Matrix double resonance

Since the phenoxyls possess an S = ground state, they have been carefully studied by electron paramagnetic spectroscopy (EPR) and related techniques such as electron nuclear double resonance (ENDOR), and electron spin-echo envelope modulation (ESEEM). These powerful and very sensitive techniques are ideally suited to study the occurrence of tyrosyl radicals in a protein matrix (1, 27-30). Careful analysis of the experimental data (hyperfine coupling constants) provides experimental spin densities at a high level of precision and, in addition, the positions of these tyrosyls relative to other neighboring groups in the protein matrix. 

The matrix elements of these terms in the chosen case (a) basis were given originally in irreducible tensor form by Brown, Kopp, Malmberg and Rydh [57] and Brown and Merer [58], and are summarised in chapter 9. All of the molecular constants appearing in (11.30) were determined from the double resonance measurements we discuss them in due course. 

All of the other required matrix elements have been given elsewhere [77] some of the constants in equation (11.51) were determined in the laser magnetic resonance study, and the remaining constants were obtained from the double resonance study. The final parameters for the 0 = 0 level were (in MHz) as follows ... 

Fig. 10. (a) Time-integrated emission spectrum and (b) PMDR (phosphorescence microwave double resonance) spectrum of Pd(2-thpy)2 at T = 1.4 K dissolved in an n-octane Shpol skii matrix. Concentration = 10 mol/1. Aexc = 330 nm. The PMDR spectrum is induced by a microwave irradiation with a frequency of 2886 MHz, which is in resonance with the energy difference between the triplet substates I and III. An intensity increase (+) signifies vibrational satellites that belong to an emission from the short-lived substate III, while a decrease (-) characterizes satellites of the emission spectrum from the long-lived substate I (Compare Ref. [61])... 

Many workers have in fact used density matrix methods for the calculation of line shapes and intensities in multiple resonance experiments, and two excellent reviews of the background theory are available. (49, 50) In addition there is also a simple guide (51) to the actual use of the method which is capable of predicting the results of quite elaborate experiments. Major applications have included the calculation of the complete double resonance spectrum from an AX spin system which gives 12 transitions in all (52) an extremely detailed study of the relaxation behaviour of the AX2 systems provided by 1,1,2-trichloroethane and 2,2-dichloroethanol (53) the effects of gating and of selective and non-selective pulses on AB and AX spin systems and the importance of the time evolution of the off-diagonal elements of the density matrix in repetitively pulsed FT NMR and spin-echo work (54) the use of double resonance to sort out relaxation mechanisms and transient responses (55) the calculation of general multiple resonance spectra (56) and triple resonance studies of relaxation in AB and AX spin systems. (57)... 

Many apparent anomalies in the spectra produced by double resonance experiments can be resolved by a density matrix treatment. Thus in A- X experiments with a reduced amplitude of the irradiated field the normal effect of the NOE upon the intensities of the transitions may be severely modified and both emission and absorption may be observed. (58) It turns out that the overall behaviour depends upon... 

The nearest-neighbour excited-state exchange matrix elements in dimers of 1,2,4,5-tetrachlorobenzene (TCB) have been independently obtained using high-resolution phosphorescent - microwave double resonance (p.m.d.r.) and o.d.m.r. techniques. The authors conclude that the matrix element for energy transfer in the triplet state of TCB is not the same for dimer and exciton states. 

For each of the two sites, labeled 1 and 2 respectively, two zero-field ODMR transitions could be observed. The resonance frequencies for these transitions are given in Table 9. Conversely, the emission spectrum belonging to each of the ODMR transitions was also measured in a phosphorescence microwave double resonance (PMDR) experiment. The PMDR spectra obtained for the two resonances at 2356 MHz and 2329 MHz, as well as the normal emission spectrum, are presented in Fig. 23. As illustrated in the figure, in PMDR one can separate the emission spectra for sites 1 and 2 in the matrix. Table 9 summarizes the main optical, ODMR, and PMDR results. 

When discussing the general aspects of FTNMR, we have to remember that all principal statements about Fourier methods have been introduced for a strictly linear system (mechanical oscillator) in Chapter 1. In Chapter 2, on the other hand, we have seen that the nuclear spin system is not strictly linear (with Kramer-Kronig-relations between absorption mode and dispersion mode signal >). Moreover, the spin system has to be treated quantummechanically, e.g. by a density matrix formalism. Thus, the question arises what are the conditions under which the Fourier transform of the FID is actually equivalent to the result of a low-field slow-passage experiment Generally, these conditions are obeyed for systems which are at thermal equilibrium just before the initial pulse but are mostly violated for systems in a non-equilibrium state (Oberhauser effect, chemically induced dynamic nuclear polarization, double resonance experiments etc.). 

Clarke and Hofeldt determined the depopulation rates for the individual triplet state spin sublevels of chlorophyll a and chlorophyll b by microwave-modulated fluorescence intensity measurements. The species was dissolved in n-octane at a temperature of 2 K. The solvent n-octane is a low-temperature host matrix which allows high-resolution spectroscopy in the chlorophyll triplet state. Triplet absorption detection of magnetic resonance as well as fluorescence-microwave double resonance techniques were applied. The experimental arrangement was described in Ref. 167. In the case of fluorescence detection, chlorophyll b was irradiated with the 457.9-nm single-mode line of an Ar" laser. Microwave transitions were... 

McManus, H. J. D., Kang, Y. S., and Kevan, L. (1993). Electron-paramagnetic-resonance and proton matrix electron-nuclear double-resonance studies of N,N,N, N -tetramethylbenzidine photoionization in sodium dodecyl-sulfate micelles— Structural effects of added alcohols. J. Chem. Soc. Faraday Trans., 89,4085-4089. 

Quantum mechanically the modulation of the fluorescent light is associated with the radio frequency coherence of the excited state density matrix. In a standard Brossel-Bitter double-resonance experiment Tt-polarized light excites the atoms initially to the m=0 state of the excited level. Fig. 16.13(b), and then interaction with the r.f. magnetic field transforms each atom into a coherent superposition of the m=0, l states. The relative phases of the probability amplitudes of these states are fixed by the phase of the r.f. field and are the same for every atom of the sample. Thus the r.f. field is able to generate substantial hertzian coherence in the excited state density matrix. The fluorescent light emitted in the direction of B is then a coherent... 

We wish to extend the density matrix formalism developed in Chapter 15 to the optical double-resonance experiments discussed in this present chapter. We must therefore modify the Liouville equations of sections 15.5 and 15.6 by including a time-dependent perturbation, JC (t), which describes the effect of the r.f. magnetic field B (t). Using equation (16.7), we have... 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

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