Diamagnetism Hamiltonian

The dominant diamagnetic Hamiltonian term is a simple one-electron operator and its expectation value, when the ground-state determinantal wave function is constructed from the set of occupied molecular spin-orbitals, is... 

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. 

The diamagnetic contribution to the shielding tensors can be defined as the derivative of this Hamiltonian with respect to the magnetic moment Uk=YkIk of nucleus K and the external magnetic field... 

When these experiments were repeated, in the absence of air, it was discovered that the intensity of the ESR signal due to the Ag11 species almost doubled.539 Reexamination of the reaction for R = Bun showed that further oxidation to a red, diamagnetic Ag complex occurred in air or with excess thiuram disulfide and this accounted for the decrease in signal intensity.540 Values of spin Hamiltonian parameters for some silver(II) complexes are given in Table 67.539-542... 

In an ESR study of the interaction of oxovanadium(IV) cupferronate with basic organic solvents, it has been shown that the coordination of basic solvent molecules leads to the destruction of the dimeric nature of the complex molecules.109 Parameters of the spin Hamiltonian of the ESR spectra of the adducts thus formed in 15 cases have been correlated with the basicity of the organic solvents. By contrast, VO(cupferronate)2 retains its diamagnetic dimeric form in the frozen solution of non-coordinating solvents such as chloroform, carbon tetrachloride, cyclohexane or benzene. 

The temperature-independent paramagnetic term is omitted hereafter (this can be included in the empirical correction of the experimental data, together with the diamagnetic term) so that we arrive at the ZFS Hamiltonian ... 

FIGURE 2.13 Mossbauer spectrum of intermediate X recorded at 80K in a parallel applied field of 8.0 T, same experimental spectrum in all panels. Solid lines in (a) and (c) are spectral simulations for sites a and b assuming diamagnetism that is, Bint = 0. The solid fines in (b) and (d) were obtained by adding, in both cases, a negative Bint. The solid fines are actually simulations for the full Hamiltonian of Equation 2.1 for a ferromagnetically coupled center. The sum of the theoretical curves in (b) and (d) fits the experimental spectrum quite well. 

The diamagnetic contributions to the NMR parameters arise from the operators obtained by double differentiation of the Hamiltonian (see Equation (2.10))... 

Here we have introduced three second-rank tensors, the rotational magnetic moment tensor T2(G) and the proton and fluorine screening tensors, T2(rotational magnetic moment and chemical shift (shielding) tensors, a further term which should be included in the Zeeman Hamiltonian describes the diamagnetic susceptibility. This term takes the form... 

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