Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

Abstract

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free-energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T. Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature

“…There has been recent work to explore formulations of QMC where the sign problem is less severe under the conditions of interest, including the configuration path integral Monte Carlo (CPIMC) 33 and density matrix quantum Monte Carlo (DQMC) 34,35 . Much of this research has been motivated by calculations on the uniform electron gas for the benchmarking and/or parameterization of finite temperature density functionals 17,36,37 . We will return to this topic in Section IV B.…”

Generalized hydrodynamics revisited

“…All local equilibrium averages therefore become functionals of the conjugate variables, or equivalently of the average conserved fields. To make these two representation clear the notation in the following will be X (r) ; ρ ℓ [y(t)] ≡ X ℓ (r |y(t)) ≡ X (r |ζ(t)) , (27) where the one-to-one relationship of (16a) -(16c) can be expressed as y(r,t) = y(r |ζ(t)) or its inverse ζ(r,t) = ζ(r |y(t)). (28) This functional relationship is local in time.…”

“…where the notation introduced in Eq. (27) has been extended for the local equilibrium average of products by defining…”

“…A direct approach by standard many-body methods is very challenging. Density functional theory (DFT) for equilibrium properties of such states has met with some significant success 27 . Applications of time dependent density functional theory (TDDFT) are still at an early stage in this context [28][29][30] .…”

Exchange-correlation thermal effects in shocked deuterium: Softening the principal Hugoniot and thermophysical properties

“…where f xc is the XC free-energy per particle given by the corrKSDT parameterization, 16,17 e xc is the zero-temperature XC energy per particle, 18 and f s is the noninteracting free energy per particle. 19 r t focus on the study of the optical and transport properties along the principal Hugoniot of deuterium with a temperature-dependent Karasiev-Dufty-Trickey (KDT16) generalized gradient approximation XC functional.…”