A harmonic oscillator model for the magnetic properties of a closed-shell system

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Abstract
It is shown that the magnetic shielding tensor of a nucleus in the presence of a charged anisotropic harmonic oscillator may be reduced to quadrature, hence providing an exactly solvable model for the effect of Van Vleck paramagnetism on the chemical shift. Two cases are examined in detail, oblate and prolate ellipsoids of revolution. In addition the electric polarizability, magnetic susceptibility and chemical shift tensors of the H2 molecule are examined in terms of the theory.