# Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †

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*T*Density-Functional Theory and Warm-Correlated Matter”. In Proceedings of the 16th International Conference on Density Functional Theory and Its Applications, Celebrating the 50th Anniversary of the Kohn-Sham Theory, Debrecen, Hungary, 31 August–4 September 2015.

## Abstract

**:**

## 1. Introduction

## 2. Exchange-Correlation at Finite-T

#### 2.1. Do We Have Reliable Thermal-XC Functionals?

#### 2.2. Can We Ignore Thermal Corrections and Use the $T=0$ Implementations?

#### 2.3. Can We Define Free and Bound Electrons in an “Unambiguous” Manner?

## 3. Future Challenges in Formulating Finite-T XC Functionals

#### 3.1. Classical-Map Hyper-Netted Chain Method

## 4. Conclusions

## Conflicts of Interest

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**Figure 1.**(Color online) Finite-T exchange and correlation free energy ${f}_{xc}({r}_{s},T)$ per electron (Hartrees) versus the reduced temperature $T/{E}_{F}$ in units of the Fermi energy. The symbols, labeled PIMC-KSDT are the fit given by Karasiev et al. (Reference [60] to the path-integral Monte Carlo (PIMC) data of Brown et al. [59]). The continuous lines, labeled CHNC-PDW are from the classical-map HNC procedure of Perrot and Dharma-wardana [42]. The temperature range $0<T/{E}_{F}\le 1$ is the region of interest for WDM studies.

**Figure 2.**(Color online) The NPA free-electron density ${n}_{f}\left(r\right)$ using PDW finite-T XC and with the $T=0$ XC. Inset: ${n}_{f}\left(r\right)$ inside the Wigner-Seitz sphere, with ${r}_{ws}\simeq $ 3.0 Bohr.

**Figure 3.**(

**a**) Here, the CHNC g(r) are compared with VMC and DMC simulation results: the interacting PDFs ${g}_{11}\left(r\right)$ and ${g}_{12}\left(r\right)$ at ${r}_{s}$ = 1 are shown. Solid lines: CHNC, boxes: DMC, dashed line: VMC [79]; Panel (

**b**) ${r}_{s}=5$, DMC [79] and HNC; In (

**c**), the paramagnetic $g\left(r\right)$ at ${r}_{s}$ = 1 and ${r}_{s}$ = 10, T = 0 are compared with DMC; (

**d**) Finite temperature PDFs (CHNC) for $T/{E}_{F}$ = 2, ${r}_{s}$ = 5 would correspond to a WDM at ≃ 3.6 eV (∼ 42,000 K).

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Dharma-wardana, M.W.C.
Current Issues in Finite-*T* Density-Functional Theory and Warm-Correlated Matter †. *Computation* **2016**, *4*, 16.
https://doi.org/10.3390/computation4020016

**AMA Style**

Dharma-wardana MWC.
Current Issues in Finite-*T* Density-Functional Theory and Warm-Correlated Matter †. *Computation*. 2016; 4(2):16.
https://doi.org/10.3390/computation4020016

**Chicago/Turabian Style**

Dharma-wardana, M. W. C.
2016. "Current Issues in Finite-*T* Density-Functional Theory and Warm-Correlated Matter †" *Computation* 4, no. 2: 16.
https://doi.org/10.3390/computation4020016