Leading corrections to local approximations

Abstract

For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential. Turning points produce quantum oscillations leading to energy corrections, which are completely different from the gradient corrections that occur in bulk systems with slowly-varying densities. Approximations that include quantum corrections are typically much more accurate than their local analogs. The consequences for density functional theory are discussed

Electronic Structure via Potential Functional Approximations

“…[16]. The small discontinuity at about x ¼ 0:2 and 0.8 is where the approximation switches from a form that is asymptotically correct in the interior to one that is asymptotically correct near the walls.…”

“…Note that the approximation for t S ðxÞ of Ref. [16] is already a considerable improvement over that used in Ref. [15].…”

Efficient formalism for warm dense matter simulations

“…Most closely related to this work is the pioneering pathintegral formalism of Yang [26,27] which goes beyond the gradient expansion at finite temperature. An advantage of PFT is that it generates leading corrections to zerotemperature local approximations [22], which become exact in the well-known Lieb limit [28]. Finite-temperature Thomas-Fermi theory [29,30] becomes relatively exact for non-zero temperatures under similar scaling [31].…”

“…In this way, one needs only find a sufficiently accurate density approximation [22]. Approximations to the non-interacting density have been derived in various semiclassical [22][23][24], and stochastic approaches [25]. Most closely related to this work is the pioneering pathintegral formalism of Yang [26,27] which goes beyond the gradient expansion at finite temperature.…”

“…PFT's coupling-constant formalism automatically generates a highly accurate kinetic energy potential functional approximation (PFA) for any density PFA [20]. In this way, one needs only find a sufficiently accurate density approximation [22]. Approximations to the non-interacting density have been derived in various semiclassical [22][23][24], and stochastic approaches [25].…”