Diamagnetic contributions

The first term is referred to as the diamagnetic contribution, while the latter is the paramagnetic part of the magnetizability. Each of the two components depend on the selected gauge origin however, for exact wave functions these cancel exactly. For approximate wave functions this is not guaranteed, and as a result the total property may depend on where the origin for the vector potential (eq. (10.61)) has been chosen. 

A common origin paramagnetic contribution can subsequently be obtained as the difference between the LORG total shielding tensor and the diamagnetic contribution from eq.(29), i.e. 

MCD results more or less confirmed the conclusions drawn from previous EPR data (27). The shapes of the MCD spectra of the putative prismane protein in the 3+, 4+, and 5+ states had not been observed for any Fe-S protein. This was not surprising, since every single type of Fe-S cluster is considered to exhibit a unique MCD spectrum. Magnetization data confirmed the S = ground state of the 5-1- state, as well as the S = 4 ground state of the 4+ state. Unexpectedly, in addition to the S = 4 contribution, a considerable diamagnetic contribution was observed for the 4-1- state. The nature of the diamagnetic contribution was not understood a physical spin mixture was considered to be a possible explanation. 

The observed proton relaxation rate, l/rlobs, is the sum of a diamagnetic contribution, 1/Tld, and the paramagnetic relaxation rate enhancement, 1/Tlp, this latter being linearly proportional to the concentration of the paramagnetic species, [Gd], In Equation (1), the concentration is usually given in mmol L 1, thus the unity of proton relaxivity, rh is mM 1 s 1. 

Fig. 7 Temperature dependence of the static magnetic susceptibility of (a) (EDT-TTFBr2)2 FeBr4 (b) (EDO-TTFBr2)2FeCl4 (c) (EDO-TTFBr2)2FeBr4 measured at an external field of B = 1 T after the core diamagnetic contributions are subtracted...

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... 

The diamagnetic contribution to the shielding tensor consists of two terms... 

From the above discussion it becomes clear that in order to eliminate the spin-orbit interaction in four-component relativistic calculations of magnetic properties one must delete the quaternion imaginary parts from the regular Fock matrix and not from other quantities appearing in the response function (35). It is also possible to delete all spin interactions from magnetic properties, but this requires the use of the Sternheim approximation [57,73], that is calculating the diamagnetic contribution as an expectation value. 

The analysis of the paramagnetic enhancement of the relaxation rates must be done after subtraction of the diamagnetic contribution from the relaxation rates of the paramagnetic sample, obtained by performing measurements on the diamagnetic analog. It is customary to refer to 1 mM concentration of paramagnetic substances to define the relaxivity of the sample. 

We have calculated the Radon core diamagnetism for actinide ions up to americium the results are reported in Table 6. These values are smaller than usually assumed in the literature. Diamagnetic contribution for localized 5f electrons are also given - From Table 6, we see that the core diamagnetism is large and has to be taken into account when a detailed analysis of the susceptibility is made. In the case of Th metal, for example, it amounts to 40% of the experimental susceptibility. 

Fig. 10.14 Measured static susceptibilities for Na and K solutions in NH3 and the calculated spin susceptibility of a set of independent electrons at 240 K (solid line). The diamagnetic contribution of the NH3 molecules has been eliminated from the measured total susceptibility by using the Wiedemann rule. Since the total susceptibility is quite small in concentrated solutions, the errors may be large. O represent data of Huster (1938) on Na solutions at 238 K represent K-NH3 data of Freed and Sugarman (1943) at the same temperature and + represent data of Suchannek et al. (1967) at room temperature for Na-NH3 solutions. From Cohen and Thompson (1968).

To evaluate ot theoretically, one must use perturbation theory. Ramsey did so (see Murrell and Harget, pp. 121-123), and found that o is the sum of two terms, a positive term od (called the diamagnetic contribution, since it decreases the applied field), and a negative term op (the paramagnetic contribution). The term op involves the usual perturbation-theory sum over excited states, and therefore is difficult to calculate however, one can use a variation-perturbation approach (Section 1.10) in op calculations. For molecular protons, od exceeds op, and aH is positive. 

The diamagnetic contribution for H2 is easily calculated theoretically, and it turns out that the paramagnetic contribution is related to something called the spin-rotation interaction constant, which can be measured experimentally. 

Few substances behave as ideal paramagnetics, even with allowance for the diamagnetic contribution of the second term in equation (55). It is found that a more practical expression for dealing with most paramagnets is a variation of the Curie— Weiss Law... 

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