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 $f(n,{n}^{\ensuremath{'}})={(n{n}^{\ensuremath{'}})}^{\ensuremath{\alpha}}$ 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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}\ensuremath{\gtrsim}0.6$ and at ${r}_{s}\ensuremath{\gtrsim}10$ for the density parameter, corresponding to relatively low densities.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 $f(n,{n}^{\ensuremath{'}})={(n{n}^{\ensuremath{'}})}^{\ensuremath{\alpha}}$ 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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}\ensuremath{\gtrsim}0.6$ and at ${r}_{s}\ensuremath{\gtrsim}10$ for the density parameter, corresponding to relatively low densities.

arXiv:1602.03624Physical Review AMar 10, 20163 citations

Improved tensor-product expansions for the two-particle density matrix

Gábor Cśanyi, Stefan Goedecker, T. A. Arias

We present a density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming the Hartree-Fock method at metallic valence electron densities. For isolated atoms and ions, it is on par with generalized-gradient approximations to the density-functional theory. We also present analytic results for the correlation energy in the low-density limit of the free-electron gas for a broad class of such functionals.We present a density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming the Hartree-Fock method at metallic valence electron densities. For isolated atoms and ions, it is on par with generalized-gradient approximations to the density-functional theory. We also present analytic results for the correlation energy in the low-density limit of the free-electron gas for a broad class of such functionals.

arXiv:cond-mat/0107536Physical Review AFeb 20, 200274 citations

Remarks on the density functional approach to the inhomogeneous electron gas

Mojmír Tomášek, V. Mikoláš

Physica A Statistical Mechanics and its ApplicationsMar 1, 19792 citations

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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}\ensuremath{\gtrsim}0.6$ and at ${r}_{s}\ensuremath{\gtrsim}10$ for the density parameter, corresponding to relatively low densities.