Local Density Approximation Results Research Articles

Hyperfine interactions for small systems including transition-metal elements using self-interaction corrected density-functional theory

The interactions between the electronic magnetic moment and the nuclear spin moment, i.e., magnetic hyperfine (HF) interactions, play an important role in understanding electronic properties of magnetic systems and in realizing platforms for quantum information science applications. We investigate the HF interactions for atomic systems and small molecules, including Ti or Mn, by using Fermi–Löwdin orbital (FLO) based self-interaction corrected (SIC) density-functional theory. We calculate the Fermi contact (FC) and spin-dipole terms for the systems within the local density approximation (LDA) in the FLO-SIC method and compare them with the corresponding values without SIC within the LDA and generalized-gradient approximation (GGA), as well as experimental data. For the moderately heavy atomic systems (atomic number Z ≤ 25), we find that the mean absolute error of the FLO-SIC FC term is about 27 MHz (percentage error is 6.4%), while that of the LDA and GGA results is almost double that. Therefore, in this case, the FLO-SIC results are in better agreement with the experimental data. For the non-transition-metal molecules, the FLO-SIC FC term has the mean absolute error of 68 MHz, which is comparable to both the LDA and GGA results without SIC. For the seven transition-metal-based molecules, the FLO-SIC mean absolute error is 59 MHz, whereas the corresponding LDA and GGA errors are 101 and 82 MHz, respectively. Therefore, for the transition-metal-based molecules, the FLO-SIC FC term agrees better with experiment than the LDA and GGA results. We observe that the FC term from the FLO-SIC calculation is not necessarily larger than that from the LDA or GGA for all the considered systems due to the core spin polarization, in contrast to the expectation that SIC would increase the spin density near atomic nuclei, leading to larger FC terms.

Thermoelasticity of tremolite amphibole: Geophysical implications

AbstractWe investigated the structure, equation of state, thermodynamics, and elastic properties of tremolite amphibole [Ca2Mg5Si8O22(OH)2] up to 10 GPa and 2000 K, using first principles simulations based on density functional perturbation theory. We found that at 300 K, the pressure-volume results can be adequately described by a third-order Birch-Murnaghan equation of state with bulk moduli K0 of 78.5 and 66.3 GPa based on local density approximation (LDA) and generalized gradient approximation (GGA), respectively. We also derived its coefficients of the elastic tensor based on LDA and GGA and found that the LDA result is in good agreement with the experimental results. At 300 K, the shear modulus G0 is 58.0 GPa based on LDA. The pressure derivative of the bulk modulus K′ is 5.9, while that of the shear modulus G′ is 1.3. The second Grüneisen parameter, or δT = [–1/(αKT)](∂KT/∂T)P, is 3.3 based on LDA. We found that at ambient conditions, tremolite is elastically anisotropic with the compressional wave velocity anisotropy AVP being 34.6% and the shear wave velocity anisotropy AVS being 27.5%. At higher pressure corresponding to the thermodynamic stability of tremolite, i.e., ~3 GPa, the AVP reduces to 29.5%, whereas AVS increases to 30.8%. To evaluate whether the presence of hydrous phases such as amphibole and phlogopite could account for the observed shear wave velocity (VS) anomaly at the mid-lithospheric discontinuity (MLD), we used the thermoelasticities of tremolite (as a proxy for other amphiboles), phlogopite, and major mantle minerals to construct synthetic velocity profiles. We noted that at depths corresponding to the mid-lithosphere, the presence of 25 vol% amphibole and 1 vol% phlogopite could account for a VS reduction of 2.3%. Thus based on our thermoelasticity results on tremolite amphibole, it seems that mantle metasomatism could partly explain the MLD.

Ab initio study of thermodynamic properties of bulk zinc-blende CdS: Comparing the LDA and GGA

In the present study, we have investigated the phonon and thermodynamic properties of bulk zinc-blende CdS by first-principle calculations within the density functional theory (DFT) and the density functional perturbation theory (DFPT) method using the quasi harmonic approximation (QHA). We calculated the phonon dispersion at several high symmetry directions, density of phonon state, temperature dependence feature of Helmholtz free energy (F), internal energy, bulk modulus, constant-volume specific heat, entropy, coefficient of the volume thermal expansion and Grüneisen parameter estimated with the local density approximation (LDA) and generalized gradient approximation (GGA) for the exchange-correlation potential and compared them with each other. For internal energy, Helmholtz free energy, constant volume heat capacity and phonon entropy the LDA and GGA results are very similar. But, the LDA gives lattice constants that are smaller than GGA while phonon frequencies, bulk modulus and cohesive energies are larger. On the other hand, the results obtained through the GGA approximation for the coefficient of the volume thermal expansion and Grüneisen parameter are larger than those obtained from LDA.

Electronic and Optical Properties of γ- and -Alumina by First Principle Calculations

The electronic and optical parameters of {\gamma}-Al2O3 and {\theta}-Al2O3 have been studied by using the first principle within the framework of density function theory (DFT). The computational approach is based on full-potential linearized augmented plane wave method (FP-LAPW) within the generalized gradient approximation (GGA), local density approximation (LDA), and modified Becke-Johnson potential (mBJ). The results show that these compounds have a direct gap ({\Gamma}-{\Gamma}) of about 5.375 eV and 4.716 eV for {\gamma}-Al2O3 and {\theta}-Al2O3, respectively. Several optical parameters of these materials are also investigated. The values of the real part of dielectric constant are found to be 3.259 and 3.694 for {\gamma}-Al2O3 and {\theta}-Al2O3, respectively, which are close to the experimental one (3.416). The refractive index is 1.806 and 1.922 for {\gamma}-Al2O3 and {\theta}-Al2O3 respectively, and shows a good agreement with the experimental result which is 1.86. GGA findings are consistent with the experimental results and are better than the other approximations. There are no salient differences between GGA and LDA results. The results advocate using this material as a transparent conducting layer in solar cell structure, which can be operated in a wide energy range.

A self-consistent GW approach to the van der Waals potential for a helium dimer.

van der Waals interaction between two helium (He) atoms is studied by calculating the total energy as a function of the He-He distance within the self-consistent GW approximation, which is expected to behave correctly in the long wavelength limit. In the Born-Oppenheimer (BO) approximation, the pair potential curve has its minimum value at 2.87 Å, which is somewhat larger than the local density approximation result, 2.40 Å, and is closer to previous quantum chemistry results. The expectation value for the interatomic distance, calculated by solving the Schrödinger equation for the two nuclei problem using the BO potential energy curve, is 30 Å, which is smaller but of the same order as previous experimental and theoretical results.

Calculated hybrid and semilocal functionals andGWelectronic structure of the metal trifluoridesMF3(M=Sc, Y, Al)

A thorough investigation of the effect of exchange and correlation on the electronic structure of wide-band-gap insulators ${\mathrm{ScF}}_{3},\phantom{\rule{0.16em}{0ex}}{\mathrm{YF}}_{3}$, and ${\mathrm{AlF}}_{3}$ is carried out using local, semilocal, and hybrid functionals in the density functional theory framework and the $GW$ approximation with four current plasmon-pole models. It is shown that the hybrid functionals, which attribute more weight to electron exchange, lead to a decent agreement with the state of the art $GW$ results, whereas the Tran-Blaha semilocal functional does not improve significantly the local density approximation results of the insulating transition-metal trifluorides, because of the high localization of the conduction band minimum states which are mainly of $d$ character, and underestimate considerably the valence-band width of the studied materials.

Elastic and electronic properties of cubic cerium oxide under pressure via first principles

The elastic and electronic properties of cubic structure CeO 2 under pressure are investigated in the frame of density functional theory (DFT). By using the local-density approximation (LDA) plus U( LDA +U) method with U = 6 eV, the calculated lattice parameters, bulk modulus and elastic properties of the cubic CeO 2 at 0 GPa and 0 K are in good agreement with the available experimental data. The pressure dependences of lattice parameters, bulk and shear modulus, Debye temperature, Young's moduli, Poisson's ratio and the compressional and shear wave velocities of the cubic CeO 2 are obtained successfully. In addition, the total density of states (TDOS) and the band gaps of the cubic CeO 2 under pressures are also investigated. By comparing the results of LDA and LDA+U, both the conventional LDA and the LDA+U methods can be used to describe the structure of the cubic CeO 2 due to the electronic localization of 4f-electron in Ce which is not so strong. However, the LDA+U approach can obtain a proper shape of the density of electronic states that agrees well with the measured values.

Effect of covalency and interactions on the trigonal splitting in NaxCoO2

We calculate the effective trigonal crystal field Delta which splits the t2g levels of effective models for NaxCoO2 as the local symmetry around a Co ion is reduced from Oh to D3d. To this end we solve numerically a CoO6 cluster containing a Co ion with all 3d states and their interactions included, and its six nearest-neighbor O atoms, with the geometry of the system, in which the CoO6 octahedron is compressed along a C3 axis. We obtain Delta near 130 meV, with the sign that agrees with previous quantum chemistry calculations, but disagrees with first-principles results in the local density approximation (LDA). We find that Delta is very sensitive to a Coulomb parameter which controls the Hund coupling and charge distribution among the d orbitals. The origin of the discrepancy with LDA results is discussed.

Electronic structure and magneto-optical properties of Co2MnX alloys where X = Ge, Sn and Pb: a First-principles investigation in the LDA+U approach

We report our ab - initio calculational results for the electronic structures and the magnetooptical (MO) properties of the ferromagnetic Co2MnX full Heusler alloys where X = Ge, Sn and Pb. Employing the +U corrections for the 3d bands of transition-metal atoms in addition to the conventional local density approximation (LDA), we investigate the correlation effect on the MO spectra in a polar geometry and the detailed electronic structures. Results show that the correlation effect results in a blue-shift of the peak positions and a large enhancement of the MO spectra up to double in magnitude compared to the LDA results. We find that our results can be attributed to the increased t 2g − e g splitting of the spin-minority d-bands of both Co and Mn atoms, which indicates a suppression of the diagonal elements of the optical conductivity in the energy region of 1–2 eV where the interband transitions are forbidden.

First-principles calculations of MnB4, TcB4, and ReB4 with the MnB4-type structure

Using the first-principles calculations method based on the density functional theory, the structure, mechanical, and electronic properties of MnB4, TcB4, and ReB4 with the MnB4 structure have been performed. The results of local density approximation indicate that all the three borides with the monoclinic MnB4-type structure are elastically stable and hard materials. The shear modulus of monoclinic MnB4 is almost equal to its bulk modulus and much higher than that of superhard material WB4. ReB4 has the largest bulk modulus (316GPa for LDA and 284GPa for GGA), indicating that it can support the large volume decrease caused by an applied load. The electronic density of states has been calculated to elucidate the bonding mechanism in these compounds and the results indicate that bonding is mostly of covalent nature. In addition to electronic properties of highly directional covalent bonds, optimal filling of bonding states, and the Debye temperature θD of the structures support that MnB4 is harder than TcB4 and ReB4.

Superconductivity and charge order of confined Fermi systems

The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with s-wave pairing order. However, the critical temperature is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents Determinant Quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential V which makes the fermion density \rho{} inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density \rho(i) passes through one fermion per site. In this ring of \rho=1, charge order is enhanced. A comparison is made between treating V within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.

First-Principles Study of Various BN, SiC, and AlN Polytypes

We have investigated the electronic and lattice properties of 48H-BN, 20H-SiC, and 30H-AlN polytypes which are sp3-bonded compounds. Their electronic and lattice properties were calculated using the total energy pseudopotential method based on the local density approximation (LDA). As for AlN polytypes (2H, 3C, 4H, 6H, 10H), we investigated using the total energy pseudopotential method based on the generalized gradient approximation (GGA) for comparison with the LDA results. 48H-BN has huge number of possible polytype structures and we chose one polytype structure as “24.24” (Zhdanov notation). “24.24” is not “2424”, which means twenty-four “+” and twenty-four “-” symbols in the Hägg notation. We treat three polytype structures of 20H-SiC as “33322322”, “33332222”, and “32322323” (Zhdanov notations). Their total energies are slightly higher by 0.22 meV/Si2C2 than that of 4H-SiC. Although all the AlN polytypes calculated by LDA have indirect band gaps with the exception of 2H-AlN, 10H-AlN(212212) calculated by GGA has a direct band gap. Its hexagonality is 60 % and “212212” is the Zhdanov notation.

Quasiparticle band structure of Zn-IV-N2compounds

Electronic energy-band structures of the Zn-IV-N${}_{2}$ compounds, with IV equal to Si, Ge, and Sn calculated in the quasiparticle self-consistent GW approximation and using the full-potential linearized muffin-tin orbital approach, are presented. A comparison is made with local-density approximation results. The bands near the gap are fitted to an effective Kohn-Luttinger-type Hamiltonian appropriate for the orthorhombic symmetry, and conduction-band effective masses are presented. Exciton binding energies and zero-point motion corrections to the gaps are estimated. While ZnSiN${}_{2}$ is found to be an indirect gap semiconductor, ZnGeN${}_{2}$ and ZnSnN${}_{2}$ are direct gap semiconductors. The gaps range from the orange-red to deep UV. The valence-band maximum is split in three levels of different symmetry, even in the absence of spin-orbit coupling, and should show transitions to the conduction band, each for a separate polarization. Spin-orbit effects are found to be surprisingly small, indicating almost exact compensation of the N-$2p$ and Zn-$3d$ contributions.

Density functional theory study of stoichiometric and nonstoichiometric ZnO grain boundaries

We present a density functional theory analysis of stoichiometric and nonstoichiometric ZnO tilt grain boundaries (GBs) that reveals under which conditions such extrinsically undoped GBs may become electrically active. In the case of ZnO the self-interaction correction (SIC) scheme used allows a more accurate description of the formation energies as well as the electronic levels than the local density approximation (LDA). The results obtained with the SIC scheme deviate in some crucial ways from the LDA results of recent years. First, stoichiometric and nonstoichiometric ZnO GBs can show occupied deep levels whenever oxygen atoms are undercoordinated. Second, ZnO GBs with an oxygen excess at the boundary plane can exhibit unoccupieddeep levels which may account for an experimentally observed weak varistor effect found in undoped polycrystalline ZnO.

Size dependence of the bulk modulus of semiconductor nanocrystals from first-principles calculations

The variation in the bulk modulus of semiconductor nanoparticles has been studied within first-principles electronic-structure calculations using the local density approximation (LDA) for the exchange correlation. Quantum Monte Carlo calculations carried out for a silicon nanocrystal Si87H76 provided reasonable agreement with the LDA results. An enhancement was observed in the bulk modulus as the size of the nanoparticle was decreased, with modest enhancements being predicted for the largest nanoparticles studied here, a size just accessible in experiments. To access larger sizes, we fit our calculated bulk moduli to the same empirical law for all materials, the asymptote of which is the bulk value of the modulus. This was found to be within 2-10% of the independently calculated value. The origin of the enhancement has been discussed in terms of Cohen's empirical law M.L. Cohen, Phys. Rev. B 32, 7988 (1985)] as well as other possible scenarios.

First-principles calculations ofMnB2,TcB2, andReB2within theReB2-type structure

The structural, mechanical, and electronic properties of ${\text{MnB}}_{2}$, ${\text{TcB}}_{2}$, and ${\text{ReB}}_{2}$ have been studied by performing first-principles calculations at the level plane-wave basis pseudopotential formalism in both aluminum diboride- and rhenium diboride-type structures. The results of local density approximation and generalized gradient approximation indicated that all three of hexagonal structures within rhenium diboride-type are energetically favorable than those of aluminum diboride-type, they are mechanically stable and also hard materials. In addition to electronic properties of highly directional covalent bonds, optimal filling of bonding states, mechanical properties, and also the Debye temperature of the structures support that the rhenium diboride-type hexagonal phase of ${\text{MnB}}_{2}$ is harder than the others. Interestingly, instead of other five structures, only ${\text{MnB}}_{2}$ within aluminum diboride-type hexagonal structure has a finite magnetic moment at the equilibrium geometry.

Effect of strain on geometric and electronic structures of graphene on a Ru(0001) surface

The atomic and electronic structures of a graphene monolayer on a Ru(0001) surface under compressive strain are investigated by using first-principles calculations. Three models of graphene monolayers with different carbon periodicities due to the lattice mismatch are proposed in the presence and the absence of the Ru(0001) substrate separately. Considering the strain induced by the lattice mismatch, we optimize the atomic structures and investigate the electronic properties of the graphene. Our calculation results show that the graphene layers turn into periodic corrugations and there exist strong chemical bonds in the interface between the graphene N × N superlattice and the substrate. The strain does not induce significant changes in electronic structure. Furthermore, the results calculated in the local density approximation (LDA) are compared with those obtained in the generalized gradient approximation (GGA), showing that the LDA results are more reasonable than the GGA results when only two substrate layers are used in calculation.

Structural properties and phase transformations under pressure of XTe compounds (X = Be, Mg, and Ca): The role of the exchange–correlation potential

We have performed first principles total energy calculations to investigate the structural properties and possible phase transitions under pressure of IIA–VI compounds: BeTe, MgTe and CaTe. We have considered the following possible structures: rock-salt, nickel arsenide, cesium chloride, zinc-blende, and in some cases wurtzite. Calculations are done using the periodic density functional theory. We employ the full potential linearized augmented plane wave method as implemented in the wien2k code. The exchange and correlation potential energies are treated according to the generalized gradient approximation (GGA) using the Perdew, Burke, Ernzerhof (PBE) parameterization, and the local density approximation (LDA). Our results show that the GGA calculations correctly predict the ground state structure of all three binary compounds: zinc-blende for BeTe, wurtzite/zinc-blende for MgTe, and rock-salt for CaTe. Under pressure, BeTe and MgTe transform to the nickel arsenide structure, while CaTe transforms from rock-salt to cesium chloride. Slightly different results are found using the LDA approximation. We discuss the role of the ionicity in the difference between the LDA and GGA results.

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

Quantum Monte Carlo (QMC) simulations and the local density approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose-Hubbard Hamiltonian confined in a harmonic trap onto the $(\ensuremath{\mu}∕U,t∕U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.

High-pressure behavior of crystalline FOX-7 by density functional theory calculations

1,1-Diamino-2,2-dinitroethylene (C2H4N4O4, FOX-7) is a newly found energetic materials with high performance and low sensitivity. We performed density functional theory (DFT) calculations within local density approximation (LDA) as well as generalized gradient approximation (GGA) to simulate the structural and electronic properties of FOX-7 crystal under high-pressure up to 4GPa. Due to the insufficient treatment of weakly intermolecular interaction, LDA underestimates the lattice parameters and volume, while GGA overestimates them. It is interesting to find that a mixing of LDA and GGA results of lattice properties can lead to fairly good agreement with experiments. Examination of pressure-induced changes of molecular geometry shows that the C–N bonds are most sensitive under compression. The change of band gap as function of external pressure was also discussed.