Abstract
We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead, it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent settings. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater Xα approximations.
Highlights
It is hard to doubt that the Achilles heel of density-functional theory (DFT) is the lack of highly accurate and at the same time generally applicable approximate functionals
We provide straightforward exchangetype approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater Xα approximations
There are several further subtle problems associated with using energy or action [in time-dependent density-functional theory (TDDFT)] functionals in order to construct approximate xc potentials
Summary
It is hard to doubt that the Achilles heel of density-functional theory (DFT) is the lack of highly accurate and at the same time generally applicable approximate functionals. We introduce a systematic way to employ problemadopted EOMs for obtaining exact determining relations for xc potentials that link the interacting and noninteracting systems of the Kohn–Sham construction for different density-functional theories In some settings, these relations were already discussed and their integrated forms are known as the zero-force and zerotorque constraint for vxc, which exist both for the static and time-dependent scalar xc potential.. Setting the vector potential to zero and making the potential timeindependent, we obtain a pointwise relation determining vxc of ground-state DFT (as in the original Hohenberg–Kohn formulation) These exact relations allow us to straightforwardly establish problem-adopted exact-exchange-type approximations without the above-mentioned drawbacks of energy- and action-functional-based approaches.
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