Abstract
Finite-temperature density functional theory (DFT) has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM).Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM) may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature Te is comparable to the electron Fermi energy EF. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge Zj. Quasi-equilibria with the ion temperature Ti ≠ Te are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in T = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-T exchange-correlation (XC) functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities ρj. Here, j counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated in situ, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-T DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented.
Highlights
This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of Warm-dense matter (WDM) systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data
There are no systems at zero temperature available to us, it is the quantum mechanics of the simpler T = 0 systems that has engaged the attention of theorists
We have argued that our current knowledge of the thermal XC-functionals is satisfactory and the stage is set for their implementation in practical density functional theory (DFT) codes
Summary
Attempts to apply thermal-DFT ( called finite-T DFT, th-DFT) to WDM-like systems were undertaken by the present author and François Perrot in the early 1980s as reviewed in Reference [21] This involved a reformulation of the neutral-pseudoatom (NPA) model that had been formulated by Dagens [22] for zero-T problems, as it has the versatility to treat solids, liquids and plasmas. Once the pair-potential is available, the Hyper-Netted Chain equation (and its modified form incorporating a bridge function) can be used to calculate an accurate gii (r ) if desired, rather than via the direct iterative procedure used in Reference [27] This finite-T NPA approach is capable of accurate prediction of phonons (i.e., milli-volt energies) in WDM systems, as shown explicitly by Harbour et al [33] using comparisons with results reported by Recoules et al [34] who used the Vienna Ab Initio Simulation Package (VASP). The ion-ion correlations are highly non-local and the LDA or its extensions are totally inadequate since they are described by the HNC approximation
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