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Journal Article

Validity of power functionals for a homogeneous electron gas in reduced-density-matrix-functional theory


Eich,  Florian G.
Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA;

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Putaja, A., Eich, F. G., Baldsiefen, T., & Räsänen, E. (2016). Validity of power functionals for a homogeneous electron gas in reduced-density-matrix-functional theory. Physical Review A, 93(3): 032503. doi:10.1103/PhysRevA.93.032503.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-3B12-9
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f(n,n′) = (nn′)α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n(k) < 1 for all wave vectors k. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳ 0.6 and at rs ≳ 10 for the density parameter, corresponding to relatively low densities.