Electronic Energy Structure of TiCu and Ti2Cu

The electronic energy structure (EES) of the valence band in tetragonal TiCu and Ti₂Cu was studied experimentally and theoretically. The experimental study of valence band EES was carried out by X-ray photoelectron spectroscopy (XPS). The calculations were performed in terms of the cluster version of multiple scattering theory in a self-consistent field approximation. The results are compared with X-ray emission spectroscopy data available in the literature. The density of state curves agree well with spectroscopic data. The major contribution to XPS is from the copper d-states. The specifics of chemical bonding in the compounds leading to the observed changes in the shape of the valence band X-ray photoelectron spectra are discussed.     

Obtaining self–consistent wave functions which satisfy the virial theorem

The virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self-consistent wave functions, the virial theorem can be satisfied, but self-consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, V_ne, V_ee, V_nn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self-consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.     

Quantum chemical simulations of hole self-trapping in semi-ionic crystals

A novel formalism is presented for reliable calculations of the energetics of hole self-trapping in semi-ionic solids with mixed valence bands. Unlike previous model-Hamiltonian-type approaches, it is based on self-consistent quantum chemical INDO simulations of the atomistic and electronic structure of a self-trapped hole, making no a priori assumptions about a particular form of its localization (if any). This formalism is applied to the problem of hole self-trapping in corundum crystals (α–Al₂O₃). The hole self-trapping is found to be energetically favorable in the form of a diatomic O₂ molecule with strong covalent bonding quite similar to the self-trapped hole (V_K-center) in alkali halides. The so-called localization energy (i.e., the energy that is required to localize the Bloch-like wave packet of the free hole on the molecule, as the first stage of further trapping) is essentially less than one-half of the upper valence band width, which is the estimate commonly used for ionic solids. © 1994 John Wiley & Sons, Inc.     

Linear response and quasiparticle calculations as probes of the Kohn-Sham eigenvalues in metals

The Kohn-Sham eigenvalues were formally introduced into density functional theory as Lagrange multipliers in the implementation of the minimum principle for the total energy of a many-electron system. No general results are available concerning the physical significance of these one-electron eigenvalues (with the exception of the highest occupied level, which equals the Fermi energy). Recent ab initio calculations of dynamical response in metals make explicit use of the Kohn-Sham band structure, and associated wave functions, through the use of spectral representations. This opens up the possibility of examining the significance of the eigenvalues at an “empirical” level, i.e., through direct comparison with the results of spectroscopic measurements. A particularly interesting example is afforded by new inelastic x-ray scattering experiments on A1. For a special wave vector transfer, q_o ≈︂ 1.5k_F, the measured spectrum provides a direct mapping of the Kohn-Sham noninteracting spectrum. For a range of wave vectors about q_o, the bare Kohn-Sham spectrum still reproduces all the main features of the measurements; this suggests that, in this metal, the Kohn-Sham eigenvalues are good approximations to the quasiparticle energies. We also discuss the interplay between Kohn-Sham bands and the energy of the “anomalous” plasmon in Cs, whose dispersion bears a signature of the excited-state band structure. Finally, and in a more formal framework, we outline the results of a first-principles comparison between quasiparticle amplitudes and Kohn-Sham wave functions at a jellium surface; the latter turn out to be excellent approximations to the former. © 1996 John Wiley & Sons, Inc.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

The two-dimensional band structure of (polyphthalocyaninato)Ni(II)

The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF ) Hartree–Fock (HF ) crystal orbital (CO ) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a_1u combination (D_4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ?_v of 2.92 eV. This value is close to the Δ?_v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at ?4.9 eV; they are predicted between ?12.2 and ?16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.     

Calculation of quasiparticle energy of molecular systems by the GW method

The quasiparticle energy of the H₂ molecule is calculated by using the GW method, in which the self‐energy operator fully depends on the frequency. The initial Green function G₀ is constructed from the wave function obtained by the Hartree–Fock approximation (HFA) and local density approximation (LDA) in the framework of the density functional theory (DFT). From the results obtained we have shown that the wave function from the DFT–LDA is more effective than that from the HFA for G₀. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 348–353, 2001     

Indirect adatom interactions via III–V semiconductor substrates

Substrate-mediated interactions between adatoms on III–V semiconductors are investigated by using the self-consistent Anderson–Newns model in the Hartree–Fock approximation. The Green function formalism of the Dyson equation approach is employed to derive Chebyshev polynomial expressions for the chemisorption energy, interaction energy, and charge transfer, in terms of the adatom separation d. An alternating s- and p-orbital model of GaSb and InAs enabled interacting hydrogen adatoms on their (100) and (111) faces to be studied. As in the metal–substrate case, the chemisorption energy decreased with increasing band widths and adbond energy and, additionally, with increasing band gap. The interaction energy was found to have a d⁻² damping factor for the (100) faces and a d⁻³ factor for the (111) faces, its magnitude being larger for smaller gaps. Self-consistency is shown to play a significant role in interaction energy calculations for small values of d. In the case of charge transfer, its variation with d is purely a self-consistent result. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 377–397, 1998.     

Theoretical studies of the band structure and optoelectronic properties of ZnOxS1−x

In the present article, we have revisited the electronic band gap nature of ZnO_xS_1?x (0 ≤ x ≤ 1) with the recently developed modified Becke and Johnson exchange potential and the calculated band gaps are found consistent with the experimental results. We expect that the band gap bowing parameter obtained in the present work will be close to the experimental one. As the optical properties of ZnO_xS_1?x (0 ≤ x ≤ 1) are very important, therefore different optical parameters like dielectric functions, refractive index and reflectivity are also calculated. The results are illustrated in terms of band structures, band gap energy as a function of oxygen composition, total and partial density of states. © 2012 Wiley Periodicals, Inc.     

Density Functional Investigations of Electronic Structure and Dehydrogenation Reactions of Al‐ and Si‐Substituted Magnesium Hydride

The effect on the hydrogen storage attributes of magnesium hydride (MgH₂) of the substitution of Mg by varying fractions of Al and Si is investigated by an ab initio plane‐wave pseuodopotential method based on density functional theory. Three supercells, namely, 2×2×2, 3×1×1 and 5×1×1 are used for generating configurations with varying amounts (fractions x=0.0625, 0.1, and 0.167) of impurities. The analyses of band structure and density of states (DOS) show that, when a Mg atom is replaced by Al, the band gap vanishes as the extra electron occupies the conduction band minimum. In the case of Si‐substitution, additional states are generated within the band gap of pure MgH₂—significantly reducing the gap in the process. The reduced band gaps cause the Mg? H bond to become more susceptible to dissociation. For all the fractions, the calculated reaction energies for the stepwise removal of H₂ molecules from Al‐ and Si‐substituted MgH₂ are much lower than for H₂ removal from pure MgH₂. The reduced stability is also reflected in the comparatively smaller heats of formation (ΔH_f) of the substituted MgH₂ systems. Si causes greater destabilization of MgH₂ than Al for each x. For fractions x=0.167 of Al, x=0.1, 0.167 of Si (FCC) and x=0.0625, 0.1 of Si (diamond), ΔH_f is much less than that of MgH₂ substituted by a fraction x=0.2 of Ti (Y. Song, Z. X. Guo, R. Yang, Mat. Sc. & Eng. A 2004 , 365, 73). Hence, we suggest the use of Al or Si instead of Ti as an agent for decreasing the dehydrogenation reaction and energy, consequently, the dehydrogenation temperature of MgH₂, thereby improving its potential as a hydrogen storage material.     

Bi掺杂锐钛矿相TiO2第一性原理计算

采用密度泛函理论(DFT)下的第一性原理平面波超软赝势方法计算了Bi掺杂前后锐钛矿相TiO2的电子结构和光学性质。结果分析发现:掺杂后Ti的电荷布居数下降,O的布居数增加;同时在TiO2禁带中引入了杂质能级,禁带宽度略微变大,但是杂质能级的作用抵消了禁带宽度变大带来的不利影响,使得掺杂后TiO2吸收带边红移并在可见光范围内吸收明显增强。     

The Photoelectron Spectrum of Tetrafluorobutatriene

The He(I_α) and He(II_α) spectra of tetrafluorobutatriene 3 (F) have been recorded for comparison with those of butatriene 3 (H). Ab initio double-zeta basis self-consistent field (SCF) and configuration interaction calculations on butatriene show that, contrary to previous assignment, no shake-up band is expected to appear in the 9–10 eV energy range of the photoelectron spectrum. Further, such SCF calculations on tetrafluorobutatriene support the use of the perfluoro effect in assigning the purely π orbital ionizations. It is argued that 3 (F) is a key compound for the study of the perfluoro effect. This is supported by a qualitative comparison of its photoelectron-spectroscopic results with those of other perfluoro systems.     

Ab-initio calculation of structural, electronic, and optical characterizations of the intermetallic trialuminides ScAl3 compound

We present first-principles study of the electronic and the optical properties for the intermetallic trialuminides ScAl₃ compound using the full-potential linear augmented plane wave method within density-functional theory. We have employed the generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for calculating the electronic band structure and optical properties. The electronic specific heat coefficient (γ), which is a function of density of states, can be calculated from the density of states at Fermi energy N(E_F). The N(E_F) of the phase L1₂ is found to be lower than that of D0₂₂ structure which confirms the stability of L1₂ structure. We found that the dispersion of the band structure of D0₂₂ is denser than L1₂ phase. The linear optical properties were calculated. The evaluations are based on calculations of the energy band structure.     

Exploring the electro‐optical properties of conjugated polymers based on oligo‐selenophene and oligo(3,4‐ethylenedioxyselenophene)

For seeking high‐efficiency narrow‐band‐gap donor materials to enhance short‐circuit current density for organic solar cells, a series of oligo‐selenophene (OS) and oligo(3,4‐ethylenedioxyselenophene) (OEDOS) with various chain lengths were designed and characterized using density functional theory (DFT) and time‐dependent DFT calculations. Based on the results, it can be seen that with increasing chain length of the oligomers in both syn‐ and anti‐adding manners, the bond length alternation is decreased which indicates that the π‐electron delocalization is increased. Also, when the chain length is increased the electronic energy gap and the optical energy gap are decreased. It can be concluded that the syn‐(OS)_n=10,14,15, anti‐(OS)_n=14 and anti‐(OEDOS)_n=7–12 oligomers can act as low‐band‐gap polymers. Therefore they can absorb more sunlight based on maximum wavelength (higher than 620 nm). Furthermore, a red shift in the simulated absorption spectra of (OS)_n and (OEDOS)_n donors is observed. It is found that (OS)_n=14,15 with syn configuration of the extended oligomers is the most suitable donor for the design of high‐performance organic solar cells possessing a narrow electronic band gap, high exciton lifetime and broad and intense absorption spectra that cover the solar spectrum leading to complete light‐harvesting efficiency.     

Étude des structures électroniques de In2O3 pur et dopé avec l’étain

The electronic structures of the sesquioxide In₂O₃ and Sn-doped In₂O₃ are examined both self-consistently within the ab initio local density functional theory and using the non self-consistent extended Hückel method. A direct band gap and a wide dispersion of the bottom of the conduction band are obtained in the non-doped case. In the doped case, a narrow, half-filled band assigned to Sn is found at the bottom of the conduction band, in agreement with the metallic and transparent characteristics observed experimentally.     

A configuration interaction study of the spin dipole-dipole parameters for formaldehyde and methylene

The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the ³A₂ (n → π*) and ³A₁ (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm^?1 and E = 0.031 cm^?1 were obtained for the ³A₂(n → π*) state and D = ?0.588 cm^?1 and E = 0.058 cm^?1 were obtained for the ³A₁ (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the ³A₂ (n n → π*) state of formaldehyde and the ³B₁ ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF ) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the ¹A₁ ground state gave an energy of ?114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C⁺O^?) in good agreement with the experimental value of 2.33 ± 0.02 Debye.     

Laser effects in excitons in a quantum wire

We investigate the effects of laser field intensity over the ground state binding energy of light and heavy hole excitons confined in GaAs/Ga_1?xAl_x As cylindrical quantum wire. We have applied the variational method using 1s‐hydrogenic wave functions, in the framework of the single band effective mass approximation with the spatial dielectric function. The polaronic effects are included in the calculation to compute the exciton binding energy as a function of the wire radius for different field of laser intensity. The valence‐band anisotropy is included in our theoretical model by using different hole masses in different spatial directions. The dressed laser donor binding energies are calculated and compared with the results of binding energy of excitons. The results show that (i) the binding energy is found to increase with decrease with the wire radius, and decrease with increase with the value of laser field amplitude, (ii) the heavy‐hole exciton in a cylindrical quantum wire is more strongly bound than the light‐hole exciton, (iii) the values of ground state binding energy for the laser field amplitude α₀ = 10 Å resemble with the values of heavy hole exciton binding energy, and (iv) the binding energy of the impurity for the narrow well wire is more sensitive to the laser field amplitude. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Radial limit of lithium revisited

Configuration interaction (CI) calculations are carried out for the ground state of lithium using a thoroughly optimized basis set of s-type Slater functions. They establish that the radial limit of the nonrelativistic energy of the ground ²S state of lithium is no higher than −7.448666443E_h. Thus, radial correlation accounts for 35.2% of the total correlation energy. The radial CI wave function predicts a significantly more accurate Fermi contact parameter than the Hartree-Fock wave function. However, the imbalanced treatment of electron correlation in the radial CI wave function leads to an excessively diffuse electron density that is worse than that of the Hartree-Fock wave function. © 1997 John Wiley & Sons, Inc.     

Linear scaling calculation of band edge states and doped semiconductors

Linear scaling methods provide total energy, but no energy levels and canonical wave functions. From the density matrix computed through the density matrix purification methods, we propose an order-N [O(N)] method for calculating both the energies and wave functions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematically and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.