is only a small difference between the linewidths of CT and CT ODA 2. 

The line-broadening data as a function of pH, typically shown for the W(IV) in Figs. 13 and 14, incorporating the known pKa values (Table II), were fitted in 5 X 5 Kubo-Sack matrices describing the exchange based on the above schemes (6, 57). The experimentally determined chemical shift and linewidth data in the absence of exchange for the aqua oxo, hydroxo oxo, and dioxo species and the pH-dependent species distribution as calculated from the acid dissociation constants for the four systems were all introduced in the different matrices and the spectra were computer simulated. For each set of chosen rate con-... 

Usually, mainly Doppler broadening determines the gain profile of a particular laser transition. Indeed, due to the different configurations achievable with gas lasers (namely, a large cavity length), the laser line can be narrower than the Doppler linewidth. Different experimental realizations of single-mode lasers are detailed elsewhere (Demtroder, 2(X)3). 

Experimental data of Gibson and Sibener appears to confirm qualitatively these predictions at least for monolayers. The phonon linewidths were broadened around T up to half of the Brillouin zone. The hybridization splitting could not be resolved, but an increase of the inelastic transition probability centered around the crossing with the Rayleigh wave and extending up to 3/4 of the zone has been observed and attributed to a resonance between the adatom and substrate modes. 

---