We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

The semiconductor ZnO has gained substantial interest in the research community in part because of its large exciton binding energy (60meV) which could lead to lasing action based on exciton recombination even above room temperature. Even though research focusing on ZnO goes back many decades, the renewed interest is fueled by availability of high-quality substrates and reports of p-type conduction and ferromagnetic behavior when doped with transitions metals, both of which remain controversial. It is this renewed interest in ZnO which forms the basis of this review. As mentioned already, ZnO is not new to the semiconductor field, with studies of its lattice parameter dating back to 1935 by Bunn [Proc. Phys. Soc. London 47, 836 (1935)], studies of its vibrational properties with Raman scattering in 1966 by Damen et al. [Phys. Rev. 142, 570 (1966)], detailed optical studies in 1954 by Mollwo [Z. Angew. Phys. 6, 257 (1954)], and its growth by chemical-vapor transport in 1970 by Galli and Coker [Appl. Phys. ...

/pdf/a-comprehensive-review-of-zno-materials-and-devices-21a3zjadem.pdf

A comprehensive review of zno materials and devices

https://zenodo.org/record/1258869/files/article.pdf

NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations

In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density (LSD) and the Perdew–Burke–Ernzerhof (PBE) functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical ...

Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional

The Interaction of Water with Solid Surfaces: Fundamental Aspects Revisited

We report total energy and electronic structure calculations for ZnO in the B4 (wurtzite), B3 (zinc blende), B1 (rocksalt), and B2 (CsCl) crystal structures over a range of unit cell volumes. We employed both the local-density approximation (LDA) and the PBE96 form of the generalized gradient approximation (GGA) together with optimized Gaussian basis sets to expand the crystal orbitals and periodic electron density. In agreement with earlier ab initio calculations and with experiment, we find that the B4 phase of ZnO is slightly lower in energy than the B3 phase, and that it transforms first to the B1 structure under applied pressure. The equilibrium transition pressure ${p}_{T1}$ is 6.6 GPa at the LDA level of theory and 9.3 GPa in the GGA, compared to experimental values around 9 GPa. This confirms a trend seen by other workers in which the LDA underestimates structural transition pressures which are more accurately predicted by the GGA. At much higher compression, we predict that the B1 phase of ZnO will transform to the B2 (cesium chloride) structure at ${p}_{T2}=260\mathrm{GPa}$ (LDA) or 256 GPa (GGA) indicating that gradient corrections are small for this material at megabar pressures. This is the first quantitative prediction of this transition in ZnO, and should be testable with diamond-anvil techniques. We predict that ZnO remains a semiconductor up to ${p}_{T2}.$ For comparison we find that the B1 to B2 transition in MgO occurs at 515 GPa with either LDA or GGA, in excellent agreement with other ab initio predictions.

LDA and GGA calculations for high-pressure phase transitions in ZnO and MgO

The total energy of ZnO as a function of unit cell volume has been calculated for the zinc-blende, wurtzite, and rocksalt structures by the ab initio all-electron periodic Hartree-Fock linear-combination-of-atomic-orbitals method using a large Gaussian basis set that was variationally optimized for the solid state. Extensive convergence tests with respect to cutoffs of the real-space Coulomb and exchange series were carried out to ensure that the calculations were performed with sufficient precision. The calculated structural properties (equilibrium lattice constant, bulk modulus, etc.) of the wurtzite and rocksalt phases are in good agreement with experiment, as is the transition pressure between them (8.57 GPa versus 9--9.5 GPa experimentally), indicating that the method can reliably predict quite small energy differences between different densities or crystal structures of a nonmetallic solid. The calculated valence-band structure was also in satisfactory agreement with experiment. Detailed analysis of the charge-density distribution supports the expected picture of a transition from mixed ionic-covalent bonding in the tetrahedrally coordinated structures to predominantly ionic bonding in the high-pressure phase.

Hartree-Fock study of phase changes in ZnO at high pressure.

Periodic Hartree-Fock total-energy calculations on two-dimensional slabs have been used to study the symmetry-conserving relaxation of the nonpolar (101\ifmmode\bar\else\textasciimacron\fi{}0) surface of ZnO. We find that it is energetically favorable for the Zn-O surface dimers to tilt slightly (by 2.3 \ifmmode^\circ\else\textdegree\fi{}) and move downwards towards the slab, and for the dimer bond to shorten significantly. Our results agree fairly well with those of a recent density-functional calculation, but disagree with empirical tight-binding theory which predicts surface bonds to shorten only slightly while the surface dimers undergo a large tilt (18 \ifmmode^\circ\else\textdegree\fi{}). The available experimental data lies between the ab initio and tight-binding results with large error bars. We have tested the effects of several refinements of our Hartree-Fock calculation, including improvements of the orbital basis set and precision tolerances, the use of thicker slabs in approximating the semi-infinite crystal, and post-self-consistent-field density-functional correlation corrections to the total energy. None of these refinements significantly changed our results. We discuss possible reasons for the disagreement between our results and those of tight-binding theory.

Ab initio study of ZnO (101¯0) surface relaxation

We describe a formulation of electronic density functional theory using localized Gaussian basis functions for systems periodic in three dimensions (bulk crystals) or two dimensions (crystal slabs terminated by surfaces). Our approach generalizes many features of molecular density functional methods to periodic systems, including the use of an auxiliary Gaussian basis set to represent the charge density, and analytic gradients with respect to nuclear coordinates. Existing quantum chemistry routines for analytic and numerical integration over basis functions can be adapted to our scheme with only slight modifications, as can existing extended Gaussian basis sets. Such basis sets permit accurate calculations with far fewer basis functions (and hence much smaller matrices to diagonalize) than plane‐wave based methods, especially in surface calculations, where in our approach the slab does not have to repeat periodically normal to the surface. Realistic treatment of molecule–surface interactions is facilitated since both molecule and surface can be treated at the same level of theory. Our real‐space method also offers opportunities to exploit matrix sparsity, since in a large unit cell many pairs of basis functions will be essentially nonoverlapping and noninteracting. Longer‐ranged Coulomb interactions are summed by a form of the Ewald technique that guarantees absolute convergence. We also give a straightforward extension to periodic systems (both two‐ and three‐dimensional) of the usual molecular formalism for analytic nuclear first derivatives (forces).

Gaussian basis density functional theory for systems periodic in two or three dimensions: Energy and forces

An ab initio study is presented concerning the chemisorption of hydrogen on a model of the (100) surface of MgO and Li‐doped MgO. The local surface environment was modeled employing cubic and tetragonal clusters composed of 8 and 12 atoms, respectively. The lattice constant for the clusters was fixed at the experimentally determined value for bulk MgO and the geometry of the adsorbate was optimized at the unrestricted Hartree–Fock (UHF) level of theory. Correlation energy was treated at the second‐order unrestricted Mo/ller–Plesset (UMP2) level at the UHF optimized geometry. It was found that H2 undergoes heterolytic dissociation at neighboring three‐coordinated Mg and O sites (denoted Mg3c and O3c) in MgO with activation energies of 4.2 and 2.4 kcal/mol at the UHF and UMP2 levels, respectively. Li‐doped MgO did not support heterolytic dissociation at neighboring Mg and O sites. Instead H2 was found to dissociate homolytically without barrier at two O3c sites and to undergo hydrogen atom abstraction at O3...

Anthony C. Hess

Papers

LDA and GGA calculations for high-pressure phase transitions in ZnO and MgO

Hartree-Fock study of phase changes in ZnO at high pressure.

Ab initio study of ZnO (101¯0) surface relaxation

Gaussian basis density functional theory for systems periodic in two or three dimensions: Energy and forces

An electronic structure study of H2 and CH4 interactions with MgO and Li‐doped MgO clusters