A new theory of the diamagnetism of neutral molecules has been developed. The theory shines light on the significance of the role played by the gauge of the potentials describing external fields. Starting out with a Lagrangian formalism and by expanding the charge and current densities in multipole series about a configurational coordinate, a molecular Hamiltonian has been derived which is completely free of these potentials, but instead contains the fields explicitly. This has the important advantage that the diamagnetic susceptibility, obtained from this Hamiltonian, does not depend on the vector potential. Therefore, the question of which gauge to choose in order to obtain the best value of the susceptibility when only approximate wavefunctions and eigenvalues are available for computation, has become immaterial. Using simple symmetry arguments it has been shown that if the molecule is subjected to a uniform magnetic field, the natural origin of the electronic coordinates is the center of nuclear charge.
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