Average Hamilton operator

The last equation defines the average Hamilton operator in the toggling frame, which is given in zeroth order by the average (H -f + H )/3. For the Hamilton operators of the chemical shielding (A. = o- in Section 3.1.1) and of the dipole-dipole interaction (A = D) are inserted. They are given in the rotating frame by... 

In the average Hamilton operator H, therefore, the dipolar terms cancel in lowest order. 

For the average Hamilton operator of the chemical shift, the effective field is in the direction of the space diagonal along a = (1,1,1). This means that the magnetization processes around an axis which is oriented at the magic angle relative to the magnetic... 

So far the theory has been completely general. In order to apply perturbation theory to the calculation of correlation energy, the unperturbed Hamilton operator must be selected. The most common choice is to take this as a sum over Fock operators, leading to Mdller-Plesset (MP) perturbation theory. The sum of Fock operators counts the (average) electron-electron repulsion twice (eq. (3.43)), and the perturbation becomes... 

For nitroxides in dilute liquid solution, the generally anisotropic spin Hamilton operator is simplified tremendously and, if imresolved proton hyperfine couplings are treated as line broadening, only the electron-Zeeman interaction and the hyperfine coupling to the magnetic nucleus (7 = 1) remain [20]. The g- and hyperfine (4-) tensors are averaged to isotropic values due to fast motion of the spin probe and the resonance condition for the irradiated microwave becomes... 

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