Exchange-correlation potentials in the adiabatic connection fluctuation-dissipation framework

2003/09/11 by Yann‐Michel Niquet, Martin Fuchs, Xavier Gonze · 1 voice
Physics and Astronomy · #Advanced Chemical Physics Studies #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies

paper · doi:10.1103/physreva.68.032507

openalex publication_date 2003/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide the expression of the exchange-correlation potential in the adiabatic connection fluctuation-dissipation (ACFD) framework, for arbitrary time-dependent (TD) kernels. We investigate the asymptotic behavior of the ACFD potential in three relevant approximations: the random-phase approximation, the exact-exchange kernel in two-electron systems, and the adiabatic local-density approximation. We show that these potentials have the expected \ensuremath-1/r+Q/r³\ensuremath-\ensuremathα/(2r⁴) tail (in closed-shell systems with spherical symmetry), where Q and \ensuremathα depend on the TD kernel and reflect the physics included in each approximation. We also discuss approximate ACFD potentials that are much simpler to compute than the exact ones while being likely of reasonable accuracy.

Citations

• New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
• Density-functional thermochemistry. III. The role of exact exchange

Discussions

• I am looking at the Exchange energy as an integral over non-interactions greens functions: $$ E_x = - \int \frac{dv}{2\pi} e^{i v \delta'} \int \frac{du}{2\pi} e^{i u \delta} \int d^3 \mathbf{r} \int [stackexchange, 4 points]

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