Excitation profiles inversion

Remade F and Levine R D 1993 Time domain information from resonant Raman excitation profiles a direct inversion by maximum entropy J. Chem. Phys. 99 4908-25... 

Lee S-Y 1998 Forward and inverse transforms between the absorption lineshape and Raman excitation profiles XVith int. Conf on Raman Spectroscopy ed A M Heyns (New York Wiley) pp 48-51... 

Lee S-Y and Feng Z W 1996 Reply to the comment on the inversion of Raman excitation profiles Chem. Phys. Lett. 260 511-13... 

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

According to Eqs. (8) and (9), the effective RF fields are scaled unsymmet-rically (in respect to the sideband number n) by the scaling factor Xn, in response to the unsymmetrical excitation profile. When K<0, the nth effective RF field becomes negative, which corresponds to a sign change of the operator Ix from positive to negative, or equivalently, a 180° phase shift is introduced to the nth effective RF field. Consequently, a phase inversion occurs in the transverse magnetization of the nth excitation band. 

The best approach, adapted from an earlier proposal by Tomlinson and Hill (19), is to specify the desired frequency-domain excitation profile in advance, and then syntheize its corresponding time-domain representation directly via inverse Fourier transformation. The result of the Tomlinson and Hill procedure is shown at the bottom of Figure 2, in which a perfectly flat, perfectly selective frequency-domain excitation is produced by the time-domain waveform obtained via inverse Fourier transformation of the desired spectrum. 

Figure 3.4. A single monochromatic radiofrequency pulse has an effective excitation bandwidth that depends inversely on the duration of the pulse. A short intense pulse is therefore able to excite over a wide frequency window (a), whereas a longer weaker pulse provides a more selective excitation profile (b).

Figure 9.14. Simulated excitation profiles of selected shaped pulses (of 10 ms duration) see Table 9.3. The inversion profiles (lower trace) were simulated with a 180(soft)-90(hard) sequence.

Universal pulses act equally on any initial magnetisation state whereas excitation and inversion pulses are designed to act on longitudinal magnetisation only. The bandwidth factor is the product of the pulse duration. At, and the excitation bandwidth, Af, which is here defined as the excitation window over which the pulse is at least 70% effective (net pulse amplitude within 3 dB of the maximum other publications may define this value for higher levels and so quote smaller bandwidth factors). Use this factor to estimate the appropriate pulse duration for the desired bandwidth. The attenuation factor is used for approximate power calibration and represents the amount by which the transmitter output should be increased over that of a soft rectangular pulse of equal duration. The Gaussian based profiles are truncated at the 1% level. 

For use in the laboratory, it is convenient to choose a simple, robust inversion pulse as the element S, and the Gaussian pulse is well suited to routine use. Example excitation profiles for this are illustrated in Fig. 9.20 and offer guidance on selection of pulse duration for a desired excitation window. For proton spectroscopy, a Gaussian pulse of around 40 ms proves suitable for many applications. 

The excitation profile of soft pulses is defined by the duration of the pulse, these two factors sharing an inverse proportionality. More precisely, pulse shapes have associated with them a dimensionless bandwidth factor which is the product of the pulse duration. At, and its effective excitation bandwidth, Af, for a correctly calibrated pulse. This is fixed for any given pulse envelope, and... 

The binomial sequences aim to improve the zero excitation profile and provide schemes that are less sensitive to spectrometer imperfections. The series may be written 1-1, 1-2-1, 1-3-3-1. .. and so on, where the numbers indieate the relative pulse widths, each separated by a delay x, and the overbar indicates phase inversion of the pulse. For off-resonance spins the pulse elements are additive at the exeitation maximum so for example, should one require 90° off-resonance excitation, 1-1 corresponds to the sequence 45x-t-45 x. Of this binomial series, it turns out that the 1-3-3-1 sequence [66] has good performance and is most tolerant of pulse imperfections by virtue of its symmetry [67]. The trajectory of spins with frequency offset l/2x from the transmitter for a net 90° pulse (1 = 11.25°) is shown in Fig. 9.26. During each... 

Whilst maximum excitation occurs at l/2t Hz from the transmitter offset, further nulls occur at offsets of n/x (n = 1, 2, 3,. .. corresponding to complete revolutions during each x) so a judicious choice of x is required to provide excitation over the desired bandwidth. The excitation profiles of the 1-1 and 1-3-1 sequences are shown in Fig. 9.25b and c. Clearly the excitation is non-uniform, so places limits on quantitative measurements, and once again there exists a phase inversion either side of the solvent. Both provide an effective null at the transmitter offset and suppression ratios in excess of 1000-fold can be achieved. 

As apparent from the previous section, a binomial sequence has a suitably tailored profile for the element S, and the series 3a-9a-19a-19a-9a-3a (Fig. 9.28a, with 26a =180° and a delay t between pulses, here termed W3 [71]) has a desirable off-resonance inversion profile for this purpose. The WATERGATE excitation profile for this is shown in Fig. 9.29a. Once again characteristic nulls also occur at offsets of n/x Hz, but between these the excitation is quite uniform and does not suffer the phase inversion of the unaccompanied 90° binomials. More recently, extended binomial sequences have been shown to provide a narrower notch at the transmit-... 

The excitation profile depends only on the inversion profile of S, not its phase properties. 

A shaped pulse must fulfil two main criteria it must be selective and it must generate the required tilt angle e.g. 90° or 180°. The selectivity of a shaped pulse, which is related to the excitation range, is inversely proportional to the pulse length. Selectivity also depends upon the shape of the pulse. Unlike hard pulses, the pulse length and the pulse shape are pre-determined by the desired excitation profile. Thus, the pulse power must be adjusted to the desired title angle of the selective pulse. The relationship between these parameters is complex but may be broken down into three steps and examined using either a spectral representation or the tools of the Bloch module of NMR-SIM. 

The Raman excitation profile is proportional to oi/((to) 2 which means that one cannot determine the time cross-correlation function directly from the observed Raman excitation profile. The indirect route is to first build a model potential energy surface for both the ground and the excited electronic states. The overlap (ijj/jih(0) is calculated by propagating the initial wave packet ij/,) on the upper electronic state and a computed resonance Raman excitation profile is obtained using Eqs. (48) and (49). The parameters of the potential energy surfaces can then be adjusted in order to get a good fit of the experimental excitation profile. In Sec. IV we shall discuss a method for a direct inversion. Another approach which has been discussed is the use of the transform theory (38,41). 

B2y, and >42 vibrations are expected to be polarized (p), depolarized (dp), and inversely polarized (tp ), respectively. These polarization properties, together with their vibrational frequencies, were used by Spiro and his coworkers to make complete assignments of vibrational spectra of the Fe-porphin skeletons of a series of heme proteins. They showed that the resonance Raman spectrum may be used to predict the oxidation and spin states of the Fe atom in heme proteins. For example, the Fe atom in oxyhemoglobin has been shown to be low-spin Fc(IIl). It should be noted that the A2y mode, which is normally Raman inactive, is observed under the resonance condition. Although the modes are rather weak in Fig. I-19, these vibrations are enhanced markedly and exclusively by the excitation near the B band since the A-term resonance is predominant under such condition. The majority of compounds studied thus far exhibit the A-term rather than the l -term resonance. A more complete study of resonance Raman spectra involves the observation of excitation profiles (Raman intensity plotted as a function of the exciting frequency for each mode), and the simulation of observed excitation proliles based on various theories of resonance Raman spectroscopy. ... 

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