Minnesota functionals | EPFL Graph Search

Minnesota Functionals (Myz) are a group of highly parameterized approximate exchange-correlation energy functionals in density functional theory (DFT). They are developed by the group of Prof. Donald Truhlar at the University of Minnesota. These functionals are based on the meta-GGA approximation, i.e. they include terms that depend on the kinetic energy density, and are all based on complicated functional forms parametrized on high-quality benchmark databases. These functionals can be used for traditional quantum chemistry and solid-state physics calculations. The Myz functionals are widely used and tested in the quantum chemistry community. Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties have, however, cast doubts on the accuracy of Minnesota functionals. Some regard this criticism to be unfair. In this view, because Minnesota functionals are aiming for a balanced description for both main-group and tr

Nonempirical hybrid functionals for advanced electronic-structure calculations

Thomas Bischoff

Electronic-structure calculations based on hybrid functionals have emerged as a standard technique used in physics, chemistry, and material science. Despite this success, hybrid functionals have the drawback of containing undetermined parameters. To overcome this deficiency, two different nonempirical determination schemes are being investigated at present, namely dielectric-dependent hybrid (DDH) functionals and hybrid functionals that satisfy Koopmans' condition. This thesis is dedicated to the examination and further development of these approaches. In particular, we show that a precise description of band gaps in condensed-matter systems can be achieved with these functionals. Moreover, we demonstrate that their accuracy is comparable to state-of-the-art

GW

methods while requiring substantially lower computational cost. First, we focus on the development of hybrid functionals satisfying Koopmans' condition. We show that the construction of those functionals can be optimized through suitably defined potential probes. By monitoring the delocalized screening charge, we achieve a measure of the degree of hybridization with the band states, which can be used to improve the band-gap estimate. We show that the application of this methodology to common semiconducting and insulating materials yields band gaps differing by less than 0.2 eV from experiment. These conceptual developments are an important step towards establishing hybrid functionals satisfying Koopmans' condition as a robust approach for band-gap predictions. Second, we examine DDH functionals and hybrid functionals satisfying Koopmans' condition for band gaps of more sophisticated materials. In particular, we focus on inorganic metal-halide perovskites which have recently drawn great scientific attention. For this class of materials, we show that both nonempirical hybrid-functional schemes yield band gaps of comparable accuracy (

\sim

0.2 eV) with respect to

GW

reference calculations. Furthermore, we discuss the suitability of nonempirical hybrid-functional schemes for the application to the screening of large sets of perovskite materials. Third, we investigate the fundamental band gap of liquid water and hexagonal ice. These materials are particularly challenging since experimental studies have not reached a consensus on the band gap yet. Therefore, we first deduce robust benchmarks on the basis of a critical review of various experimental studies in the literature. Then, we compute the band gap through state-of-the-art

GW

methods as well as nonempirical hybrid functionals. We show that theoretical calculations and experimental references are in good agreement with each other and we discuss critical aspects which are essential to ensure a consistent description of the band gap. Finally, we investigate band-edge levels as obtained with hybrid-functional calculations. The CaF

_2

/Si(111) interface serves thereby as an ideal test case to examine the accuracy of different theoretical schemes. The comparison with experiment reveals that global hybrid functionals and self-consistent

GW

methods provide the most accurate description of the interfacial band alignment.

EPFL2021

Band offsets of lattice-matched semiconductor heterojunctions through hybrid functionals and G(0)W(0)

Wei Chen, Alfredo Pasquarello, Karim Steiner

To assess the accuracy of hybrid functional and many-body GW methods, we study the band offsets for a set of lattice-matched semiconductor heterojunctions, including AlAs/GaAs(100), AlP/GaP(100), Si/GaP(110), Ge/GaAs(110), Ge/AlAs(110), Ge/ZnSe(110), and ZnSe/GaAs(110). The band-edge positions are first obtained for the bulk semiconductors and then aligned through the lineup of a local reference potential at the interface. The band-edge positions critically depend on the electronic-structure method, while the interface dipole is already well accounted for with semilocal density functionals. The two advanced electronic-structure schemes yield consistent valence-band offsets in close agreement with experiment, slightly improving upon semilocal functionals. At variance, conduction-band offsets are subject to larger deviations and improve with the accuracy of the calculated band gaps. In case one is willing to take band gaps from experiment, the best description of the band alignment for the present heterojunctions is achieved by relying on the calculated valence band offsets rather than on hybrid functionals in which the exchange mixing parameter is adjusted.

American Physical Society2014

System-Dependent Density Based Dispersion Correction

Density functional approximations fail to provide a consistent description of weak molecular interactions arising from small electron density overlaps. A simple remedy to correct for the missing interactions is to add a posteriori an attractive energy term summed over all atom pairs in the system. The density-dependent energy correction, presented herein, is applicable to all elements of the periodic table and is easily combined with any electronic structure method, which lacks the accurate treatment of weak interactions. Dispersion coefficients are computed according to Becke and Johnson’s exchange-hole dipole moment (XDM) formalism, thereby depending on the chemical environment of an atom (density, oxidation state). The long- range ∼R-6 potential is supplemented with higher-order correction terms (∼R-8 and ∼R-10) through the universal damping function of Tang and Toennies. A genuine damping factor depending on (iterative) Hirshfeld (overlap) populations, atomic ionization energies, and two adjustable parameters specifically fitted to a given DFT functional is also introduced. The proposed correction, dDXDM, dramatically improves the performance of popular density functionals. The analysis of 30 (dispersion corrected) density functionals on 145 systems reveals that dDXDM largely reduces the errors of the parent functionals for both inter- and intramolecular interactions. With mean absolute deviations (MADs) of 0.74-0.84 kcal mol-1, PBE-dDXDM, PBE0-dDXDM, and B3LYP-dDXDM outperform the computationally more demanding and most recent functionals such as M06-2X and B2PLYP-D (MAD of 1.93 and 1.06 kcal mol-1, respectively).

2010

Nonempirical hybrid functionals for advanced electronic-structure calculations

Thomas Bischoff

GW

\sim

0.2 eV) with respect to

GW

GW

_2

GW

methods provide the most accurate description of the interfacial band alignment.

EPFL2021