Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations

Abstract

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

Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory

“…Consideration of more "difficult" conditions involving larger density gradients, such as aluminum calculations to temperatures above 10 eV, or of other elements that are less free-electron like, require further developments of orbital-free functionals. Potential research areas include the search for advanced orbital-free functionals of higher order in the density gradients [30]; the development of accurate local pseudopotentials, as the transferability of the current pseudopotentials across densities and temperatures remains an issue, and for some elements and conditions they have been simply unattainable; the development of density functionals with a density decomposition, such as has been explored for transition metals at zero temperature [31].…”

Comment on “Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation”

“…See Fig. 6 7 .) The physical justification is that such contributions are comparatively small even though the lower branch of G substantially exceeds unity because n is small (hence one expects n 5/3 to be smaller yet), so a GGA underestimate of G in that region should be a satisfactory approximation.…”

“…PBE2 has been supplanted by our VT84F, a non-empirical OFKE GGA functional which obeys all of the foregoing bounding and asymptotic properties 7 . X-C did not test it.…”

Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

“…for arbitrary proper n. Nevertheless, progress on functionals t approx θ that do meet those constraints and do a reasonably good job of reproducing conventional KS binding energy curves, equations of state, etc., 35,37,38 suggests that one should try those functionals.…”