Properties of Collective Electrons

According to the collective-electron model developed in the last paragraph, each state is filled with two electrons, one of each spin, 

In the case of free atoms, it was shown possible to understand intuitively how the exchange correlations give rise to internal mag- 

Substitution into equation 9 and summation over all excited states and over N molecules gives 

The diamagnetic term for molecules is given by equation 12, just as in the case of atoms, except that the r for the electrons may be considerably greater in molecules than in atoms. Van Vleck (628) has emphasized that temperature-independent susceptibilities cannot be accounted for by equation 12 alone since contributions of the type expressed by equation 55 are always present and may even be of sufficient magnitude to give a net positive, temperature-independent susceptibility from field-induced atomic moments. 

In a series of comprehensive magnetochcmical investigations, Pascal (501,602) found that the molecular susceptibility of diamagnetic, organic compounds can be closely represented by 

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