Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory

Abstract

Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are non-local functionals based on the linear-response kernel of the homogeneous electron gas, i.e. the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model, to construct a simple non-local KE functional (named KGAP) which depends on the band gap energy. In the limit of vanishing energy-gap (i.e. in the case of metals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, which is accurate for metals. For a series of semiconductors (with different energy-gaps), the KGAP performs much better than SM, and results are close to the state-of-the-art functionals with complicated density-dependent kernels.

Semilocal kinetic energy functionals with parameters from neutral atoms

“…The non-local functionals have been quite successful in describing simple metals and some semiconductors with pseudopotentials (discussed later in this chapter) due to better description of linear response. 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].…”

A New Model to Predict Optimum Conditions for Growth of 2D Materials on a Substrate

“…Starting from the most stable structure, one atom in the center region (or in the edge region) is moved step by step in one of the degrees of freedom, such as the X-axis, while the Y- and Z-coordinates and all other atoms are kept fixed to determine U′(0…xi′…0,X3M) for calculating Lx1, Ly1, Lz1 (or Lx2, Ly2, Lz2). Clearly, it is an easy task for traditional ab initio algorithms and recently-developed DFT [45,46].…”

“…The difference may have resulted from the limited computational precision of DFT. For calculating U0 and U′(0…xi′…0,X3M) in Equation (13) and (16), it is well known that the calculation results of DFT depend significantly on the specifically employed basis sets and exchange-correlation functionals of the electron density, for which the recent work [45,46] might provide better choices.…”

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 .…”