Kinetic energy density of nearly free electrons. I. Response functionals of the external potential

Abstract

Free electrons have a uniform kinetic energy density (KED), which evolves into a spatially varying quantity as the electrons respond to the gradual imposition of an external potential. In this paper and a companion paper, we examine two sets of functionals for describing the local, non-negative KED that emerges after such a perturbation. In this paper, we emphasize potential functionals, deriving the first-and secondorder deviations from the free-electron KED as functionals of the perturbing potential, also reconsidering the analogous functionals for the local density of states and the electron density. (In the second paper, we use these results to re-express the KED response in terms of functionals of the induced electron density.) We develop reciprocal-space formulations of the response kernels to complement previously known real-space forms. The first-order function is straightforward to obtain, but the second-order function requires considerable effort. To manage the derivations, we relate the KED response to that of the one-electron Green function, and then examine the latter in detail. Finally, we provide extensive validation of the derived response functions based on asymptotic analysis of an integral representation, numerical integration of the same generating integral, and application to the linear potential model.

Random Structure Searching with Orbital-Free Density Functional Theory

“…However, kinetic energy functional development is an active area of research, 26 − 32 and numerous approximate functionals, having various desirable features, are available. 9 − 12 Some, like ours, enforce the T s ≥ T W constraint by construction.…”

Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

“…Specifically, we have used the variables in Eqs. (16), (17) and the approximate relationship Eq. (21) between F τ and F σ .…”

“…Both semilocal and non-local functionals have achieved mixed successe in treating condensed phases and their ingredient atoms, molecules, and clusters and solids. Such functionals are either constraint-based and non-empirical [8][9][10][11][12][13][14][15][16][17][18] or semi-empirical 19,20 . With any significant ground-state advance, an obvious, important associated step is generalization to a non-interacting free energy functional F s .…”

Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes

“…33,36,37 On the other hand, the parameter range corresponding to densities r s 2 and temperatures 0.01 θ < 1 is highly important for numerous applications. For example, recently it was shown that the static non-linear density response functions of the electron gas can be used for the construction of advanced kinetic energy functionals required for orbital-free density functional theory (OF-DFT) based simulations 38,39 with applications at ambient 40 as well as extreme conditions. 41,42 Additionally, non-linear density response functions can extend quantum fluid models (quantum hydrodynamics and time-dependent orbital-free density functional theory) beyond the weak perturbation regime.…”