An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low-and high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility. PACS numbers:The homogeneous electron gas (HEG) is a fundamentally important system for understanding many-fermion physics. In the absence of exact analytical solutions for its energetics, high-precision numerical results have been critical to insight. Recently published [1] restricted path integral Monte Carlo (RPIMC) data for the HEG over a wide range of temperatures and densities open the opportunity to obtain closed form expressions for HEG thermodynamics, in particular the exchange and correlation (XC) contributions. Such expressions extracted from Monte Carlo data are well-known for the zero-T HEG, where they have played a major role in understanding inhomogeneous electron-system behavior. We provide the corresponding thermodynamical expressions for wide temperature and density ranges.Density functional theory (DFT) is the motivating context. For ground-state DFT, the most basic exchangecorrelation (XC) density functional is the local density approximation (LDA). It approximates the local XC energy per particle, ε xc , as the value for the HEG at the local density, ε LDA xc (n(r)) ≈ ε HEG xc (n)| n=n(r) [also see Eq. (3) [5] for the spin-polarized T = 0 K HEG also validate the spininterpolation formulae used in that case, the local spin density approximation (LSDA). All more refined ε xc approximations reduce to the LSDA in the weak inhomogeneity limit.Finite-temperature DFT [6-8] increasingly is being used to study matter under diverse density and temperature conditions [9][10][11][12][13][14]. In it, the XC free-energy is defined by decomposition of the universal free-energy density functional (independent of the external potential). With the T -dependence suppressed for now, that functional isThe first two terms are the non-interacting kinetic energy and entropy (also known as the Kohn-Sham KE and entropy), F H [n] is the classical electron-electron Coulomb energy, and the XC free energy by definition iswith T [n] and S[n] the interacting system kinetic energy and entropy and U ee [n] the full quantum mechanical electron-electron interaction energy. Just as for T = 0 K, the existence theorems of finite-T DFT are not constructive for F xc , so approximations must be devised. Common practice [9] in simulations is to use a. This gives only the implicit T -dependence provided by n(r, T ). However, there is substantial evidence from both finite-T Hartree-Fock [12,15] and finite-T exac...

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We report the first wholly non-empirical generalized gradient approximation, non-interacting free energy functional for orbital-free density functional theory and use that new functional to provide forces for finite-temperature molecular dynamics simulations in the warm dense matter (WDM) regime The new functional provides good-to-excellent agreement with reference Kohn-Sham calculations under WDM conditions at a minuscule fraction of the computational cost of corresponding orbital-based simulations. PACS numbers: 31.15.E-, 71.15.Mb, 05.70.Ce, 65.40.G-Compared to ordinary condensed matter, the warm dense matter (WDM) regime [1, 2] poses experimental accessibility issues (e.g. inertial confinement fusion hohlraums [3]) that make computational characterization of WDM thermodynamics particularly significant. Current practice, for example Refs. [4, 5], is ab initio molecular dynamics (AIMD) with Born-Oppenheimer electronic forces on the ions from finite-T Kohn-Sham (KS) density functional [6-8] calculations. Computational costs for KS-AIMD scale no better than N 3 b per MD step, with N b the number of occupied KS orbitals. N b grows unfavorably with increasing T . KS-AIMD thus becomes prohibitively expensive at elevated T and path integral Monte Carlo (PIMC) simulations, which have comparable computational cost, come into play [2].A long-standing potential alternative to KS-DFT, orbital-free DFT (OFDFT), would scale linearly with system size. Use of OFDFT for WDM has been limited by clearly inadequate functionals, e.g. , for the non-interacting kinetic energy (KE) part T s of the free energy (though TF is, of course, the proper KS limit for high T and high material densities [5]). Ground-state two-point orbital-free KE functionals [10] are, unfortunately, of little utility for extension to WDM because those two-point functionals which treat different material phases equally well are both parameterized and introduce substantial extra computational complexity. Therefore we have focused on single-point functionals.Here we provide a new, non-empirical, generalized gradient approximation (GGA) T s functional and its associated entropy functional. They extend and rationalize the constraint-based, mildly empirically parameterized GGA functionals recently published [11]. We show that the new functionals make OFDFT-AIMD competitive with finite-T KS-AIMD calculations for accuracy and far faster. For deuterium in the WDM regime, the OFDFT AIMD and reference KS results agree well at intermediate T , 6 × 10 4 → 1.8 × 10 5 K. In the range