Exchange-only virial relation from the adiabatic connection

Abstract

The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength $\lambda$ at $\lambda =0$. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on $v$-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit ($\lambda \searrow 0$) involving the exchange-correlation potential $v_{\mathrm{xc}}^{\lambda }$, which exists by assumption of $v$-representability. On the other hand, a local-exchange potential $v_{\mathrm{x}}$ is not warranted to exist as such a limit.

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Cited by in corpus (2)

• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
• Density-functional theory for the Dicke Hamiltonian