Semilocal Pauli–Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids

Abstract

Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of nonlocal functionals, possibly employing system-dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that, instead, properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian level of theory, can indeed achieve similar accuracy as nonlocal functionals and can be accurate for both metals and semiconductors, without the need for system-dependent parameters.

Semilocal kinetic energy functionals with parameters from neutral atoms

“…where the first term is the von Weizsäcker term T vW and the second term has two parameters C 2 and p, which need to be fixed. The RATIONAL p form unifies two previous kinetic energy functionals: Pauli-Gaussian [51] and LKT [50]. Any positive value of p yields a quite well performing kinetic functional.…”

“…Following the constraintbased development of energy functionals, we construct a new family of functionals: RATIONAL, which has two free parameters C 2 and p. The C 2 parameter is related to the gradient expansion of the kinetic energy via the small-s expansion. The parameter p unifies previously studied Pauli-Gaussian [51] and LKT functionals [50] into one parametrized family.…”

“…The general trend seems to imply that while the non-local functionals do achieve better performance, improvements do come at the cost of specialization to a certain type of system [47,48,49]. Semilocal functionals do have a lower performance if we directly compare the best performing non-local functional and best performing semilocal on a chosen material but semilocal functionals are easily applied to any type of system (periodic, isolated) and have a competitive average performance [50,51]. However there are known limitations for performance on solids [52,53,54].…”

Nonlocal kinetic energy density functionals for isolated systems obtained via local density approximation kernels

“…, which associates with the average density ( 0  ) in the unit cell for extended systems. Unfortunately, the average density in isolated systems is not well defined [25].…”

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

“…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 .…”