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γ-Al2O3 is a defective spinel phase of alumina with cation site vacancies randomly distributed. Its structure and properties are not well understood. There has been long-standing controversy as to whether the cation vacancies are located at the tetrahedral sites or the octahedral sites. Based on an empirical pair potential calculation and first-principles electronic structure studies, we have concluded that cation vacancies are preferentially located at the octahedral sites in bulk γ-Al2O3. Our calculation shows that the electronic structure of γ-Al2O3 differs from that of α-Al2O3 in fine details. γ-Al2O3 has a smaller band gap and wider valence bandwidths. The calculated density of states (DOS) of γ-Al2O3 is in good agreement with recent experimental XPS and XES data. Site- and orbital-resolved partial DOS (PDOS) of Al atoms shows significant dependence on the local coordinations. The PDOS of an oxygen adjacent to a vacancy differs substantially from that of a fully coordinated anion.

The electronic structure and bonding in the (Na15/32Bi½)TiO3 (NBT) crystal and its solid solution with BaTiO3 (BT) are studied by first-principles local density calculations. For the solid solution. an ordered superstructure (Na15/32Bi15/32Ba1/16)TiO3 with 320 atoms in a large celi is proposed. The results show that both NBT and NBT-BT are semiconductors with a band gap of about 1 eV. NBT is shown to be a harder crystal than PbTiO3 and PbZrO3 by having a larger calculated bulk modulus. This can be attributed partly to the increased covalent character of bonding in NBT and NBT-BT crystals. The calculated O K edges for a number of related crystals are presented and compared. It is suggested that electron energy loss near-edge structure measurements can be an effective tool to characterize the samples for different piezoelectric materials.

The electronic structure and bonding of Gd{sub 3}Sc{sub 2}Ga{sub 3}O{sub 12} (GSGG), Gd{sub 3}Sc{sub 2}Al{sub 3}O{sub 12} (GSAG), and Gd{sub 3}Ga{sub 5}O{sub 12} (GGG) crystals with a garnet structure are studied by means of first-principles local-density calculations. The results are compared with a similar calculation on yttrium aluminum garnet [Y{sub 3}Al{sub 5}O{sub 12} (YAG)]. The calculated equilibrium volumes of the three crystals are close to the measured volumes with a slight overestimation for GGG. GGG also has a smaller bulk modulus than the other three crystals. The calculated density of states and their atomic and orbital decompositions are presented and contrasted. All four crystals show very similar band structures and interatomic bonding. However, it is found that in GSGG and GSAG crystals, the Sc atom at the octahedral site shows a higher covalent character and an increased bond order in comparison to Ga or Al at the same site. This result may provide some insight into the significant difference in the radiation hardness of Cr{sup 3+}:Nd{sup 3+}:GSGG as compared to Nd{sup 3+}:YAG. (c) 2000 The American Physical Society.

Al K, Al L2,3, O K, Y L2,3, and Y M2,3 energy-loss near-edge structures (ELNESs) of Y3Al5O12 (YAG) were measured using a dedicated scanning transmission electron microscope equipped with a parallel electron energy-loss spectrometer system. An attempt was made to interpret the experimental edges with the help of calculated near-edge structures. An ab initio orthogonalized linear combination of atomic orbitals method, within the local density approximation (LDA), was used to calculate the electronic structure of YAG. Site-decomposed and symmetry projected local densities of states (LDOS) and photo-absorption cross-sections (PACS) were compared to experimental ELNES spectra. There is reasonable agreement between the five different, measured spectra and calculated near-edge structures. PACS calculations correlated better than LDOS with the experimental edges in terms of relative intensities of the peaks. Through a comparison with site-decomposed LDOS calculations, several features of the experimental...

Based on ab initio calculations of electronic structure and properties of five crystals: $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3},$ ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12},$ ${\mathrm{YAlO}}_{3},$ ${\mathrm{Y}}_{4}{\mathrm{Al}}_{2}{\mathrm{O}}_{9},$ ${\mathrm{Y}}_{2}{\mathrm{O}}_{3},$ with different Al to Y ratios and local coordinations, it is concluded that the electronic properties of the Y-Al-O system cannot be simply scaled according to cation ratio, and any of the fundamental properties cannot be transferred from one crystal to another. This finding has an implication on the segregation of Y at the internal boundaries in alumina and the precipitate phases contained therein. It is speculated that possible Y-Al interaction may explain the ``Y effect'' in the Y-containing aluminum oxide. The electronic structure and bonding of ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12},$ ${\mathrm{YAlO}}_{3},$ and ${\mathrm{Y}}_{4}{\mathrm{Al}}_{2}{\mathrm{O}}_{9}$ crystals are discussed in considerable detail in relation to their complex structures.

The electronic structure of yttrium aluminum garnet $({\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12})$ is studied by means of first-principles local-density calculations. Results on band structure, density of states, partial density of states, effective charges, bond order, charge-density distributions, equilibrium lattice constant, bulk modulus, and pressure coefficient as well as the pressure dependence of the band gap are presented. The calculated results are in good agreement with experimental data. The differences in chemical bonding for Al ions at the octahedral and tetrahedral sites are clearly delineated and their implications discussed.

The electronic structure of crystalline Y2O3 is investigated by first-principles calculations within the local-density approximation (LDA) of the density-functional theory. Results are presented for the band structure, the total density of states (DOS), the atom-and orbital-resolved partial DOS. effective charges, bond order, and charge-density distributions. Partial covalent character in the Y-O bonding is shown, and the nonequivalency of the two Y sites is demonstrated. The calculated electronic structure is compared with a variety of available experimental data. The total energy of the crystal is calculated as a function of crystal volume. A bulk modulus B of 183 Gpa and a pressure coefficient B' of 4.01 are obtained, which are in good agreement with compression data. An LDA band gap of 4.54 eV at Gamma is obtained which increases with pressure at a rate of dE(g)/dP = 0.012 eV/Gpa at the equilibrium volume. Also investigated are the optical properties of Y2O3 up to a photon energy of 20 eV. The calculated complex dielectric function and electron-energy-loss function are in good agreement with experimental data. A static dielectric constant of epsilon(O)= 3.20 is obtained. It is also found that the bottom of the conduction band consists of a single band, and direct optical transition at Gamma between the top of the valence band and the bottom of the conduction band may be symmetry forbidden.

The electronic structure of a microporous titanosilicate framework, ETS-10 is calculated by means of a first-principles self-consistent method. It is shown that without the inclusion of the alkali atoms whose positions in the framework are unknown, ETS-10 is an electron deficient system with 32 electrons per unit cell missing at the top of an otherwise semiconductor-like band structure. The calculated density of states are resolved into partial components. It is shown that the states of the missing electrons primarily originate from the Ti—O bond. The local density of states of the Ti-3d orbitals in the ETS-10 framework is quite different from the perovskite BaTiO3. The possibilities of ETS-10 crystal being ferroelectric or having other interesting properties are discussed.

The electronic structure and the Fermi surfaces of the organic superconductor {kappa}-(BEDT-TTF){sub 2}Cu[N(CN){sub 2}]Br are elucidated by first-principles calculations. The results show very narrow bands, high state density at the Fermi level, and a small band effective mass of 0.28m{sub 0} for the closed hole orbit. The topological features of the Fermi surfaces with multiple sheets are more complicated than that of {kappa}-(BEDT-TTF){sub 2}Cu(NCS){sub 2}. Fermi electron distribution on the central C{double_bond}C double bond reveals the nonequivalency of the two central C atoms. {copyright} {ital 1997} {ital The American Physical Society}

The optical properties of poly(di-n-hexylsilane) are studied by first-principles local-density calculations based on the crystal structure recently determined by x-ray diffraction. The one-dimensional nature of the band, the orbital composition of the states, the charge distribution of the highest-occupied-molecular-orbitals--lowest-unoccupied-molecular-orbitals states on the Si backbone, the effective masses, and the anisotropic optical conductivity are all clearly delineated. \textcopyright{} 1996 The American Physical Society.

The electronic structure and the optical properties of the organic superconductor \ensuremath{\kappa}-(BEDT-TTF${)}_{2}$Cu(NCS${)}_{2}$ are fully elucidated by means of first-principles self-consistent local-density calculation. The band effective masses on the Fermi surfaces are found to be ${\mathit{m}}_{\mathrm{\ensuremath{\alpha}}}^{\mathit{b}\mathrm{*}}$=1.77 m and ${\mathit{m}}_{\mathrm{\ensuremath{\beta}}}^{\mathit{b}\mathrm{*}}$=3.50 m, and the density of state at the Fermi level is 12.8/eV cell. These results are quite different from the existing calculations based on semiempirical methods, and are in much better agreement with experiments. Remarkable similarities in the electronic structure between the organic superconductors and the alkali-doped fullerene superconductors are pointed out and the implications discussed.

The electronic structure and bonding of the complex ceramic crystal Y10[SiO4]6N2 is studied by a first-principles method. It is shown that this crystal is an insulator with a direct band gap of 1.3 eV. It has some unique properties related to the one-dimensional chain structure in the c-direction and the planar N-Y bonding in the x-yplane.

The electronic structures of the ternary superconductors MoRuP and ZrRuP in the orthorhombic (o-) and hexagonal (h-) phases were calculated by a first-principles method and then compared. For h-MoRuP, the theoretically predicted structure was used. Based on the comparative studies of the electronic structures of the known superconductors of o-MoRuP (Tc=15.5 K), o-ZrRuP (Tc=4 K), and h-ZrRuP (Tc=13 K), it is argued that h-MoRuP may have a transition temperature Tc exceeding 20 K.

The electronic structure and magnetic properties of crystalline Li3FeN2 were studied by a first-principles method. It is shown that Li3FeN2 is nearly a half metal with a large degree of spin polarization at the Fermi level. The calculated Fe moment of 1.49μB is in good agreement with the measured value. It is also shown that the ferromagnetic interaction is along the one-dimensional chain of Fe atoms, modified by the large degree of polarization of the Li ions. Based on the analysis of the spin-polarized band structure and the density of states, it is argued that a genuine half metal in the ternary Fe nitride compounds may be possible.

The electronic structure and the optical properties of the cubic hydrate H[sub 2]-H[sub 2]O at high pressure are elucidated by means of first-principles local-density calculations. The results are compared with the [ital Ic] phase of ice. It is shown that the encapsulated H[sub 2] molecules interact weakly with the H[sub 2]O network. The valence-band structure is only slightly modified while the conduction band becomes very different. A number of important physical properties including the bulk modulus, optical-absorption spectrum, refractive index, pressure dependence of the gap, etc., are predicted for H[sub 2]-H[sub 2]O.

The positron lifetimes of two organic superconductors, {kappa}-(ET){sub 2}Cu(NCS){sub 2} and {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br, are measured as a function of temperature across {Tc}. A drop of positron lifetime below {Tc} is observed. Positron-electron momentum densities are measured by using 2D-ACAR to search for the Fermi surface in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br. Positron density distributions and positron-electron overlaps are calculated by using the orthogonalized linear combination atomic orbital (OLCAO) method to interprete the temperature dependence due to the local charge transfer which is inferred to relate to the superconducting transition. 2D-ACAR results in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br are compared with theoretical band calculations based on a first-principles local density approximation. Importance of performing accurate band calculations for the interpretation of positron annihilation data is emphasized.

The electronic structure and the optical properties of the cubic phase of ice and an idealized ordered-phase of ice In have been studied by means of first-principles local density calculations. The use of extended basis set in the calculation is essential for highly accurate results. Almost identical results are obtained for the Ic and the idealized Ih phase. Comparison with available experimental data show very good agreement. Extension of the present calculation to other high pressure phases are discussed.

The addition of suitable dopants to ZrO[sub 2] can induce dramatic phase stabilization, and this dopant-induced phase stabilization is the basis of transformation toughening of zirconia-based structural ceramics. We have determined the electronic structure of three phases of ZrO[sub 2], cubic, tetragonal, and monoclinic, using vacuum-ultraviolet and x-ray-photoemission spectroscopies, coupled with [ital ab] [ital initio] band-structure and optical property calculations using the orthogonalized linear-combination-of-atomic-orbitals method, in an attempt to understand the complex interaction of the stabilizing dopants and associated atomic defects with the crystal structures of ZrO[sub 2] and their phase transitions. The experimental samples were single or polycrystalline stabilized materials which contain atomic defects, while the calculations were performed for undoped idealized ZrO[sub 2] structures without atomic defects. Reasonable agreement is found between experiment and theory at this level. The primary difference among the three phases of ZrO[sub 2] is the hybridization or mixing of the Zr 4[ital d] ([ital x][sup 2][minus][ital y][sup 2] and [ital z][sup 2]) and the Zr 4[ital d] ([ital xy], [ital yz], and [ital zx]) bands, which form the conduction bands as the symmetry decreases from cubic to monoclinic. This leads to a complex evolution of the O 2[ital p] to Zr 4[ital d]more » and the O 2[ital s] to Zr 4[ital d] interband transitions. In addition, in the real materials, the presence of yttrium stabilizer introduces additional Y 4[ital p] valence bands and Y 4[ital d] conduction bands. The effective coordination of zirconium by oxygen is reduced from eightfold to sevenfold by the presence of the stabilizing ions and defects and this leads to the introduction of an occupied Zr 4[ital d] valence band suggestive of the presence of Zr[sup 2+].« less

The electronic structure, the linear optical properties, and the structural properties of α-Al 2 O 3 in the corundum structure are studied by means of first-principles local density calculations. An indirect band gap of 6.29 eV is obtained, which is almost the same as the direct band gap of 6.31 eV at Γ. The calculated density of states are compared with X-ray photoemission and photoabsorption measurements. Real space charge density analysis shows Al 2 O 3 to be highly ionic with an effective charge formula of Al 2 +2.75 O 3 -1.83 . The calculated dielectric function is in general agreement with the experimental vacuum ultraviolet data

The electronic structure and the linear-optical properties of the nonlinear-optical crystal \ensuremath{\beta}-${\mathrm{BaB}}_{2}$${\mathrm{O}}_{4}$ (BBO) have been calculated using a first-principles band-structure method with the local-density approximation. The results are compared with those of another nonlinear-optical crystal ${\mathrm{LiB}}_{3}$${\mathrm{O}}_{5}$ (LBO). An indirect band gap of 5.52 eV and a direct gap of 5.61 eV at \ensuremath{\Gamma} for BBO are obtained, which are to be compared with the measured optical gap of 6.43 eV. It is shown that the electronic structure of the BBO is dominated by the characteristic ionic (${\mathrm{B}}_{3}$${\mathrm{O}}_{6}$${)}^{\mathrm{\ensuremath{-}}3}$ group in which the two different O sites show markedly different bonding structures. Comparison of charge-density distributions in BBO and LBO shows that the ionic groups are linked together in forming a networklike structure. The Ba atom in the BBO crystal is found to be bonded to the O ions in the adjacent layers in a partly covalent, partly ionic manner due to the presence of large semi-core-like 5p orbitals. The calculated optical properties for both BBO and LBO crystals are in good agreement with the measured vacuum ultraviolet spectrum especially in the region of absorption threshold. The agreements between theory and experiment near the absorption edges are much closer than that reflected by the gap values alone.

The electronic structure and the optical properties of Y3Fe5O12 crystal are calculated using the local spin density approximation+U approach. The intra-atomic correlation effect of the Fe 3d electrons is shown to be important in describing the insulating nature of the crystal. With a choice of the parameters U=3.5 eV and J=0.8 eV in the model Hamiltonian, a gap of 2.66 eV is obtained and a significant lowering of the occupied potion of the Fe 3d states is observed. The calculated optical absorption in the range 3–6 eV is from the bulk O 2p to the Fe 3d band states. The calculated spin magnetic moments are in good agreement with experiment.

The electronic structure, the linear optical properties, and the structural properties of α-Al 2 O 3 in the corundum structure are studied by means of first-principles local density calculations. An indirect band gap of 6.29 eV is obtained, which is almost the same as the direct band gap of 6.31 eV at Γ. The calculated density of states are compared with X-ray photoemission and photoabsorption measurements. Real space charge density analysis shows Al 2 O 3 to be highly ionic with an effective charge formula of Al 2 +2.75 O 3 -1.83 . The calculated dielectric function is in general agreement with the experimental vacuum ultraviolet data

The electronic structure of the ferroelectric crystal NaNO2 is studied by means of first-principles local density calculation. Band structure and density of states show very localized bands, typical of a molecular solid. An indirect band gap of 2.95 eV is obtained. Detailed charge density analysis shows the Na atom to be completely ionized, while the NO2 group form a strongly bonded ionic unit with substantial covalent bonding character between O and N atoms. Calculation of the electronic dielectric function shows strong absorption features at 3.0, 5.8, 11.1, and 12.0 eV. The anisotropic nature of the optical absorption in NaNO2 is revealed by resolving the dielectric function into three principal directions. The calculated static dielectric constant for NaNO2 in the x-, y-, z- directions are 1.60, 1.58, and 2.20 respectively in good agreement with the experiment.

The electronic, optical, and structural properties of fcc C{sub 60} crystal are studied as a function of cell volume by means of first-principles local-density calculations. The calculated equilibrium volume, bulk modulus, and the pressure-versus-volume relation are in good agreement with experimental measurements. Changes in the band structure, density of states, bonding pattern, dielectric constant, and optical spectrum with pressure are analyzed and discussed. It is found that the band gap and the absorption threshold energy decrease with increasing pressure while the static dielectric constant increases with increasing pressure. The charge-density map shows that at a pressure of 13 GPa covalent bonding between C atoms in different C{sub 60} molecules may form and metallization of C{sub 60} at ultrahigh pressure is unlikely. These results are in line with some very recent experimental observations.

The electronic structure, the charge-density distribution, and the optical-absorption spectrum of a ${\mathrm{CaF}}_{2}$ crystal are studied by means of a first-principles local-density calculation. The calculated imaginary part of the dielectric function is in good agreement with experimental measurement up to 27.0 eV. We have also used a simplified self-interaction-correction (SIC) model to address the problem of band-gap underestimation in the local-density calculation. Although some marginal improvement in the optical result has been achieved, there is no strong evidence of unequivocal rectification other than an increment in the band gap. This study shows additional (non-SIC) correction to the conduction-band states of ${\mathrm{CaF}}_{2}$ may also be necessary.

The band structures of {alpha}-rhombohedral B{sub 12} ({alpha}-{ital r}-B{sub 12}) and {alpha}-tetragonal B{sub 50} ({alpha}-{ital t}-B{sub 50}) crystals have been calculated by means of the first-principles orthogonalized linear combination of atomic orbitals method. It is shown that {alpha}-{ital r}-B{sub 12} is a semiconductor with an indirect band gap of 1.70 eV and {alpha}-{ital t}-B{sub 50} is a metal with a semiconductorlike band structure near the Fermi level. The intra-icosahedral and inter-icosahedral bondings in these two crystals are elucidated by resolving the density of states into various partial components, and by studying the valence-charge-density distributions. There is strong evidence for weak three-center bonding in the B crystals, but the traditional view regarding the bonding pattern in icosahedral B{sub 12} may be oversimplified. The total energies of {alpha}-{ital r}-B{sub 12} and {alpha}-{ital t}-B{sub 50} are calculated as a function of crystal volumes without change in the symmetry of the crystals. The equilibrium volume, the bulk moduli, and the cohesive energies obtained are in good agreement with available experimental data and some other recent calculations. Using the wave functions obtained from the band-structure calculation, the frequency-dependent interband optical conductivities in {alpha}-{ital r}-B{sub 12} and {alpha}-{ital t}-B{sub 50} crystals are also calculated. The realmore » and imaginary parts of the dielectric-function curve are shown as a function of photon energy up to 40 eV for {alpha}-{ital r}-B{sub 12} and up to 10 eV for {alpha}-{ital t}-B{sub 50}. They are significant differences in the optical properties of these two crystals because of the different nature of the band structures. For {alpha}-{ital r}-B{sub 12}, a large plasmon excitation at 31 eV is predicted.« less

The electronic structure and optical properties of crystalline C 60 and their pressure dependence have been studied by first-principles local density calculations. It is shown that fcc C 60 has a low dielectric constant and an optical spectrum rich in structures. The spectrum shows five disconnected absorption bands in the 1.4 to 7.0 eV region with sharp structures in each band that can be attributed to critical point transitions. This is a manifestation of the localized molecular structure coupled with long range crystalline order unique to the C 60 crystal. At a sufficient high pressure, the structures in the optical spectrum start to merge due to the merging of the bands. These results are in good agreement with some recent experimental measurements.

The electronic structure and the Fe moment distribution in Nd5Fe17 are calculated using the first-principles orthogonalized linear combination of atomic orbitals method. It is shown that there is no obvious correlation of the Fe moment with the nearest neighbor Fe–Fe separations. There is a reasonable correlation with the number of nearest Fe neighbors, NNN except for NNN=12. When the averaged Fe moments within the same group of Fe atoms of same NNN are plotted against the average Fe–Fe distances, the results are in good agreement with similar data derived from neutron diffraction analysis. The calculated total moment per formula unit and the average Fe moment are also in good agreement with experimental values.

The electronic structure of Y3Fe5O12 (YIG) crystal was calculated using the spin-polarized orthogonalized linear combination of atomic orbitals method in the local spin-density approximation. It is shown that YIG has a ferrimagnetic ordering with Fe spin magnetic moments of −0.62μB and +1.56μB at the octahedral 16(a) site and the tetrahedral 24(d) site, respectively. The origin of ferrimagnetism in the two Fe sublattices can be traced to the different ordering of the eg and t2g levels for the spin-up and spin-down electrons.

The electronic structures and the linear optical properties of superconducting fcc ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ and insulating bcc ${\mathrm{K}}_{6}$${\mathrm{C}}_{60}$ are calculated by means of a first-principles method within the local-density approximation. The calculated optical properties for these two crystals as well as those of fcc ${\mathrm{C}}_{60}$ are in very good agreement with recent electron-energy-loss spectra measurements.

The electronic and optical properties of C{sub 60} in the fcc lattice have been studied by a first-principles method. It is shown that C{sub 60} has a low dielectric constant and an optical spectrum rich in structures; this is drastically different from diamond and graphite. The spectrum shows five disconnected absorption bands in the 1.4 to 7.0 eV region with sharp structures in each band that can be attributed to critical-point transitions. This is a manifestation of the localized molecular structure coupled with long-range crystalline order.

The electronic structure and optical properties of KTiOPO{sub 4} have been calculated using a first-principles self-consistent method. It is shown that the electronic structure is characterized by localized molecular units of TiO{sub 6} and PO{sub 4}. Effective-charge calculation shows K and Ti to be highly ionized while P is also positively ionized because of the charge transfer to O atoms. The presence of the short Ti-O bonds in KTiOPO{sub 4} has a profound effect on its electronic structure. The calculated optical properties and their anisotropy are in good agreement with recent experimental measurement.

Results of site-specific and orbital-resolved partial density of states of YBa{sub 2}Cu{sub 3}O{sub 7} obtained from a first-principles self-consistent calculation using the orthogonalized linear combination of atomic orbitals method are presented. Special features in the bonding of the apical oxygen, O(4) are emphasized. The usefulness of these results in the interpretation of some experimental data is discussed.

The electronic structures, the charge-density distributions, and the optical-absorption spectra in MgO, {alpha}-Al{sub 2}O{sub 3}, and MgAl{sub 2}O{sub 4} crystals are studied by means of the first-principles self-consistent orthogonalized linear combination of atomic orbitals method. The calculated band structures of MgO and {alpha}-Al{sub 2}O{sub 3} are compared with experimental data and previous calculations. It is concluded that the electronic structure and optical properties of the spinel MgAl{sub 2}O{sub 4} cannot be taken as a simple average of that of MgO and {alpha}-Al{sub 2}O{sub 3}. By direct space integration of the calculated charge, it is shown that the ionic nature of these crystals should be best described by the formulas Mg{sup 1.83+}O{sup 1.83{minus}}, Al{sub 2}{sup 2.63+}O{sub 3}{sup 1.75{minus}}, and Mg{sup 1.79+}Al{sub 2}{sup 2.63+}O{sub 4}{sup 1.76{minus}}. The charge-density maps also reveal that there are open channels of very low electron density in MgAl{sub 2}O{sub 4}, which may be important in ionic conductivity. The calculated optical dielectric functions for the three crystals are compared with recent vacuum ultraviolet data for an energy range up to 40 eV and show good overall agreement. The existence of an excitonic peak near the absorption edge tends to sharpen the edge, thereby increasing the gap as comparedmore » with the one-electron local-density calculations. For absorption spectra beyond the excitonic peak, most of the experimentally resolved structures are reproduced by the calculations without the need of an adjustment to widen the gap. It appears that the high conduction-band states in these three crystals, calculated by using the local-density approximation, are reasonably accurate.« less

The band structures of the ferromagnetic compounds FeB, ${\mathrm{Fe}}_{2}$B, and ${\mathrm{Fe}}_{3}$B were calculated using a spin-polarized version of the first-principles self-consistent orthogonalized linear-combination-of-atomic-orbitals method. Results on the band structure, density of states (DOS), and site-, orbital-, and spin-decomposed partial DOS are presented. Mulliken population analysis indicates B to be an electron accepter in these compounds due to the low-lying levels of the B 2s and B 2p states relative to the Fermi level. It is also shown that the moment on B is slightly polarized opposite to the Fe moments. The magnetic structure and bonding in these three compounds are further revealed by the presentation of contour maps for the charge density and the spin density. Our calculation shows an average spin magnetic moment of 1.26, 1.95, and 1.94${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ per Fe site and -0.10, -0.23, and -0.29${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ per B site in FeB, ${\mathrm{Fe}}_{2}$B, and ${\mathrm{Fe}}_{3}$B, respectively. The results are in reasonable agreement with photoemission and neutron-scattering measurements. The nature of the Fe-B bond is discussed in connection with the electronic structure of ${\mathrm{Nd}}_{2}$${\mathrm{Fe}}_{14}$B intermetallic compounds and that of the ${\mathrm{Fe}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{B}}_{\mathit{x}}$ metallic glasses.

The band structure and the interband optical conductivity of a ${\mathrm{LiB}}_{3}$${\mathrm{O}}_{5}$ crystal with excellent nonlinear optical properties are studied by means of a first-principles method. The electronic structure is characterized by highly localized bands with a direct gap of 7.37 eV at \ensuremath{\Gamma} and a very low static dielectric constant of 2.7. The optical absorption curve shows several prominent structures but with very small directional anisotropy. The calculated frequency-dependent refractive index is in good agreement with experimental data.

The electronic structure, bonding, and optical properties of a new quaternary crystal ${\mathrm{Y}}_{3}{\mathrm{Si}}_{5}{\mathrm{N}}_{9}\mathrm{O}$ have been calculated using a first-principles method. The results are compared with the other four Y-Si-O-N quaternary crystals in the ${\mathrm{SiO}}_{2}\text{\ensuremath{-}}{\mathrm{Y}}_{2}{\mathrm{O}}_{3}\text{\ensuremath{-}}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ phase equilibrium diagram. ${\mathrm{Y}}_{3}{\mathrm{Si}}_{5}{\mathrm{N}}_{9}\mathrm{O}$ has a smaller band gap, larger optical dielectric constant, and stronger covalent bonding, which is attributed to its high N content in the crystal.

The crystal structure and electronic properties of the quaternary compound ${\mathrm{YSiO}}_{2}\mathrm{N}$ are investigated theoretically. It is shown that one of the possible low-symmetry structures obtained by an ab initio geometry optimization has a space group of $\mathrm{P}{6}_{1}22.$ This is different from the space group of $\mathrm{P}{6}_{1}$ that was suggested more than 25 years ago based on intensity calculations of the measured powder diffraction pattern. Using the newly determined structure, the electronic structure and bonding of this complex ceramic crystal is studied by the first-principles OLCAO method. It is shown that this crystal is an insulator with a calculated direct band gap of 4.35 eV within the local density approximation and strong Si-O and Si-N bonding. There is also considerable bonding between the Y ions and anions. The specific ${\mathrm{S}\mathrm{i}\ensuremath{-}\mathrm{O}}_{2}{\mathrm{N}}_{2}$ local bonding unit introduces several distinctive features to the occupied density of states. An interband optical absorption calculation shows major absorption peaks at 7.9 and 25.7 eV. The estimated optical dielectric constant is 3.75 while the plasma excitation frequency for ${\mathrm{YSiO}}_{2}\mathrm{N}$ is 20.0 eV.

The electronic structure and bonding in two complex crystals, yttrium oxyorthosilicate ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and yttrium pyrosilicate ${\mathrm{Y}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7},$ were studied by means of first-principles local density calculations. Both crystals are ionic insulators with large band gaps. It is shown that their electronic structure and bonding cannot be represented by the weighted sums of those of \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$ and ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}.$ On average, the Si-O (Y-O) bond in the ternary crystals tends to be weaker (stronger) than the respective bond in \ensuremath{\alpha}-${\mathrm{SiO}}_{2}({\mathrm{Y}}_{2}{\mathrm{O}}_{3}).$ It is further shown that the specific local atomic coordinations can lead to significantly different partial density of states that should be experimentally detectable. The bulk and optical properties of these two crystals were also calculated. We find the bulk modulus of ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}({\mathrm{Y}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7})$ to be 134.8 GPa (140.2 GPa). The optical dielectric constants for the two crystals are estimated to be 3.11 and 3.44, respectively. In the absence of any experimental data, these values are presented as theoretical predictions.

ZrW 2 O 8 has a negative thermal expansion, and exists in two crystalline forms. The stable cubic a phase transforms into an orthorhombic γ-phase at a low pressure of 0.21 GPa. A further increase in pressure beyond 1.5 GPacan induce an amorphous phase. The band structures of both α and y phases of ZrW 2 O 8 are studied using a first-principles method based on density-functional theory. α-ZrW 2 O 8 has an indirect band gap of 2.84 eV. while γ-ZrW 2 O 8 has a direct band gap of 2.17 eV. The electronic structure and bonding are discussed in the context of atom-resolved and orbital-resolved partial density of states, the Mulliken effective charges, and the bond orders. It is shown that γ-ZrW 2 O 8 has a larger total crystal bond order than α-ZrW 2 O 8 , due to the formation of additional W-O bonds. For the a phase, the calculated bulk modulus of 63 GPa is found to be in good agreement experimental values.

The ground-state electronic structure and bonding of two important laser crystals, BeAl{sub 2}O{sub 4} and LiYF{sub 4}, were calculated using a first-principles method based the local approximation of the density-functional theory. The results were compared with similar calculations on several other laser crystals including yttrium aluminum garnet (Y{sub 3}Al{sub 5}O{sub 12}). The geometry of each crystal was optimized first with all internal parameters relaxed. The bulk moduli B were obtained by fitting the calculated total energies at different volumes to the Murnaghan equation of state. It was found that LiYF{sub 4} (B=90.0GPa) is much softer than BeAl{sub 2}O{sub 4} (B=217.3GPa). In BeAl{sub 2}O{sub 4}, Be and Al atoms have very similar local electronic structure and the crystal resembles that of {alpha}-Al{sub 2}O{sub 3} (sapphire). LiYF{sub 4} is a highly ionic crystal while BeAl{sub 2}O{sub 4} has a significant amount of covalent mixing. The density of states, their atomic and orbital decompositions, the effective charges, the bond order, and the charge distributions in these two crystals are presented and contrasted.

The electronic structure and the optical properties of a model of negative-curvature fullerene suggested by Vanderbilt and Tersoff are studied by detailed first-principles local-density calculations. It is shown that this hypothetical material is a semiconductor with an indirect band gap of 0.48 eV and a large ratio of electron-hole effective masses. The optical properties are very different from those of graphite or C{sub 60} fullerene.

The first‐principles orthogonalized linear combination of atomic orbitals method (OLCAO) in the local density approximation is used to study the electronic structure‐density of states (DOS), and Fermi surface (FS) of superconducting potassium carbides. (AIP)

We have studied the electronic structure and the distribution of magnetic moments in amorphous Fe metallic glass by means of first‐principles calculations. Large periodic models containing 100 and 200 atoms in a cubic cell are constructed using the Monte Carlo technique. The electronic structures are calculated within the real‐space OLCAO scheme using the spin‐polarized potentials obtained from the crystalline calculation. Results are presented for the spin‐projected density of states (DOS), the partial DOS, and spin magnetic moments. It is shown that spin moments in a‐Fe is mainly determined by the minority spin band because the Fermi level is located near the middle of this band. The site‐specific distribution of Fe moments in an amorphous environment is analyzed as a function of local short‐range order such as the number of nearest‐neighbor atoms and the average nearest‐neighbor distances. Extension of similar calculations to a‐Fe1−x–Bx metallic glasses is also discussed.

The structure of EST-10, a member of synthetic microporous titanosilicates, was recently determined by an ingenious combination of experimental and simulational techniques. However, the locations of the alkali atoms in the framework remain elusive and its electronic structure is totally unknown. Based on first-principles local density calculations, the possible locations of the alkali atoms are identified and its electronic structure and bonding fully elucidated. ETS-10 is a semiconductor with a direct band gap of 2.33 eV. The Na atoms are likely to locate inside the seven-member ring pore adjacent to the one-dimensional Ti-O-Ti-O- chain.

The electronic structure and the optical properties of \ensuremath{\alpha}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$, \ensuremath{\beta}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$, and ${\mathrm{Si}}_{2}$${\mathrm{N}}_{2}$O crystals are studied by means of first-principles local-density calculations. Together with the earlier published result on \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$, a comparative study of the electronic bonding and optical excitations in these crystals becomes possible. It is found that the electronic structure of the \ensuremath{\beta} and the \ensuremath{\alpha} phases of ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ are similar, but with some subtle differences that can be traced to different stacking sequences of the atomic layers and the slightly different local bonding structure. The electronic structure of the ${\mathrm{Si}}_{2}$${\mathrm{N}}_{2}$O crystal cannot be adequately described as a simple superposition of ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ and \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$. The presence of both Si-N and Si-O bonds in ${\mathrm{Si}}_{2}$${\mathrm{N}}_{2}$O crystals affects the local potential and results in a downward shift of the O levels. The calculated density of states (DOS) and the orbital-resolved partial DOS are in good general agreement with the photoemission and x-ray emission measurements. Better resolution in the calculated DOS shows that the upper valence band has five peaks rather than three.Effective charge calculation suggests the ionic formulas of the four crystals to be \ensuremath{\alpha}-(${\mathrm{Si}}^{+2.52}$${)}_{3}$(${\mathrm{N}}^{\mathrm{\ensuremath{-}}1.89}$${)}_{4}$, \ensuremath{\beta}-(${\mathrm{Si}}^{+2.50}$${)}_{3}$(${\mathrm{N}}^{\mathrm{\ensuremath{-}}1.87}$${)}_{4}$, \ensuremath{\alpha}-(${\mathrm{Si}}^{+2.60}$)(${\mathrm{O}}^{\mathrm{\ensuremath{-}}1.30}$${)}_{2}$, and (${\mathrm{Si}}^{+2.54}$${)}_{2}$(${\mathrm{N}}^{\mathrm{\ensuremath{-}}1.90}$${)}_{2}$(${\mathrm{O}}^{\mathrm{\ensuremath{-}}1.25}$). The calculated optical properties of the four crystals show similar features in the gross absorption spectra but with differences in the peak positions. It is shown that all four crystals have intrinsic absorption tails, and those of ${\mathrm{Si}}_{2}$${\mathrm{N}}_{2}$O and \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$ are larger than those of \ensuremath{\alpha}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ and \ensuremath{\beta}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$. This is explained by the nature of the wave function at the conduction-band minimum. The difference in the intrinsic band gap and the extrapolated optical gap is pointed out. Comparison with experimental data on amorphous ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ shows good agreement with the optical conductivity of the crystalline phases. It is also shown that ${\mathrm{Si}}_{2}$${\mathrm{N}}_{2}$O and \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$ crystals have negligible optical anisotropy, while for \ensuremath{\alpha}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ and \ensuremath{\beta}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ the in-plane component of the dielectric function in the long-wavelength limit is smaller than the corresponding component parallel to the c axis. The calculated refractive indices are in good agreement with the limited data available.

The electronic structure and optical properties of rhombohedral ${\mathrm{LiNbO}}_{3}$ have been studied by a first-principles method in the local-density approximation (LDA). An approximate k-dependent and energy-dependent self-energy-correction scheme is then applied to the LDA result, yielding a direct band gap of 3.56 eV at \ensuremath{\Gamma}. It is shown that the calculated dielectric function with the self-energy-corrected eigenvalues is in much better agreement with the optical and refractive index data than those from LDA. The calculated negative optical birefringence is in excellent agreement with experiment. Valence-charge analysis indicates the ionic formula for ${\mathrm{LiNbO}}_{3}$ to be ${\mathrm{Li}}^{0.98}$${\mathrm{Nb}}^{3.67}$(${\mathrm{O}}^{\mathrm{\ensuremath{-}}1.55}$${)}_{3}$.