Larmor diamagnetic susceptibility

A qualitative explanation of these abnormally large diamagnetic susceptibilities as arising from the Larmor precession of electrons in orbits including many nuclei3 has come to be generally accepted. With the aid of simple assumptions, I have now developed this idea into an approximate quantitative treatment, described below. 

Additional evidence on electron-cloud radii is given by diamagnetic susceptibility and by refractive index. For the well-known Larmor-Langevin theory of diamagnetism (11—13) gives for the molecular diamagnetic susceptibility —Xm the formula... 

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

The quantum mechanics treatment of diamagnetism has not been published. It seems probable, however, that Larmor s theorem will be retained essentially, in view of the marked similarity between the results of the quantum mechanics and those of the classical theory in related problems, such as the polarisation due to permanent electric dipoles and the paramagnetic susceptibility. f Thus we are led to use equation (30), introducing for rK2 the quantum mechanics value... 

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