Abstract
A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.
Highlights
We show that we can develop a relativistic (current) density-functional theory (RDFT) formalism based on this effective QED theory using the constrained-search formalism [32, 33] in a quite similar way to non-relativistic density-functional theory (DFT)
We have examined a RDFT based on an effective QED without the photon degrees of freedom
The formalism is appealing since it is simpler than RDFT based on full QED
Summary
The basic formulation of the relativistic extension of density-functional theory (DFT) was first laid down by generalizing the Hohenberg-Kohn theorem [1] to a Hamiltonian based on quantum electrodynamics (QED) with the internal quantized electromagnetic field and an external classical electromagnetic field [2,3,4,5]. These early works did not address the subtle issues of QED renormalization. Hartree atomic units (a.u.) are used throughout the paper
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