Isotropic mixing 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 ... 

The isotropic-mixing Hamiltonian possesses full rotational symmetry and also commutes with the square of the total spin angular momentum... 

In a system, consisting of N spins 1 /2, the operators (with 1 n < N) commute with and with an effective isotropic-mixing Hamiltonian... 

Under an isotropic-mixing Hamiltonian, coherence transfer between Bj and a term such as Bj = with the same coherence order p = -1... 

NMR pulse sequence without getting tied up in the details of pulse phases and a mountain of sine and cosine terms only the essential elements of the sample net magnetization will be described at each point. Finally, the formal Hamiltonian description of solution-state NMR will be described and applied to explain two related phenomena strong coupling ( leaning of multiplets) and TOCSY mixing (the isotropic mixing sequence). 

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

In this section, we restrict the discussion to constants of motion during Hartmann-Hahn experiments that are induced by the symmetry of the mixing Hamiltonian and to selection rules for cross-peak signals in two-dimensional isotropic-mixing experiments. 

In the case of an isotropic effective mixing Hamiltonian of the form... 

The improved Figgis isotropic Hamiltonian (Eq. 195) accounting for the Cl of 4 Tig terms can also be applied, and this better accommodates the actual CF strength through the Cl-mixing parameter A. Again a closed form for the magnetic susceptibility is available (Table 25). 

A similar result was expected in Ref. 221 for cps(c>) = 1 — cp(cr), but the obtained difference between the recombination rates in the opposite limits was half as much kc for the slowest conversion and kj2 for the fastest one. This is because the isotropic Ag mechanism determining the spin conversion in Ref. 221 mixes the singlet with the 7b) sublevel only. In the rate approximation one can easily get the same, assuming that the spin transitions between the singlet and triplet RIPs occurs with equal rates in the forward and backward directions as in Eq. (3.585b). However, the transition from the slow to the fast conversion limit resulting from the rate approximation differs somehow from that obtained with the Hamiltonian approach in Ref. 221. 

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

FySy), where = E", (Schleucher et al., 1994). This Hamiltonian can be implemented using a heteronuclear Hartmann-Hahn mixing sequence that creates an effective Hamiltonian = 2TrJ f (FySy + F S ) that is embedded between two 9(f I,S)y pulses. A heteronuclear isotropic Hartmann-Hahn (HIHAHA) transfer step (Quant et al., 1995a Quant, 1996) can be used for in-phase COS-CT, for example, from S to F (Sattler et al., 1995a). CQS-CT mixing steps yield sensitivity-improved experiments and are especially useful for experiments that are based on gradient echoes. 

Mixing sequences for total through-bond correlation spectroscopy in solids (TOBSY) have been developed for fast MAS experiments. Possible sequences with the desired Hamiltonian (the homonuclear isotropic J interaction) have been identified using lowest order average Hamiltonian theory combined with numerical simulations as a function of the MAS frequency. An experimental TOBSY spectrum of a uniformly C-labelled decapeptide at 20 kHz MAS has been obtained using one of the new sequences. The spectrum allows to assign the resonances to the respective spin systems. 

Symmetric anisotropy The basis of this Hamiltonian can no longer be restricted to determinants with the same Ms value as was done for the isotropic interactions. The inclusion of magnetic anisotropy in the model causes the removal of the degeneracy of the different Ms levels and eventually mixing of the wave functions with different spin moment. Here, we have to consider four CSFs the three components of the triplet plus the singlet. To facilitate the determination of the matrix elements of the model... 

From the temperature dependence of EPR spectral intensities over the range 9-18 K it is possible to estimate J, the isotropic exchange coupling constant for the irons of their spin-coupled centers This procedure yields J = 14 1 cm for uteroferrin and J = 11 1 cm for the splenic enzyme (taking the exchange Hamiltonian, Hex = + JSi S2). This low value for J has been corroborated by H NMR studies at room temperature for uteroferrin /. Recent studies of mixed-valence, spin-coupled Fe(ni)-Fe(III) model compounds for uteroferrin indicate that such low values for J are consistent with iron atoms joined by a p-hydroxo or p-phenoxo bridge . ... 

---