On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory

Abstract

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 $f(n,n^{\prime })=(n{n}^{\prime }{)}^{\alpha }$ 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 $\alpha$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition $n(\mathbf{k})<1$ for all wave vectors $\mathbf{k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $\alpha$ 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 $\alpha \gtrsim 0.6$ and at $r_s\gtrsim 10$ for the density parameter, corresponding to relatively low densities.

arXiv commentPhys. Rev. A (in print, 2016)

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Cited by in corpus (2)

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