Dephasing

Figure Al.6.23. Schematic representation of dephasing and reversal on a race track, leading to coherent rephasing and an echo of the starting configuration. From Phys. Today, (Nov. 1953), front cover.

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Nitzan A 1988 Activated rate processes in condensed phases the Kramers theory revisited Adv. Chem. Phys. 70 489 Onuchic J N and Wolynes P G 1988 Classical and quantum pictures of reaction dynamics in condensed matter resonances, dephasing and all that J. Phys. Chem. 92 6495... 

If we neglect pure dephasing, the general tensor element of the third order hyperpolarizability relates to those of the first order polarizability tensor according to... 

I CRS interferogram with a frequency of A = coj + 2c0j - cOq, where cOp is the detected frequency, coj is the narrowband frequency and coj the Raman (vibrational) frequency. Since cOq and coj are known, Wj may be extracted from the experimentally measured RDOs. Furthemiore, the dephasing rate constant, yj, is detemiined from the observed decay rate constant, y, of the I CRS interferogram. Typically for the I CRS signal coq A 0. That is, the RDOs represent strongly down-converted (even to zero... 

Figure Bl.3.7. A WMEL diagram for the seventh order Raman echo. The first two field actions create the usual Raman vibrational coherence which dephases and, to the extent that inliomogeneity is present, also weakens as the coherence from different cliromophores walks oflP. Then such dephasing is stopped when a second pair of field actions converts this coherence into a population of the excited vibrational state / This is followed by yet another pair of field actions which reconvert the population into a vibrational coherence, but now one with phase opposite to the first. Now, with time, the walked-oflP component of the original coherence can reassemble into a polarization peak that produces the Raman echo at frequency oi = 2(o - (O2...

An alternative fifth order Raman quasi-echo experiment can also be perfomied [130. 131. 132. 133 and 134]. Unlike the true Raman echo which involves only two vibrational levels, this process requires the presence of tliree very nearly evenly spaced levels. A WMEL diagram for the Raman quasi-echo process is shown in figure Bl.3.8. Here again the first two field actions create a vibrational coherence which is allowed to dephase. This is followed by a second pair of... 

Figure Bl.3.8. A WMEL diagram for die three-colour fifth order qiiasi-Ramaii echo . As usual, the first pair of field actions creates the Raman coherence which is allowed both to dephase and walk off with time. This is followed by a second pair of field actions, which creates a different but oppositely phased Raman coherence (now hf) to the first. Its frequency is at oi - = e y Provided that frequencies are identified...

Loring R F and Mukamel S 1985 Selectivity in coherent transient Raman measurements of vibrational dephasing in liquids J. Chem. Phys. 83 2116-28... 

Vanden Bout D, Fretas J E and Berg M 1994 Rapid, homogeneous vibrational dephasing in ethanol at low temperatures determined by Raman echo measurements Chem. Phys. Lett. 229 87-92... 

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

FID does not die away before the deadtime has elapsed. In die case of inliomogeneously broadened EPR lines (as typical for free radicals in solids) the dephasing of the magnetizations of the individual spin packets (which all possess slightly different resonance frequencies) will be complete within the detection deadtime and, therefore, the FID signal will usually be undetectable. 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

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