On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory
| Autor: | Putaja, A., Eich, F. G., Baldsiefen, T., Rasanen, E. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 93, 032503 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.93.032503 |
| Popis: | 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 $f(n,n')=(n n')^\alpha$ 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. Comment: Phys. Rev. A (in print, 2016) |
| Databáze: | arXiv |
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