A hydrodynamic model for diamagnetic induced currents in molecules

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Abstract
The current set up when a single bound electron moves in a magnetic field obeys simple hydrodynamic equations, which arise from a variational principle. When the ground state is not degenerate they have a unique solution, determined by the unperturbed electron density. The theory is closely related to Wick's irrotational flow model for the currents in a rotating molecule, to Tillieu and Guy's variational method, and London and Rebane's ideas of gauge invariance. Difficulties arise when there is more than one electron, when the wave function has nodes, or when it is degenerate; but the method may be useful for calculating magnetic properties of some small molecules.