Hartmann-Hahn transfer evolution periods

In a system consisting of two coupled spins 1/2, Hartmann-Hahn transfer can be conveniently analyzed based on the one-to-one correspondence between the evolution of the density operator in the zero-quantum space that is spanned by the operators (ZQ),, (ZQ)y, and (ZQ) [Eq. (14)] and the magnetization trajectory of a single, uncoupled spin in the usual rotating frame (Muller and Ernst, 1979 Chingas et al., 1981 Kadkhokaei et al., 1991 see Fig. 2). This equivalence can be used for the construction of zero-quantum analogs of well-known composite pulses. Effective phase shifts of the zero-quantum field can be implemented by short periods of precession about the z axis of the zero-quantum frame... 

Fourier transformation over an incremented Hartmann-Hahn evolution period yields the eigenfrequencies of the (effective) Hartmann-Hahn Hamiltonian. In solid samples with resolved heteronuclear dipolar couplings (Muller et al., 1974), this approach yields heteronuclear dipolar oscillation spectra (Hester et al., 1975) if the heteronuclear spins are Hartmann-Hahn matched during the evolution period of the experiment. In liquid state NMR, Fourier transformation over incremented homonu-clear Hartmann-Hahn transfer periods yields so-called coherence-transfer... 

Inadvertent homonuclear Hartmann-Hahn transfer during the application of heteronuclear decoupling sequences in a detection period can give rise to undesirable linewidth anomalies (Barker et al., 1985 Shaka and Keeler, 1986). However, no application of Hartmann-Hahn transfer during the detection period of an NMR experiment is known to the authors from the literature. Potential applications include the direct (single shot) acquisition of Hartmann-Hahn coherence-transfer functions in the detection period rather than in an evolution period (Luy et al., 1996). 

The most important criteria for experimental Hartmann-Hahn mixing sequences are their coherence-transfer properties, which can be assessed based on the created effective Hamiltonians, propagators, and the evolution of the density operator. Additional criteria reflect the robustness with respect to experimental imperfections and experimental constraints, such as available rf amplitudes and the tolerable average rf power. For some spectrometers, simplicity of the sequence can be an additional criterion. Finally, for applications with short mixing periods, such as one-bond heteronuclear Hartmann-Hahn experiments, the duration Tj, of the basis sequence can be important. 

In multidimensional NMR experiments that contain several evolution and mixing periods, even more combinations are possible (Griesinger et al., 1987b). In these experiments, Hartmann-Hahn mixing periods with in-phase coherence transfer are of particular advantage, because the resolution is often limited in the indirectly detected frequency dimensions. 

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