mBEEF: An accurate semi-local Bayesian error estimation density functional

Abstract

Adsorption of transition-metal atoms on boron nitride nanotube: A density-functional study J. Chem. Phys. 125, 044711 (2006) (2012)]. The functional is designed to give reasonably accurate density functional theory (DFT) predictions of a broad range of properties in materials physics and chemistry, while exhibiting a high degree of transferability. Particularly, it improves upon solid cohesive energies and lattice constants over the BEEF-vdW functional without compromising high performance on adsorption and reaction energies. We thus expect it to be particularly well-suited for studies in surface science and catalysis. An ensemble of functionals for error estimation in DFT is an intrinsic feature of exchange-correlation models designed this way, and we show how the Bayesian ensemble may provide a systematic analysis of the reliability of DFT based simulations.

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…[143][144][145][146][147] Moreover, a KS can distinguish and quantify the orbital overlap, [148] the nonlocality of the KED at the nuclear cusp, [133] in the tail of the density, [133,149] and in the quasi-two-dimensional regime. [150] Due to these remarkable features, a KS is the main KED dependent ingredient for recent nonempirical (or semi-empirical) [66,67,148,[151][152][153] and highly empirical [28] meta-GGA XC functionals. …”

“…The meta-Bayesian error estimation functional (mBEEF) functional [28] has been developed combining the machine learning approach [130] with the Bayesian error estimate. [344] The mBEEF exchange enhancement factor (Equation 5) is…”

“…For example, meta-GGAs can more accurately describe both surfaces energies and surface chemisorption. [28,30,31] Furthermore current state-ofthe-art meta-GGA functionals can achieve the accuracy of hybrid functionals, which belong to the higher, fourth rung of the Jacob's ladder. This is of utmost importance since hybrid functionals contain additionally a fraction of the nonlocal Hartree-Fock exchange, which requires a much larger computational cost than meta-GGA functionals.…”

“…[12,18] However, due to their simplicity, GGA functionals are generally unable to describe with good accuracy different electronic regimes [19][20][21][22] despite some recent progresses. [23][24][25][26] As a relevant example, we mention the failure of GGAs to correctly describe both surfaces and chemisorption energies, [27][28][29][30][31] which is instead more easily achievable at higher rungs.The third rung is the topic of this Review. At this level, in addition to the GGA variables, other input quantities are considered: the Laplacian of the density (r 2 q) and/or the positive-defined KS kinetic energy density (KED)…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Meta-generalized gradient approximations (meta-GGAs) [31][32][33][34][35][36][37][38][39][40][41][42] are the most sophisticated semilocal functionals, incorporating important exact conditions and having an improved overall accuracy with respect to the GGA functionals. The meta-GGA functionals use as an additional ingredient to the GGA ones the Kohn-Sham positive KE density:…”