arXiv subjects

Lázaro Calderín

Publications and source records attributed to Lázaro Calderín.

3 recordsLinked to original sources

arXiv2016

The importance of finite-temperature exchange-correlation for warm dense matter calculations

Effects of explicit temperature dependence in the exchange-correlation (XC) free-energy functional upon calculated properties of matter in the warm dense regime are investigated. The comparison is between the KSDT finite-temperature local density approximation (TLDA) XC functional [Phys.\ Rev.\ Lett.\ \textbf{112}, 076403 (2014)] parametrized from restricted path integral Monte Carlo data on the homogeneous electron gas (HEG) and the conventional Monte Carlo parametrization ground-state LDA XC functional (Perdew-Zunger, "PZ") evaluated with $T$-dependent densities. Both Kohn-Sham (KS) and orbital-free density functional theory (OFDFT) are used, depending upon computational resource demands. Compared to the PZ functional, the KSDT functional generally lowers the direct-current (DC) electrical conductivity of low density Al, yielding improved agreement with experiment. The greatest lowering is about 15\% for T= 15 kK. Correspondingly, the KS band structure of low-density fcc Al from KSDT exhibits a clear increase in inter-band separation above the Fermi level compared to the PZ bands. In some density-temperature regimes, the Deuterium equations of state obtained from the two XC functionals exhibit pressure differences as large as 4\% and a 6\% range of differences. However, the Hydrogen principal Hugoniot is insensitive to explicit XC $T$-dependence because of cancellation between the energy and pressure-volume work difference terms in the Rankine-Hugoniot equation. Finally, the temperature at which the HEG becomes unstable is $T\geq$ 7200 K for $T$-dependent XC, a result that the ground-state XC underestimates by about 1000 K.

cond-mat.mtrl-sci↗

arXiv2014

Scaling of the known exact explicit forms of the non-interacting kinetic-energy density functional

It has been previously proven that the Kohn-Sham kinetic energy functional scales homogeneusly under generalized coordinate scaling, in a way that is obeyed by the von Weizäcker functional, but seems to be in contradiction with the scaling of the Thomas-Fermi functional. A very puzzling situation, taking in to account that the von Weizäcker and Thomas-Fermi functionals are exact cases of the Kohn-Sham kinetic energy functional for two electron systems, and the non-interacting electron gas, respectively. The apparent contradiction is resolved in this paper.

quant-ph↗

arXiv2014

Scaling Invariance of Density Functionals

Based on the homogeneity ($F[n_{λm}]=λ^{p(m)}F[n]$) and invariance ($F[n_{λm_0}]=F[n]$) properties of a functional of the electron density under uniform scaling of the coordinates in the density $n_{λm}(\mathbf{r})=λ^{m} n(λ\mathbf{r}),\,(λ\in\mathbb{R}^+,\, m\in\mathbb{R})$, it is proven that homogeneity implies invariace and therefore all homogeneous scaling functionals have the representation $F[n]=\frac{m-m_0}{p(m)} \int_V\,\frac{δF[n]}{δn(\mathbf{r})}\,n(\mathbf{r})\,d^3r$. Also, the homogeneity ($p(m)$) and invariant ($m_0$) degrees of density functionals related to the Kohn-Sham theory are calculated. Besides, it is shown that the functional density and the electron density itself satisfy the general equation representing the local scaling invariance of a functional $λ\frac{d}{dλ} f([n_{λm_0}],\mathbf{r},\mathbf{r'}) = \sum_{i=1}^3 \frac{d}{d x_i} [ x_i f([n_{λm_0}],\mathbf{r},\mathbf{r'}) ] + \sum_{j=1}^3 \frac{d}{d x_j'} [ x_j' f([n_{λm_0}],\mathbf{r},\mathbf{r'}) ] $. The equation simplifies for cases where the functional density depends only on the density and/or its gradient, and general forms of the solutions are provided, in particular for the non-interacting kinetic energy density is shown to take the form $t_s(n,\nabla n)= n(\mathbf{r})^{3} g[ \frac{\partial_{x_1} n(\mathbf{r})}{n(\mathbf{r})^2}, \frac{\partial_{x_2} n(\mathbf{r})}{n(\mathbf{r})^2}, \frac{\partial_{x_3} n(\mathbf{r})}{n(\mathbf{r})^2}]$ .

math-ph↗