Calculation of point defects in rutile TiO 2 by the screened-exchange hybrid functional

The formation energies of the oxygen vacancy and titanium interstitial in rutile TiO 2 were calculated by the screened-exchange (sX) hybrid density functional method, which gives a band gap of 3.1 eV, close to the experimental value. The oxygen vacancy gives rise to a gap state lying 0.7 eV below the conduction band edge, whose charge density is localized around the two of three Ti atoms next to the vacancy. The Ti interstitial (Ti int) generates four defect states in the gap, whose unpaired electrons lie on the interstitial and the adjacent Ti 3d orbitals. The formation energy for the neutral oxygen vacancy is 1.9 eV for the O-poor chemical potential. The neutral Ti interstitial has a lower formation energy than the O vacancy under O-poor conditions. This indicates that both the O vacancy and Ti int are relevant for oxygen deficiency in rutile TiO 2 but the O vacancy will dominate under O-rich conditions. This resolves questions about defect localization and defect predominance in the literature. © 2012 American Physical Society.

Systematic construction of models for the exchange hole of density functional theory.

Dans ce travail, nous étendons le nombre de conditions physiques actuellement con- nues du trou d’échange exact avec la dérivation de l’expansion de quatrième ordre du trou d’échange sphérique moyenne exacte. Nous comparons les expansions de deux- ième et de quatrième ordre avec le trou d’échange exact pour des systèmes atomiques et moléculaires. Nous avons constaté que, en général, l’expansion du quatrième ordre reproduit plus fidèlement le trou d’échange exact pour les petites valeurs de la distance interélectronique. Nous démontrons que les ensembles de base de type gaussiennes ont une influence significative sur les termes de cette nouvelle condition, en étudiant com- ment les oscillations causées par ces ensembles de bases affectent son premier terme. Aussi, nous proposons quatre modèles de trous d’échange analytiques auxquels nous imposons toutes les conditions actuellement connues du trou d’échange exact et la nou- velle présentée dans ce travail. Nous évaluons la performance des modèles en calculant des énergies d’échange et ses contributions à des énergies d’atomisation. On constate que les oscillations causeés par les bases de type gaussiennes peuvent compromettre la précision et la solution des modèles.

EXACT AND APPROXIMATE RELATIONS FOR THE SPIN-DEPENDENCE OF THE EXCHANGE ENERGY IN HIGH MAGNETIC FIELDS

The exchange energy of an arbitrary collinear-spin many-body system in an external magnetic field is a functional of the spin-resolved charge and current densities, E(x)[n(up arrow), n(down arrow), j(up arrow), j(down arrow)]. Within the framework of density-functional theory (DFT), we show that the dependence of this functional on the four densities can be fully reconstructed from either of two extreme limits: a fully polarized system or a completely unpolarized system. Reconstruction from the limit of an unpolarized system yields a generalization of the Oliver-Perdew spin scaling relations from spin-DFT to current-DFT. Reconstruction from the limit of a fully polarized system is used to derive the high-field form of the local-spin-density approximation to current-DFT and to magnetic-field DFT.

Exchange energy shifts under dense plasma conditions

The variation of the energy interval between the intercombination line ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) of He-like aluminium with plasma density and temperature is investigated. Since such energy interval is equivalent to the exchange energy of the state 1s2p(P-3(1)), we consider the dependence of this energy shift on the plasma environment. It was found that the shifts of exchange energy increase ( decrease) with the increase of electron density ( electron temperature), and the shifts of exchange energy become more sensitive to the electron density as the electron temperature decreases, i. e. in the strongly coupled plasma regime. An approximately linear relation is found between the shifts of exchange energy and the electron density. The results show that dense plasma effects are very important for the simulation of the spectral fine structure. The relative shifts between the intercombination ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) are discussed for diagnostic applications.

Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals

Formation of single-walled carbon nanotube via the interaction of graphene nanoribbons : ab initio density functional calculations

The interaction of bare graphene nanoribbons (GNRs) was investigated by ab initio density functional theory calculations with both the local density approximation (LDA) and the generalized gradient approximation (GGA). Remarkably, two bare 8-GNRs with zigzag-shaped edges are predicted to form an (8, 8) armchair single-wall carbon nanotube (SWCNT) without any obvious activation barrier. The formation of a (10, 0) zigzag SWCNT from two bare 10-GNRs with armchair-shaped edges has activation barriers of 0.23 and 0.61 eV for using the LDA and the revised PBE exchange correlation functional, respectively, Our results suggest a possible route to control the growth of specific types SWCNT via the interaction of GNRs.

Interface of graphane with copper : a van der Waals density-functional study

Various forms of hydrogenated graphene have been produced to date by several groups, while the synthesis of pure graphane has not been achieved yet. The study of the interface between graphane, in all its possible hydrogenation configurations, and catalyst metal surfaces can be pivotal to assess the feasibility of direct CVD growth methods for this material. We investigated the adhesion of graphane to a Cu(111) surface by adopting the vdW-DF2-C09 exchange-correlation functional, which is able to describe dispersion forces. The results are further compared with the PBE and the LDA exchange-correlation functionals. We calculated the most stable geometrical configurations of the slab/graphane interface and evaluated how graphane's geometrical parameters are modified. We show that dispersion forces play an important role in the slab/graphane adhesion. Band structure calculations demonstrated that in the presence of the interaction with copper, the band gap of graphane is not only preserved, but also enlarged, and this increase can be attributed to the electronic charge accumulated at the interface. We calculated a substantial energy barrier at the interface, suggesting that CVD graphane films might act as reliable and stable insulating thin coatings, or also be used to form compound layers in conjunction with metals and semiconductors.

Carbon monoxide adsorption on molybdenum phosphides: Fourier transform infrared spectroscopic and density functional theory studies

Molybdenum phosphide (MoP) and supported molybdenum phosphide (MoP/gamma-Al2O3) have been prepared by the temperature-programmed reduction method. The surface sites of the MoP/gamma-Al2O3 catalyst were characterized by carbon monoxide (CO) adsorption with in situ Fourier transform infrared (FT-IR) spectroscopy. A characteristic IR band at 2037 cm(-1) was observed on the MoP/gamma-Al2O3 that was reduced at 973 K. This band is attributed to linearly adsorbed CO on Mo atoms of the MoP surface and is similar to IR bands at 2040-2060 cm(-1), which correspond to CO that has been adsorbed on some noble metals, such as platinum, palladium, and rhodium. Density functional calculations of the structure of molybdenum phosphides, as well as CO chemisorption on the MoP(001) surface, have also been studied on periodic surface models, using the generalized gradient approximation (GGA) for the exchange-correlation functional. The results show that the chemisorption of CO on MoP occurred mainly on top of molybdenum, because the bonding of CO requires a localized mininum potential energy. The adsorption energy obtained is DeltaH(ads) approximate to -2.18 eV, and the vibrational frequency of CO is 2047 cm-1, which is in good agreement with the IR result of CO chernisorption on MoP/gamma-Al2O3.

Density-functional study of lanthanum, ytterbium, and lutetium dimers

La-2, Yb-2, and Lu-2 have been studied by use of the density-functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, MPW1PW91, and PBE1PBE. In these density-functional methods, the exchange functional is from either Becke's three-parameter HF-DFT hybrid exchange functional (B3), pure DFT exchange functional of 1988 (B), a modification of the half-and-half HF/DFT hybrid method (BH), Perdew-Wang 1991 (PW91), or Barone's modified PW91 (MPW1), while the correlation functional is from either Lee, Yang, and Parr (LYP), Perdew-Wang 1991 (PW91), or Perdew 86 (P86). PBE1PBE is the generalized-gradient-approximation exchange-correlation functional of Perdew, Burke, and Ernzerhof. For La-2, the calculated bond distance is in reasonable agreement with the experiment, but the calculated vibrational frequency is underestimated significantly compared with the experiment. Only BP86 and B3P86 have the best performance in reproducing the experimental dissociation energy for La-2. For the van der Waals dimer Yb-2, three functionals, B3LYP, BLYP, and BHLYP have excellent performance in reproducing the spectroscopic constants compared with both the experiment and previous theoretical studies.

Effect of spatial nonlocality on the density functional band gap

We show that for a large class of exchange-correlation functionals the local exchange-correlation potential obtained within an optimized effective potential severely underestimates the band gap. On the other hand, the corresponding nonlocal potential obtained from a generalized Kohn-Sham scheme provides a much better description of the band gap, in good agreement with experiments. These results strongly indicate that a local exchange-correlation potential, however good the exchange-correlation approximation, cannot capture the delicate interplay between correlation effects and spatial localization in the KS band structure, unless the (cumbersome) contribution from the derivative discontinuity of the exchange-correlation energy functional is considered.