Echo peak

Figure B2.1.10 Stimulated photon-echo peak-shift (3PEPS) signals. Top pulse sequence and iuterpulse delays t and T. Bottom echo signals scaimed as a fiinction of delay t at tluee different population periods T, obtained with samples of a tetrapyrrole-containing light-harvesting protein subunit, the a subunit of C-phycocyanin.

Passino S A, Nagasawa Y, Joo T and Fleming G R 1997 Three-pulse echo peak shift studies of polar solvation dynamics J. Phys. Chem. A 101 725-31... 

Shortly thereafter came reports of integrated three-pulse photon echoes, especially using the echo peak shift to provide information about spectral diffusion [21, 23]. In one experiment [10, 23] the peak shift shows an intriguing oscillation at short times with a period of about 180 fs, followed by a slower relaxation with a decay time of 1.4 ps. The three-pulse echo amplitude can also be heterodyned, leading to 2DIR experiments [24 26]. The latter experiments provide a wealth of information, and there are several ways to extract the desired spectral diffusion dynamics [149]. 

Figure 6. Theoretical [98] and experimental [10] three pulse echo peak shifts as a function of waiting time t2, for HOD/D2O at room temperature.

Extensive analysis of the EPR and redox behavior of this unusual copper protein led to the hypothesis that the protein might contain a Cu(A) site similar to that in cytochrome oxidase (Riester et ai, 1989) and that the unusual seven-line EPR is due to the Cu(A)-type site. An alternative interpretation of this EPR is based on electron spin-echo spectroscopy as well, and that is that the seven-line EPR is due to a half-met Cu—Cu pair and to unusual type I sites (Jin et ai, 1989). Three sets of spin-echo peaks can be attributed to nitrogens on imidazole ligands to a CuA-type site and to another imidazole on the half-met site. The electron spin-echo spectra of cytochrome oxidase are similar, although there is not enough copper in cytochrome oxidase for a half-met site. Conceivably, the property of delocalization of the paramagnetic electron could be effected by the proposed bridging between Cub and heme as (nomenclature summarized by Capaldi, 1990), which are proposed to be 3-4 A apart. 

Thus in this case the peak shift t does not decay to zero. Figure 17 shows three-pulse echo peak shift data for a dye molecule, IR144, dissolved in ethanol and a plastic matrix (glass), PMMA, at room temperature. At long... 

Figure 18. The normalized electronic transition frequency correlation function M(t) 1= S(i)] obtained from the experimental three-pulse photon echo peak shifts and transient grating data for IR144 in ethanol (—) total W(t) ( ) ultrafast Gaussian component in M(t) ( ) oscillatory component that arises from intramolecular vibrational motion.

Figure 19. Comparison of calculated and measured signals using the M(t) shown in Fig. 18. (a) Three-pulse echo peak shift, (b) transient grating, and (c) transient absorption. A pulse duration of 16 fs (20 fs for transient grating) and a detuning of 230 cm-1 are used in the calculated signals. The peak near T = 0 in the transient grating and transient absorption signals, usually referted to as the coherent artifact, arises from the ultrafast decay (sum of intramolecular vibrational contribution and -100 fs ultrafast solvation dynamics) in M(t).

Fig. 4 Instrumental setup (a) and representative peaks (b) of echo-peak technique. An unknown sample is first injected and the mobile phase flows directly to the separation column. Within a short delay, a reference standard solution is injected and the switching valve turns to a different position to allow the mobile phase to flow through a short precolumn (as shown by dashed arrows) prior to passing through the same separation column. Two chromatographic peaks are therefore recorded, one for the unknown sample (solid line) and the other for the reference solution (dotted line). A and B mobile phases, LC liquid chromatograph, MS mass spectrometer...

In addition, a new technique termed ECHO peak technique could be considered [23, 24], With this new technique, two injections are carried out in each analysis, namely within a short time period (typically 30-50 s) the unknown sample and a standard solution. As a result, the peak of the analyte from the standard elutes in close proximity to the peak of the analyte from the sample, thus forming the so-called echo peak (Fig. 4). It is expected that both peaks elute so closely that they are affected in the same manner by the coeluted matrix components, which usually have... 

DeBoeij WP, Pshenichnikov MS, Wiersma DA. On the relation between the echo-peak shift and Brownian oscillator correlation function. Chem Phys Lett 1996 253 53-60. 

The three-pulse-echo peak shift is another two-dimensional echo technique, so far applied only to electronic transitions (122,123). It integrates over r3 and keeps rx and r2 as the time variables. The data are reduced by tracing the maximum in as a function of r2, resulting in a onedimensional decay curve. Although the implementation of this type of echo spectroscopy is quite different, the essential information content is much the same as in the Raman echo approach. 

Figures 2.13, 9.1, and 9.2 demonstrate the formation of an echo following a tt pulse. Application of additional tt pulses can be used to form a train of echoes. It is clear that the dephasing of magnetizations following an echo is of the same form as the initial dephasing during the FID and that application of a second tt pulse at 3T causes a second echo at 4t, etc. The envelope formed by the echo peaks decays according to the real T2, rather than T2, and Fourier transform of each echo provides a set of partially relaxed spectra, from which T2 of each line may be determined. (Carr and Purcell first recognized the value of such a long sequence of TT pulses,104 and their names are usually used to depict the method, but the technique that we described for the spin echo in Chapter 2 and that discussed here include a refinement by Meiboom and Gill,105 as discussed later.)...

Figure 25 summarizes the processes included in the calculation in a pictorial fashion. The procedure outlined in Figs. 24 and 25 is combined with the calculated electronic couplings for B850 (Sections III.C and VI.E), a line-shape function obtained by htting photon-echo peak shift data and static disorder from hole-burning and other experimental methods the absorption spectrum and photon-echo peak shift decay are calculated for B850, without adjustable parameters [40] (Fig. 26). The agreement with both experimental measures is rather good, including the slow decay of the echo peak shift evident from 200 fs to Ips. What do the timescales evident in the peak shift decay of...

Figure 26. Comparison for the absorption spectrum and three-pulse-echo peak shift determined from experiment for the B850 band of LH2 with that calculated using the model described in the text. Parameters are the same as in Fig. 23 right panel), plus a spectral density (see Ref. 40).

Figure 27. Illustration of the ansatz described by Eq. (34). The points represent the exact calculated photon-echo peak shift, while the solid hne is calculated via Eq. (34). The insert shows the population term [Eq. (35)]. The Left panel is for a disorder (a) of 160 cm, and the right panel is for a = 320 cm. Other parameters are as in Eigs 23 and 26.

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