Local Density Approximation Approximation Research Articles

Ab initio study of structural, mechanical and electronic properties of 3d transitional metal carbide in cubic rocksalt (rs), zincblende (zb), and cesium chloride (cc) structures by using LDA and GGA Approximation.

This study rigorously investigates three 3d transition metal carbide (TMC) structures via LDA and GGA approximations. It examines cohesive energy (Ecoh), Vickers hardness (Hv), mechanical stability, and electronic properties. Notably, most 3d TMCs exhibit higher cohesive energy than nitrides, and rs-TiC demonstrates a Vickers hardness of 25.66 GPa, outperforming its nitride counterpart. The study employs theoretical calculations to expedite research, revealing mechanical stability in CrC and MnC (GGA) and CrC (LDA in cc structure), while all 3d TMCs in rs and seven in zb structures show stability. Charge transfer and bonding analysis reveal enhanced covalency along the series, influenced by the interplay between p orbitals of carbon and d orbitals of the metal. Most 3d TMCs exhibit metallic properties, excluding zb-TiC and zb-FeC in all phases. An inverse correlation between elastic constant C44 and electronic states near the Fermi level (EF) emerges, guiding applications and design. This study efficiently uncovers 3d TMC properties, offering insights for applications and design. We employed the Vienna ab initio Simulation software (VASP) to perform computations based on density functional theory (DFT). Our approach incorporated both the projector augmented wave (PAW) and PW91 general gradient approximation (GGA) methods within the local density approximation (LDA).

First principles calculation to investigate the structural, electronic, elastic, mechanical, and optical properties of K2NiP2 ternary compound

First-principles calculations of the structural, electronic, elastic, mechanical, and optical properties of the K2NiP2 ternary compound using density functional theory as implemented in the quantum espresso package have been performed. The calculations have been done using the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE, PBEsol) exchange-correlation functionals and the local density approximation (LDA). The lattice parameters have been found to agree with the available experimental results. Direct bandgaps have been obtained as 0.630, 0.588, and 0.525 eV when using the GGA-PBE, GGA-PBEsol, and LDA approximations, respectively. In all three scenarios, the valence bands have been noted to be majorly formed by Ni-3d and P-2p states with little contribution from the other states, whereas the conduction bands have been observed to be mainly formed by P-2p states with a small contribution from the other states. The K2NiP2 has been found to be mechanically stable, ductile, and ionic. The optical properties showed that the compound under investigation has a high refractive index and absorption coefficients covering the ultraviolet–visible regions, thus indicating its potential for photovoltaic applications. The bandgaps obtained using LDA were smaller than those obtained using GGA. This is because LDA underestimates the bandgaps.

Co-, Fe-, Ni-doped and co-doped rutile GeO2: insights from ab-initio calculations

Abstract Rutile germanium oxide (rutile GeO2), a semiconductor, can act as a half-metallic compound and is a promising material for spintronic and optoelectronic applications. Calculations were performed using the Korringa–Kohn–Rostoker (KKR) approach and the coherent potential approximation (CPA), which were further combined with two approximations, the local density approximation (LDA) and the self-interaction corrected LDA approximation (LDA-SIC), to study the electronic structure of bulk rutile GeO2 doped and co-doped with three transition-metal impurities: Fe, Co, and Ni. The doping value was set to 10%, while the co-doping level was set to 5% for each impurity. The main findings of this work are: (1) a direct ultrawide bandgap of 4.80 eV is observed and the rutile GeO2 exhibits an N-type semiconducting property. (2) Doped and co-doped GeO2 acquire a magnetic behavior and exhibit half-metallicity. (3) The mechanism responsible for these properties is also studied. (4) The critical temperature can reach 334 K when GeO2 is doped with Fe, while it rises to 398 K when it is co-doped with Fe and Co. (5) The spin polarization can be improved by co-doping. It can be inferred that rutile GeO2 doped or co-doped with (Co, Fe) transition metals can be considered to be potential candidates for spintronic and optoelectronic applications.

Optoelectronic and thermodynamic properties, infrared and Raman spectra of NbO2 and Nb2O5 from DFT formalism

All Niobium(Nb)-based materials have been widely investigated in recent decades due to a series of special applications in the high-tech industry, namely, in the aerospace sectors, for example, as metallic superalloys and, also, in the electro-electronic in which they are used as microcapacitors. We report the results of a theoretical study of the Niobium Dioxide (NbO2) and Niobium Pentoxide (Nb2O5) which is based on the ab initio plane-wave pseudo-potential model from Density Functional Theory (DFT), within both the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA), for the exchange and correlation potential. The structural properties, the electronic band structure, the electronic density of states, the reflectivity and the optical absorption are calculated from the nanostructures optimized at their lowest energy levels and, the comparison reveals good agreement of the calculated lattice parameters with theoretical and experimental results. An indirect bandgap E(ZΓ) was obtained within the GGA and LDA approximations of calculation for both NbO2 and Nb2O5. In addition, the optical absorptions and the reflectivities were shown to be sensitive to the plane of polarization of the incident light in the range of ultraviolet radiation to visible spectrum. The theoretical peaks of the infrared (IR) and Raman spectra in the frequency range of 0–1000 cm−1 was estimated and assigned, considering the norm-conserved pseudopotentials. The thermodynamic potentials, the specific heat at constant volume of the nanostructures are also calculated, which dependence on the temperature are specified.

Ab-initio study of structural stability, electronic and optical properties of X2GeSe (X = P and Sb) monolayers

This paper investigated the structural stability, electronic and optical properties of X2GeSe (X = P and Sb) monolayers in a hexagonal structure. The calculations are based on the density functional theory using the plane wave method in the Quantum-Espresso computational package for local density approximation (LDA) and the generalized gradient approximation (GGA). The results of phononic calculations indicate that P2GeSe and Sb2GeSe monolayers are dynamically stable in LDA and GGA approximations. The electronic section of X2GeSe (X = P and Sb) monolayers showed that both compounds are semiconductors. The P2GeSe and Sb2GeSe monolayers in the LDA approximation exhibit a direct bandgap at the Γ point with a quantity of 0.88 and 0.84 eV, respectively. Also, P2GeSe and Sb2GeSe monolayers have an indirect bandgap in the GGA approximation in the Г−K path whit amount of 1.07 and 1.02 eV, respectively. For X2GeSe monolayers (X = P and Sb), the optical gaps calculated from the absorption spectrum confirm the electronic bandgap results. The optical calculations showed that the static dielectric constant ε1(0) decreases in the x and z directions but increases in the y-direction with increasing constant atomic radius from P to Sb atom. According to the results, in both LDA and GGA approximations, the maximum reflections of the P2GeSe monolayer are in the ultraviolet domain of the electromagnetic spectrum and for the Sb2GeSe monolayer, the maximum of reflections occurs in the infrared domain. This result makes the studied monolayers a potential candidate for use in optoelectronic devices as a reflector layer of the electromagnetic beam. The calculated of the energy loss spectrum L(ω) diagram shows that the significant collective excitations of the electron charge density in the crystal, which is considered as the plasmonic peak, are in the y-direction. The values of the static refractive index n0, obtained from the squares of the real part of the dielectric function at zero energy, n0=ε1(0), are very close to that of the refractive index diagram at zero energy. For every examined monolayer, the static refractive index in the y-direction is larger than other x and z directions in both LDA and GGA approximations. Examination of the optical properties of the X2GeSe (X = P and Sb) monolayers in different x, y, and z-directions explains the anisotropy of the studied structures.

Structural, elastic, electronic, thermal, and phononic properties of yttrium carbide: First-principles calculations

In this paper, structural, electronic, elastic, phononic, and thermal properties of YC in both rock-salt (B1) and CsCl (B2) phases are studied. Calculations have been performed by using QUANTUM-ESPRESSO/PWSCF computational package which is based on density functional theory (DFT) and pseudo-potential method. Local density approximation (LDA) and generalized gradient approximation (GGA) have been used for modeling the exchange and correlation effects. According to the total energy diagram versus unit cell volume, the YC compound in the B1 phase is more stable than that of the B2 phase at ambient pressure. The computed elastic parameters indicated that the B2 phase did not satisfy the mechanical stability conditions at ambient pressure and is considered to be an unstable phase of the YC structure.The analysis of the enthalpy versus pressure diagram predicts that the structural phase transition from the B1 phase to the B2 phase occurs at pressures 51 GPa and 71.5 GPa, for various LDA and GGA approximations, respectively. Based on the phonon dispersion curves at ambient pressure, the B1 phase of the YC compound is dynamically stable, while at high pressure, the YC compound in the B2 phase has shown stability. Using calculated elastic constants, the small amount of Zener anisotropy factor A shows a strongly anisotropic nature of the YC structure. The higher amount of the calculated Poisson's ratio (~0.40) than that of the corresponding critical value (~0.33) together with the positive values of Cauchy pressure within the LDA and GGA approximations present the ductility and metallic behavior of the YC compound in the B1 phase. The band structure and total density of states calculations also verify the metallic behavior of the YC compound in the stable B1 phase. From PDOS calculations, overlapping the 4d orbital of the Y atom and 2p orbital of the C atom near the Fermi level indicates that these orbitals have significant contributions to the bonding between the Y and C atoms. This bonding is substantiated by the corresponding electron density distribution. The thermodynamic calculations indicated that the heat capacity increases regularly and continuously with the increase in temperature T, toward the classical Dulong-Petit value of 6R for the bulk structure of the YC compound with two atoms in the primitive cell. It can also be predicted for the YC compound that the smaller lattice parameter within the LDA approximation compared to the GGA approximation causes stiffness increases, followed by an increase in the Debye temperature. The increasing trend of entropy versus temperature indicates the endothermic behavior of the YC compound.

Magnetic Properties of Carbon Co-Doped (Zn,Mn)O Using LDA and LDA-SIC Approximations

In this paper, we used the ab-initio calculations, based on the Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA), to simulate the magnetic properties of ZnO, doped and co-doped with manganese and carbon, respectively. For this purpose, we have used two different approximations: the Local Density Approximation (LDA) and the Local Density Approximation-Self-Interaction Correction (LDA-SIC). Numerical results are presented for the compound Zn1 − 0.06Mn0.06O1−xCx when doping and co-doping is performed with Mn and C as doping elements. Total and partial DOSs are given for different concentrations using the two approximations, LDA and LDA-SIC. It is found that for 6% with doping by Mn the system becomes magnetic. The co-doping with carbon changes the behavior of the system : it becomes also magnetic for 4, 6 and 10% concentrations within both, LDA and LDA-SIC approximations. Furthermore, we have discussed the type of mechanism of exchange interaction and found that the double exchange is responsible for the appearing magnetism in the system, within the LDA and p-d interaction for LDA-SIC approximation. For 10% of carbon, we have found that the critical temperature approaches 280 K in the LDA approximation solely; and is about 305 K in the LDA-SIC approximation.

Investigation of the Perovskite KSrX3 (X = Cl and F) Compounds, Examining the Optical, Elastic, Electronic and Structural Properties: FP-LAPW Study

The optical and electronic density of states (DOS) and elastic and structural properties of crystalline perovskites KSrX3 (X = Cl and F) are examined using the full potential linearized augmented plane wave (FP-LAPW) technique in the context of the Perdew, Burke and Ernzerhof’s (PBE) generalized gradient approximation (GGA), the local density approximation (LDA) and the modified Becke-Johnson exchange potential (mBJ-GGA), while the structural properties of the KSrX3 are calculated using LDA, GGA and Wu-Cohen (WC) functionals. Our findings are that the KSrF3 compound has a direct energy band gap (E g) at (Γ–Γ) with 5.54 eV, 5.42 eV, and 10.35 eV using PBE-GGA, LDA and mBJ-GGA approximations, respectively. The KSrCl3 compound also has an indirect energy band gap (M–Γ) with 4.45 eV, 4.3 eV, and 7.88 eV, as discovered using PBE-GGA, LDA and mBJ-GGA approximations, respectively. The coefficient of extinction, index of refraction, dielectric function and the fountains of apex of the optical spectra are examined with regard to the computed electronic structure.

Pressure effect on structural, electronic and thermodynamic investigations of europium filled skutterudite EuFe4Sb12: LDA and LSDA approximations

Numerical calculations based on the full potential muffin-tin orbitals method (FP-LMTO) within the local density approximation (LDA) and the local spin-density approximation (LSDA) to investigate the structural, electronic and thermodynamic properties of filled skutterudite EuFe4Sb12 are presented. The electronic band structure and density of states profiles prove that this material is a conductor. The present investigation is also extended to the elastic constants, such as the bulk modulus B, anisotropy factor A, shear modulus G, young's modulus E, Poisson's ratio ν, and the B/G ratio with pressure in the range of 0–40GPa. The sound velocities and Debye temperatures are also predicted from the above constants. The variations of the primitive cell volume, expansion coefficient α, bulk modulus B, heat capacity (Cp and Cv), Debye temperature θD, Helmholtz free energy A, Gibbs free energy G, entropy S, and internal energy U with pressure and temperature in the range 0–3000K are calculated successfully.

First‐principles study of structural, electronic, elastic, and optical properties of cubic KNbO3 and KTaO3 crystals

Cubic KNbO3 and KTaO3 crystals are studied using the first‐principles VASP code. By employing local density approximation (LDA), GGA‐PBE, and HSE06, the lattice parameters are optimized and compared with available experimental data, and the best agreement is achieved with HSE06. Electronic structures such as density of states, band structures, and charge‐density distribution are discussed in detail for both crystals. The single‐crystal elastic constants, polycrystalline elastic modulus, compressibility, Poisson's ratio, and anisotropy factors are obtained from the Voigt–Reuss–Hill approximation. The elastic anisotropy is modeled and visualized in the light of the elastic properties of both systems. The bandgaps of the two crystals are calculated with LDA, PBE, HSE06, and GW approximations (GW0), and the results of HSE06 and GW0 agree well with experimental data. Then the more reliable optical properties of KNbO3 and KTaO3 are acquired based on the bandgaps with HSE06, in which the previous scissors operator correction is avoided. Both crystals are brittle, and KTaO3 exhibits higher hardness and stiffness than KNbO3. Some novel results, such as Debye temperatures, sound velocities, and the extreme values of Young's modulus are obtained.

Optical and Magnetic Properties of Half-metallic (Zn, Mn)O Behaviors with LDA and LDA-SIC Approximations

Based on first-principles spin-density functional calculations, the optical and magnetic properties of Mn-doped ZnO diluted magnetic semiconductors with acceptor defects by Zn vacancies (VZn) are studied, using the Korringa–Kohn–Rostoker method (KKR) combined with the coherent potential approximation (CPA). Ferromagnetic and half-metallic behaviors were observed and confirmed with the local-moment-disordered (LMD) state energy for local density approximation (LDA) and local density approximation-self-interaction correction (LDA-SIC). The mechanism of hybridization and the interaction between magnetic ions in P-type (Zn, Mn)O are also investigated. Moreover, the optical absorption spectra obtained by ab-initio calculations confirm the ferromagnetic stability based on the charge state of magnetic impurities.

Theoretical study on electronic properties and pressure-induced phase transition in β-CdP 2

In this paper, both the local density approximation (LDA) and the generalized gradient approximation (GGA) are used to investigate the structural and electronic properties of the β modification of CdP 2 ( β-CdP 2) at zero pressure. In addition, the energy band structure, electron density of states (DOS) and projected density of states (PDOS) analysis of β-CdP 2 are presented. What is more, we study the properties of β-CdP 2 in the pressure range of 0–20 GPa, show the variations of the cell volume and band gap with the pressure for both LDA and GGA approximation. Then, the bulk modulus B 0 and its first pressure derivative B 0 ′ obtained by fitting different equations of state (EOS) to the pressure–volume ( P– V) relation at ambient pressure are presented and compared with the available experimental data. At the end of our study, we for the first time find that a pressure-induced structural phase transition from the tetragonal phase ( β-CdP 2) to a orthorhombic phase (α-CdP 2) when the pressure is increased to a value between 20 and 25 Gpa in theory.

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.

Density functional theory for non-relativistic fermions in the unitarity limit

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d = 4 − ε spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E = E LDA ( 1 + c s ( 3 N ) − 2 / 3 ) , where E LDA is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c s = 1.68 , which is significantly larger than the result for non-interacting fermions, c s = 0.5 .

Electronic structure of ScN and YN: density-functional theory LDA and GW approximation calculations

The desirable physical properties of hardness, high temperature stability, and conductivity make the early transition metal nitrides important materials for various technological applications. To learn more about the nature of these materials, the local-density approximation(LDA) and GW approximation i.e. combination of the Green function G and the screened Coulomb interaction W, have been performed. This paper investigates the bulk electronic and physical properties of early transition metal mononitrides, ScN and YN in the rocksalt structure. In this paper, the semicore electrons are regarded as valance electrons. ScN appears to be a semimetal, and YN is semiconductor with band gap of 0.142 eV within the LDA, but are in fact semiconductors with indirect band gaps of 1.244 and 0.544 eV respectively, as revealed by calculations performed using GW approximation.

Computational design ofSi∕SiO2interfaces: Stress and strain on the atomic scale

In this paper, we present results of a comparative computational study of silicon oxide interfaces with (100), (111), and (110) silicon surfaces. Density functional theory (DFT) in the local density approximation (LDA) and generalized gradient approximation with plane wave basis set and in the LDA approximation with localized numerical atomic orbitals are applied to investigate the relation between the structure and topology of chemical bonds and stress and strain effects at different $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Si}{\mathrm{O}}_{2}$ interfaces, which play a crucial role in electronics materials and devices. The resulting stress energies are discussed in terms of chemical, mechanical, and electric polarization components. According to our observations, chemical and mechanical components in the interface energy are not sufficient for description of silicon suboxide systems including $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Si}{\mathrm{O}}_{2}$ interfaces and the long range electrostatic interactions provide a non-negligible contribution. We uncovered computationally an effect of thermodynamic stabilization of oxygen incorporation in silicon lattice, which may have potential implications for nanoscale electronic device design. The trends in the stress energies derived from the results of the calculations are independent from the DFT approaches applied in this study.

Using the local density approximation and the LYP, BLYP and B3LYP functionals within reference-state one-particle density-matrix theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e. its integrand contains only the coordinates of two electrons, say r 1 and r 2, and it has a Dirac delta function δ(r 1 - r 2 as a factor. Since Brueckner and Hartree–Fock orbitals are often very similar, any local exchange functional that works well with Hartree–Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle–Salvetti correlation-energy functional and the LYP variant are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: one is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.

Orbital energy analysis with respect to LDA and self-interaction corrected exchange-only potentials

The self-interaction correction of Perdew and Zunger with the optimized effective potential using the Krieger–Li–Iafrate approximation is analyzed for atomic and molecular systems in the exchange-only context. Including the self-interaction correction (SIC) orbital by orbital shows that the appropriate asymptotic behavior of the exchange potential can be achieved if just the contribution of the highest occupied molecular orbital (HOMO) is considered. However, if a good description of the exchange potential in the valence region is required, and consequently a good description of the HOMO energy, then all electrons of the valence shell must be taken into account. In contrast, the lowest unoccupied molecular orbital (LUMO) is described adequately if just the HOMO SIC contribution is employed. In addition, if the lowest occupied orbital is also considered in the SIC approximation, there is an improvement in the description of the exchange potential in inner regions of an atom. When all electrons in an atom or in a molecule are considered in the SIC approximation, there exists a linear relationship between their occupied orbital energies and those obtained with the local density approximation (LDA). This indicates that the SIC and LDA occupied orbital energies are related by a shift. Furthermore, for a set of atoms or molecules there is a linear relationship between HOMO energies obtained with LDA and those obtained with the SIC approximation. Using both observations, the shift between the occupied orbital energies LDA and SIC is reported. We found that this shift (obtained for the occupied orbitals) cannot be applied to the virtual orbitals, in particular to the LUMO. However, we do find an additional linear relationship between LUMO energies obtained with LDA and those obtained with the SIC approximation. The difference between the LUMO and HOMO energy (GAP) obtained with the LDA and SIC approximations is compared with that obtained with an exact local-multiplicative exchange potential and all are compared with experimental vertical excitation energies. Whereas the LDA GAP underestimates the excitation energies, the GAP obtained with the SIC approximation and with an exact local-multiplicative exchange potential overestimates this quantity. From an analysis of the exchange energy for simple molecules, and with a similar approach to the modified Xα method, we found a linear relationship between the SIC and Hartree–Fock (HF) methods. We show numerically that the nondiagonal terms of the exact orbital representation of the exchange energy can be approximated by the SIC approach.

Periodic Density Functional LDA and GGA Study of CO Adsorption at the (001) Surface of MgO

The deficiencies of the local density approximation (LDA) to describe weakly adsorbed species on ionic surfaces are exposed in the current study of CO on the (001) surface of MgO. The authors applied a periodic formulation of density functional theory with crystal orbitals and charge density expanded as linear combinations of atomic orbitals of Gaussian form. The binding was investigated for four orientations of the CO molecule; either the carbon or oxygen atom of CO down over either the surface magnesium cation or oxygen anion. The authors find that the carbon down over the magnesium cation is the only noticeably attractive configuration, when basis set superposition error is corrected for, and estimate the binding energy of CO to be 1.9 kcal/mol for the Perdew, Burke, and Enzerhof (PBE96) functional. The binding energy obtained in the LDA approximation is as large as 7.4 kcal/mol. For the C-down-over-Mg configuration, the CO stretching frequency shift is only 4 cm{sup {minus}1} for the PBE96 functional. This binding energy, vibrational shift, and analysis of density of states indicate that little chemical bonding accompanies the adsorption. The values of binding energy and vibrational shift support a suggestion by Nygren and Pettersson that the CO adsorption discussedmore » by He et al. actually takes place at defect sites on the (001) surface of MgO.« less

Elastic properties of potential superhard phases ofRuO2

First-principles plane-wave pseudopotential and full-potential linearized-augmented plane-wave methods have been used to study the elastic and electronic properties of several potential superhard ${\mathrm{RuO}}_{2}$ phases. The structures, relative stabilities, and the elastic constants and bulk moduli of these phases have been calculated within local-density approximation (LDA) and generalized gradient approximation (GGA). In ${\mathrm{RuO}}_{2},$ the LDA and GGA approximations yield smaller and larger lattice constants, respectively, for the $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}{\mathrm{RuO}}_{2}$ structure. The internal structural parameter for oxygen atoms in the $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{}$ structure has a volume dependence that differs from the experimental result and therefore implies a significantly different compression mechanism. The calculated bulk moduli are very similar for the fluorite and $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{}$ structures and therefore apparently independent of the internal structural parameter. The structure and stability of a hypothetical orthorhombic ${\mathrm{RuO}}_{2}$ phase is investigated.