Abstract
We construct a gauge-invariant approximation of the energy density of an interacting electron gas in the presence of a non-uniform magnetic field. The interaction is approximated by a slowly varying local potential. The magnetic field is a superposition of a constant field B and that due to a magnetic dipole μ, thus making the energy density suitable for direct calculation of chemical-shift tensors of, for example, interacting closed-shell systems. Unlike a similar theory for the magnetic susceptibility, the field-dependent exchange energy does not diverge.
Highlights
We present the basic requirement for an electron-gas calculation of the chemicalshift tensor: a gauge-invariant approximation to the ground-state energy density of an interacting electron gas in the presence of a constant magnetic field and a magnetic dipole
Cina and Harris [7] did this for the slowly varying magnetic field, and, assuming additivity of the densities of the components, made the first electron-gas calculation of the diamagnetic susceptibility of the triplet hydrogen state. They had to leave out the lowest-order direct-exchange contribution, because it diverged
Following the section with our calculations, we remark on the finiteness of the exchange contribution and on how the energy-density functional may be used to calculate a chemical-shift tensor
Summary
We present the basic requirement for an electron-gas calculation of the chemicalshift tensor: a gauge-invariant approximation to the ground-state energy density of an interacting electron gas in the presence of a constant magnetic field and a magnetic dipole. Cina and Harris [7] did this for the slowly varying (locally constant) magnetic field, and, assuming additivity of the densities of the components, made the first electron-gas calculation of the diamagnetic susceptibility of the triplet hydrogen state. They had to leave out the lowest-order direct-exchange contribution, because it diverged. With the energy-density functional of an interacting electron gas in such a field, one could calculate the interaction contribution to the chemical-shift tensors of interacting closed-shell systems. Following the section with our calculations, we remark on the finiteness of the exchange contribution and on how the energy-density functional may be used to calculate a chemical-shift tensor
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