Ideal isotropic mixing

The Ideal Isotropic Mixing (TOCSY Spin-Lock) Hamiltonian... 

Now let s look at something we do not know the answer to the ideal isotropic mixing Hamiltonian. This is the ideal TOCSY mixing sequence that leads to in-phase to in-phase coherence transfer. The ideal sequence of pulses creates this average environment expressed by the Hamiltonian. The Zeeman Hamiltonian that represents the chemical shifts goes away and we have only the isotropic (i.e., same in all directions) /-coupling Hamiltonian ... 

Fig. 12. Coherence-transfer functions under ideal isotropic-mixing conditions for a system of three coupled spins, which represents a typical H spin system of serine in DjO, with = 4.5 Hz, Jafi = 9 Hz, and = -15 Hz. In the simulations represented by the solid lines, the two-spin approximation is assumed to be valid. The dashed curves result when the exact three-spin case is calculated. The a-/3 transfer function demonstrates the worst case, in which the two-spin approximation predicts a maximum at the same time that the exact three-spin isotropic mixing transfer function reaches a minimum. (Adapted from Remerowski et al., 1989, courtesy of Taylor Francis.)...

Ideal isotropic-mixing transfer functions have also been published for spin systems that are characteristic for spin systems of fully C-labeled amino acids (Bax et al., 1990b Eaton et al., 1990). For example. Fig. 14 shows the magnetization-transfer functions for the forked five-spin isotropic... 

Fig. 15. Polarization-transfer efficiency in a spin system consisting of three spins 1/2 under ideal isotropic-mixing conditions (effective ///-TOCSY coupling topology). (A) Damped transfer functions - t U12I) as a function of the relative coupling constant...

THE HAMILTONIAN MATRIX STRONG COUPLING AND IDEAL ISOTROPIC (TOCSY) MIXING... 

Isotropic effective /-coupling tensors (/) with a scaling factor s 1 are characteristic for ideal homonuclear Hartmann-Hahn experiments and, in particular, for homonuclear isotropic mixing experiments (see Section X). Isotropic effective /-coupling tensors can also be created between heteronuclear spins i and m (see Section XI) however, this results in a reduced effective coupling constant with a scaling factor i 1/3 [see Eq. (115)]. 

Fig. 24. Illustration of the effect of adding an uncompensated pulse to an isotropic-mixing sequence. The offset dependence of S shown for = 10 Hz under ideal...

Data. Assume for Al-Zn alloys that a2Y is isotropic, the enthalpy of mixing of Al-Zn solutions is independent of temperature, and the entropy of mixing, s, is ideal that is,... 

Refinement of the individual isotropic parameters of all atoms yields a small negative 5 of Si 1. It is unfeasible that Nd atoms are statistically mixed in the same sites with Si because their volumes are too different ( 27 for Nd versus 1 K for Si). Given the density of the alloy, it is also impossible that all sites except this one are partially occupied. Therefore, the negative 5sii is likely due to the fact that Si atoms have only a fraction of the scattering ability of Nd atoms, and individual displacement parameters of the former cannot be reliably determined from this experiment. Another possible reason is the non-ideality of the selected peak shape function, or other small but unaccounted systematic errors. One of these is an unknown polarization constant of the employed monochromator (see Eq. 2.69). Another possibility is a more complex preferred orientation. As a result, the isotropic displacement parameters of two independent sites occupied by Si were constrained to be identical in a way, the Si atoms were refined in an overall isotropic approximation. 

---