Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field

The Journal of Chemical Physics
Anirban Mandal, Katharine L C Hunt

Abstract

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels ...Continue Reading

References

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Jul 26, 2006·The Journal of Chemical Physics·Mykhaylo Krykunov, Jochen Autschbach
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May 3, 2014·The Journal of Chemical Physics·Silvio PipoloRoberto Cammi
Feb 12, 2015·The Journal of Chemical Physics·E I TellgrenT Helgaker
Jul 24, 2015·The Journal of Chemical Physics·Anirban Mandal, Katharine L C Hunt

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