Exchange-only virial relation from the adiabatic connection
Laestadius, Andre; Csirik, Mihaly Andras; Penz, Markus; Tancogne-Dejean, Nicolas; Ruggenthaler, Michael; Rubio, Angel; Helgaker, Trygve
Peer reviewed, Journal article
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Date
2024Metadata
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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 λ at λ = 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 (λ ↘ 0) involving the exchange–correlation potential vλ
xc, which exists by assumption of v-representability. On
the other hand, a local-exchange potential vx is not warranted to exist as such a limit.