Three-pulse echo

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... 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

ESE envelope modulation. In the context of the present paper the nuclear modulation effect in ESE is of particular interest110, mi. Rowan et al.1 1) have shown that the amplitude of the two- and three-pulse echoes1081 does not always decay smoothly as a function of the pulse time interval r. Instead, an oscillation in the envelope of the echo associated with the hf frequencies of nuclei near the unpaired electron is observed. In systems with a large number of interacting nuclei the analysis of this modulated envelope by computer simulation has proved to be difficult in the time domain. However, it has been shown by Mims1121 that the Fourier transform of the modulation data of a three-pulse echo into the frequency domain yields a spectrum similar to that of an ENDOR spectrum. Merks and de Beer1131 have demonstrated that the display in the frequency domain has many advantages over the parameter estimation procedure in the time domain. 

Three-pulse echo experiments on isolated chromophores probe the 1 —> 2 transition in addition to the fundamental Therefore, in order to model nonlinear spectra, in addition to the trajectories for mp(t) and (t), one needs the trajectory for this 1 > 2 transition frequency and in addition to the excited... 

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.

The first type of experiment we describe is a stimulated three-pulse echo (3PE) peak shift measurement. In this experiment, the two echo signals symmetrically placed at -kj + k2 + kj and k - k2 + k3 are recorded simultaneously. A sequence of such signals recorded at different values of the population period T is shown in Fig. 14 (see Fig. 12 during the period T,... 

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 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).

Figure 12.4 The pulse scheme of the three-pulse echo sequence to determine Xe diffusion coefficients in polymers and other porous systems. The shaded areas are magnetic field gradient pulses with amplitude g and length 8. The time between the two gradient pulses A determines the time during which the diffusion path length is...

Figure 12 Frequency-resolved vibrational echo. The three-pulse echo signal from hemoglobin-CO is spectrally analyzed in the separate diagrams Ri and R2 (at o) from R3 (at a>o — A). (Results from Ref. 117.)... 

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. 

The electron spin echo of Ag°(B) has a very short phase memory time but relatively strong aluminum modulation can be identified. However, the phase memory time is too short to carry out a quantitative analysis of the modulation. This also precludes us from getting analyzable modulation from deuterated adsorbate molecules in a three pulse echo experiment. So the data is insufficient to locate Ag°(B) in the zeolite lattice without additional information. 

Scholes GD, Larsen DS, Fleming GR, Rumbles G, Burn PL (2000) Origin of line broadening in the electronic absorption spectra of conjugated polymers Three-pulse-echo studies of MEH-PPV in toluene. Phys Rev B 61(20) 13670-13678... 

The result (46) for correlated Gaussian variables was used in our three-pulse-echo spectral study of hemoglobin [80, 81], where/was found to be close to unity. 

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).

The characteristic time of the three-pulse echo decay as a function of the waiting time T is much longer than the phase memory time (which governs the decay of a two-pulse echo as a function of x), since the phase information is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

In electron-spin-echo-detected EPR spectroscopy, spectral information may, in principle, be obtained from a Fourier transformation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of the echo is used as the main source of information in ESE experiments. Recording the intensity of the two-pulse or three-pulse echo amplitude as a function of the external magnetic field defines electron-spin-echo- (ESE-)... 

The stimulated (three-pulse) echo decay may also be modulated, but only by the nuclear frequencies co 2 and... 

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