Local Generalized-gradient Approximation Research Articles

Benchmark Assessment of Density Functional Methods on Group II-VI MX (M = Zn, Cd; X = S, Se, Te) Quantum Dots.

In this work, we build a benchmark data set of geometrical parameters, vibrational normal modes, and low-lying excitation energies for MX quantum dots, with M = Cd, Zn, and X = S, Se, Te. The reference database has been constructed by ab initio resolution-of-identity second-order approximate coupled cluster RI-CC2/def2-TZVPP calculations on (MX)6 model molecules in the wurtzite structure. We have tested 26 exchange-correlation density functionals, ranging from local generalized gradient approximation (GGA) and hybrid GGA to meta-GGA, meta-hybrid, and long-range corrected. The best overall functional is the hybrid PBE0 that outperforms all other functionals, especially for excited state energies, which are of particular relevance for the systems studied here. Among the DFT methodologies with no Hartree-Fock exchange, the M06-L is the best one. Local GGA functionals usually provide satisfactory results for geometrical structures and vibrational frequencies but perform rather poorly for excitation energies. Regarding the CdSe cluster, we also present a test of several basis sets that include relativistic effects via effective core potentials (ECPs) or via the ZORA approximation. The best basis sets in terms of computational efficiency and accuracy are the SBKJC and def2-SV(P). The LANL2DZ basis set, commonly employed nowadays on these types of nanoclusters, performs very disappointingly. Finally, we also provide some suggestions on how to perform calculations on larger systems keeping a balance between computational load and accuracy.

Transition energies and direct-indirect band gap crossing in zinc-blende AlxGa1−xN

The electronic and optical properties of zinc-blende (zb) Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N over the whole alloy composition range are presented in a joint theoretical and experimental study. Because zb-GaN is a direct (${\ensuremath{\Gamma}}_{v}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{c}$) semiconductor and zb-AlN shows an indirect (${\ensuremath{\Gamma}}_{v}\ensuremath{\rightarrow}{X}_{c}$) fundamental band gap, the ternary alloy exhibits a concentration-dependent direct-indirect band gap crossing point the position of which is highly controversial. The dielectric functions of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N alloys are measured employing synchrotron-based ellipsometry in an energy range between 1 and 20 eV. The experimentally determined fundamental energy transitions originating from the $\ensuremath{\Gamma}$, $X$, and $L$ points are identified by comparison to theoretical band-to-band transition energies. In order to determine the direct-indirect band gap crossing point, the measured transition energies at the $X$ point have to be aligned by the calculated position of the highest valence state. Thereby density-functional theory (DFT) based approaches to the electronic structure, ranging from the standard (semi)local generalized gradient approximation (GGA), self-energy corrected local density approximation (LDA-1/2), and meta-GGA DFT (TB-mBJLDA) to hybrid functional DFT and many-body perturbation theory in the $GW$ approximation, are applied to random and special quasirandom structure models of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N. This study provides interesting insights into the accuracy of the various numerical approaches and contains reliable ab initio data on the electronic structure and fundamental alloy band gaps of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N. Nonlocal Heyd-Scuseria-Ernzerhof-type hybrid-functional DFT calculations or, alternatively, $GW$ quasiparticle calculations are required to reproduce prominent features of the electronic structure. The direct-indirect band gap crossing point of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N is found in the Al rich composition range at an Al content between $x=0.64$ and $0.69$ in hybrid functional DFT, which is in good agreement with $x=0.71$ determined from the aligned experimental transition energies. Thus our study solves the long-standing debate on the nature of the fundamental zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N alloy band gap.

First principles calculations and experiment predictions for iodine vacancy centers in SrI2

AbstractWe present the electronic structure, lattice relaxation, and formation energies of iodine vacancy defects in SrI2 for the one‐electron, two‐electron, and ionized charge states. We use a local generalized gradient approximation as well as non‐local hybrid functionals within the framework of density functional theory, as it is commonly accepted that the latter can improve accuracy of the band gap and hence relevant energy levels. Comparison is made to published results on chlorine vacancy defects in NaCl calculated with similar methods and functionals, and also to a recent first‐principles study of one‐ and two‐electron occupancy in MgO vacancy centers. Using the parameters that are calculable from first principles in SrI2 as a starting point, we incorporate available experimental data and adaptations of simple models to predict a range of results that can help guide or interpret future experiments such as absorption energy, configuration coordinate curves, vibrational lineshape, thermal trap depth, and Mollwo–Ivey comparison to alkaline‐earth fluorides. magnified imageCharge density contour in the F center in SrI2.