LCAO Research Articles

Elastic properties of rare earth pyrochlores R2Ti2O7 (R = Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu): Ab initio calculations

The experimental elastic constants of R2Ti2O7 (R = Gd–Lu), in particular for R = Tb, Dy, Ho published in scientific literature up to now are slightly different, so this makes an ab initio investigation of the current elastic constants for the whole rare-earth row R2Ti2O7 (R = Gd-Lu). The aim of this paper is to give the ab initio calculations of the structural and elastic properties for a whole row of rare-earth titanate pyrochlores in terms of the MO LCAO approximation, using hybrid DFT Hamiltonian PBE0, with periodic code CRYSTAL14. First, the geometry optimization was performed using the analytical energy gradients, with respect to atomic coordinates and unit cell parameters. All-electron Gaussian basis sets were adopted for Titanium and Oxygen and for Rare-Earth atoms internal shells up to 4f are replaced by the pseudopotentials. The results obtained are discussed and the agreement between the calculated values and experimental data are quite satisfactory.

Study of electronic structure and Compton profiles of transition metal diborides

We report Compton profiles (CPs) of transition metal diborides (MB2; M= Ti and Zr) using a 740GBq 137Cs Compton spectrometer measured at an intermediate resolution of 0.34a.u. To validate the experimental momentum densities, we have employed the linear combination of atomic orbitals (LCAO) method to compute the theoretical CPs along with the energy bands, density of states (DOS) and Mulliken's population response. The LCAO computations have been performed in the frame work of density functional theory (DFT) and hybridization of Hartree-Fock and DFT (namely B3LYP and PBE0). For both the diborides, the CPs based on revised Perdew-Burke-Ernzerhof exchange and correlation functions (DFT-PBESol) lead to a better agreement with the experimental momentum densities than other reported approximations. Energy bands, DOS and real space analysis of CPs confirm a metallic-like character of both the borides. Further, a comparison of DFT-PBESol and experimental data on equal-valence-electron-density scale shows more ionicity in ZrB2 than that in TiB2, which is also supported by the Mulliken's population based charge transfer data.

First-Principles Study of the Elastic Properties of Nitrates

Elastic properties of nitrates LiNO3, NaNO3, KNO3 and NH4NO3 are studied from first principles in gradient approximation of the density functional theory by method of linear combination of atomic orbitals using CRYSTAL software complex. Elastic constants and modules, hardness, Poisson coefficient, and anisotropy parameters are calculated. Sound velocity, Debye temperature, thermal conductivity and Gruneisen parameter are evaluated. Mechanical stability, anisotropy and the series dependencies are shown for the examined compounds. Strong elastic anisotropy indicates anisotropy of interatomic interactions. The elastic constants are in good agreement with available experimental data.

Analytic second nuclear derivatives of Hartree-Fock and DFT using multi-resolution analysis.

We present the formalism, implementation, and numerical results for the computation of second derivatives with respect to nuclear displacements of molecules in the formalism of multi-resolution analysis. The highly singular nuclear potentials are partially regularized to improve the numerical stability. Vibrational frequencies are well reproduced to within an RMS of a few cm-1 compared to large basis set LCAO (linear combination of atomic orbitals) calculations. Intermolecular modes, hindered rotations, and heavy atoms may lead to loss of precision. Tight precision thresholds are therefore necessary to converge to numerically stable results.

Electronic and optical response of Cr-doped MoSe2 and WSe2: Compton measurements and first-principles strategies

In this paper, we present energy bands, density of states and Mulliken's population (MP) data using the linear combination of atomic orbitals (LCAO) method. To compare the theoretical momentum densities, we have also employed 100mCi 241Am Compton spectrometer to measure the Compton profiles of Cr0.5X0.5Se2 (X=Mo and W). The experimental Compton data have been used to check the performance of various exchange and correlation energies for the present mixed dichalcogenides within the LCAO scheme. It is seen that CPs based on the hybridization of Hartree-Fock and density functional theory give a better agreement with the experimental data than other schemes employed in the present investigations. All theoretical approximations show an indirect band gap between the Γ and K points of the Brillouin zone. Further, equal-valence-electron-density scaled experimental data predict a more ionic character in Cr0.5W0.5Se2 than in Cr0.5Mo0.5Se2, which is in tune with our MP data. Going beyond the computation of electronic properties using LCAO, we have also reported accurate electronic and optical properties using the modified Becke-Johnson (mBJ) potential within the full potential augmented plane wave (FP-LAPW) method. Optical properties computed using the FP-LAPW-mBJ method show the feasibility of using both the mixed dichalcogenides in photovoltaic devices.

Theory and Applications of Generalized Pipek-Mezey Wannier Functions.

The theory for the generation of Wannier functions within the generalized Pipek-Mezey approach (Lehtola, S.; Jónsson, H. J. Chem. Theory Comput. 2014, 10, 642) is presented and an implementation thereof is described. Results are shown for systems with periodicity in one, two, and three dimensions as well as isolated molecules. The generalized Pipek-Mezey Wannier functions (PMWF) are highly localized orbitals consistent with chemical intuition where a distinction is maintained between σ- and π-orbitals. The PMWF method is compared with the so-called maximally localized Wannier functions (MLWFs) that are frequently used for the analysis of condensed matter calculations. Whereas PMWFs maximize the localization criterion of Pipek and Mezey, MLWFs maximize that of Foster and Boys and have the disadvantage of mixing σ- and π-orbitals in many cases. The PMWF orbitals turn out to be as localized as the MLWF orbitals as evidenced by cross-comparison of the values of the PMWF and MLWF objective functions for the two types of orbitals. Our implementation in the atomic simulation environment (ASE) is compatible with various representations of the wave function, including real-space grids, plane waves, and linear combinations of atomic orbitals. The projector-augmented wave formalism for the representation of atomic core electrons is also supported. Results of calculations with the GPAW software are described here, but our implementation can also use output from other electronic structure software such as ABINIT, NWChem, and VASP.

Artificial nodes in the H2+ wave functions expanded using Gaussian-type orbitals or Laguerre-type orbitals

In Hartree-Fock calculations for atoms and molecules, multicenter-expansion methods are commonly used, especially those based on linear combinations of atomic orbitals (LCAO) using Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Artificial nodes, which are not expected to exist in real wave functions, arise in many calculations. For the hydrogen molecular ion (H2+) there are no nodes in the exact solution of its ground state ((1σg) 2Σg). The occurrence of artificial nodes and the cause of the problem are investigated for this state. Calculations of LCAO with GTOs and of single-center expansion (SCE) with Laguerre-type orbitals (LTOs) have been performed as part of this study. It is found that an excess of diffuse basis functions is responsible for artificial nodes.

Accurate Electronic, Transport, and Bulk Properties of Zinc Blende Gallium Arsenide (Zb-GaAs)

We report accurate, calculated electronic, transport, and bulk properties of zinc blende gallium arsenide (GaAs). Our ab-initio, non-relativistic, self-con-sistent calculations employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. We strictly followed the Bagayoko, Zhao, and William (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Our calculated, direct band gap of 1.429 eV, at an experimental lattice constant of 5.65325 A, is in excellent agreement with the experimental values. The calculated, total density of states data reproduced several experimentally determined peaks. We have predicted an equilibrium lattice constant, a bulk modulus, and a low temperature band gap of 5.632 A, 75.49 GPa, and 1.520 eV, respectively. The latter two are in excellent agreement with corresponding, experimental values of 75.5 GPa (74.7 GPa) and 1.519 eV, respectively. This work underscores the capability of the local density approximation (LDA) to describe and to predict accurately properties of semiconductors, provided the calculations adhere to the conditions of validity of DFT.

<i>Ab-Initio</i> Computations of Electronic, Transport, and Structural Properties of <i>zinc-blende</i> Beryllium Selenide (<i>zb</i>-BeSe)

We report results from several ab-initio computations of electronic, transport and bulk properties of zinc-blende beryllium selenide (zb-BeSe). Our nonrelativistic calculations utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). The key distinction of our calculations from other DFT calculations is the implementation of the Bagayoko, Zhao and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), in the LCAO formalism. Our calculated, indirect band gap is 5.46 eV, from Γ to a conduction band minimum between Г and X, for a room temperature lattice constant of 5.152 A. Available, room temperature experimental band gaps of 5.5 (direct) and 4 - 4.5 (unspecified) point to the need for additional measurements of this gap. Our calculated bulk modulus of 92.35 GPa is in excellent agreement with experiment (92.2 ± 1.8 GPa). Our predicted equilibrium lattice constant and band gap, at zero temperature, are 5.0438 A and 5.4 eV, respectively.

Accurate Electronic, Transport, and Related Properties of Wurtzite Beryllium Oxide (w-BeO)

We report details of our ab-initio, self-consistent density functional theory (DFT) calculations of electronic and related properties of wurtzite beryllium oxide (w-BeO). Our calculations were performed using a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. Unlike previous DFT studies of BeO, the implementation of the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by the work of Ekuma and Franklin (BZW-EF), ensures the full physical content of the results of our calculations, as per the derivation of DFT. We present our computed band gap, total and partial densities of states, and effective masses. Our direct band gap of 10.30 eV, reached by using the experimental lattice constants of a = 2.6979 Å and c = 4.3772 Å at room temperature, agrees very well the experimental values of 10.28 eV and 10.3 eV. The hybridization of O and Be p states in the upper valence bands, as per our calculated, partial densities of states, are in agreement with corresponding, experimental findings.

Numerical Research of Materials Crystal Lattice Parameters Based on Rare-Earth Metals

Geometrical parameters (coordinates and angles) of CeO 2 crystal lattice by molecular dynamics method are calculated. Calculated parameters of crystal lattice are applied for definition the energy band structure via Hartree-Fock method in an approximation to CO LCAO (crystal orbitals as linear combination of atomic orbitals) and using the model of cyclic cluster. Calculated minimum energy band p-d is within the value range of experimental data. Valence band maximum is 4.2 while minimum energy band p-d width is 2.8 eV Quantum-chemical calculations are accelerated by Schwarz inequality and direct inversion method in iterative subspace. The obtained mathematical model is implemented into software package for calculating material properties.

Quantum chemical simulations of titanium dioxide nanotubes used for photocatalytic water splitting

Titanium dioxide nanotubes (NTs) built from various initial 2D models of TiO2 (a promising catalyst for water splitting) are investigated via density functional theory using the B3LYP hybrid exchange-correlation functional in the localized basis set of a linear combination of atomic orbitals. For TiO2 NTs (eight different types of morphology) created from four initial 2D structures, full geometry optimization is performed and the main energy parameters, such as the band gap width, energy positions of the valence band top and the conduction band bottom, and NT formation and strain energy, are calculated. Analysis of the NT strain and formation energies enables us to choose their most stable configuration, which can further be employed to simulate NTs doped with impurity atoms capable of serving as efficient centers for the photocatalytic dissociation of water molecules.

Electron momentum distribution and electronic response of ceramic borides

Isotropic Compton profiles of transition metal based ceramics TaB and VB have been measured using 137Cs (661.65keV) γ-ray Compton spectrometer. The experimental momentum densities are compared with those deduced using linear combination of atomic orbitals (LCAO) with Hartree-Fock (HF), density functional theory (DFT) with Wu-Cohen generalized gradient approximation (WCGGA) and also the hybridization of HF and DFT (namely B3PW and PBE0) schemes. It is found that LCAO-DFT-WCGGA scheme based profiles give an overall better agreement with the experimental data, for both the borides. In addition, we have computed the Mulliken's population (MP) charge transfer data, energy bands, density of states and Fermi surface topology of both the borides using full potential-linearized augmented plane wave (FP-LAPW) and LCAO methods with DFT-WCGGA scheme. Cross-overs of Fermi level by the energy bands corresponding to B-2p and valence d-states of transition metals lead to metallic character in both the compounds. Equal-valence-electron-density profiles and MP analysis suggest more ionic character of VB than that of TaB.

Crystal structure and vibrational properties of RFe3(BO3)4(R = Ce – Lu) ferroborate crystal:ab initiocalculations

The ab initio calculations of the crystal structure and lattice dynamics of ferroborate crystal family R Fe 3 (BO 3 ) 4 ( R = Ce, Pm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu), S.G. R 32, has been carried out within the framework of the MO LCAO approach by using density functional theory and effective 4 f -in-core pseudopotential for rare earth element. The fully optimized geometry as well as vibrational frequencies has been calculated.

Vplyv zalyshkovoyi vzayemodiyi na izoskalyarni dypol'ni mody u vazhkykh yadrakh

The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the finite nuclear size. It is shown that if the dipole momentum reaches a certain critical value, the novel type of supercriticality occurs; namely, the wave function of the highest occupied electron bound state changes its localization from the negatively charged nucleus to the positively charged one. This phenomenon can be interpreted as a spontaneous creation of an electron-positron pair in vacuum, with each of the created particles being in the bound state with the corresponding nucleus and partially screening it.

LCAO-based theoretical study of PbTiO3 crystal to search for parity and time reversal violating interaction in solids.

An experiment towards the search for the interaction of the Schiff moment (S) of the (207)Pb nuclei with electrons in PbTiO3 crystal which violates the time reversal (T) and space parity (P) symmetries was proposed by Mukhamedjanov and Sushkov [Phys. Rev. A 72, 034501 (2005)]. The interpretation of the experiment in terms of the Schiff moment requires knowledge of an electronic density gradient parameter (usually designated as X) on the Pb nucleus in the crystal, which is determined by the electronic structure of the crystal. Here we propose a theoretical approach to calculate the properties in solids which are directly sensitive to the changes of valence electron densities in atomic cores but not in the valence spatial regions (Mössbauer parameters, hyperfine structure (HFS) constants, parameters of T,P-odd Hamiltonians, etc. [L. V. Skripnikov and A. V. Titov, Phys. Rev. A 91, 042504 (2015)]). It involves constructing the crystalline orbitals via the linear combination of atomic orbitals and employs a two-step concept of calculating such properties that was earlier proposed by us for the case of heavy-atom molecules. The application of the method to the PbTiO3 crystal results in the energy shift, Δε=0.82×10(6)S((207)Pb)eaB (3)eV, due to the T,P-odd interactions. The value is compared to the corresponding parameter in diatomic molecules (TlF, RaO, PbO), which have been proposed and used in the past decades in the search for the nuclear Schiff moment. We also present the calculation of the electric field gradient at the Pb nucleus in PbTiO3 for the comparison with other solid-state electronic structure approaches.

Electronic structure of cubic ScF3 from first-principles calculations

The ground state properties of cubic scandium trifluoride (ScF3) perovskite were studied using first-principles calculations. The electronic structure of ScF3 was determined by linear combination of atomic orbital (LCAO) and plane wave projector augmented-wave (PAW) methods using modified hybrid exchange-correlation functionals within the density functional theory (DFT). The comprehensive comparison of the results obtained by two methods is presented. Both methods allowed us to reproduce the lattice constant found experimentally in ScF3 at low temperatures and to predict its electronic structure in good agreement with known experimental valence-band photoelectron and F 1s x-ray absorption spectra.

Improvement of initial guess via grid‐cutting for efficient grid‐based density functional calculations

AbstractWe introduced an efficient initial guess method, namely the grid‐cutting, which is specialized for grid‐based density functional theory (DFT) calculations. It produces initial density and orbitals through pre‐DFT calculations in an inner simulation box made by cutting out the outer region of a full‐size one. To assess its performance, we carried out DFT calculations for small molecules included in the G2‐1 set and two large molecules with various combinations of mixing and diagonalization conditions, relative size of the inner box, and grid spacing. For all cases, the grid‐cutting method was more efficient than conventional ones such as extended Hückel, superposition of atomic densities, and linear combination of atomic orbitals. For instance, it was about 20% faster in computational time and about 45% smaller in the number of self‐consistent‐field cycles than the superposition of atomic densities because it provided high‐quality initial density and orbitals closer to the corresponding fully converged values. In addition, it showed good performance for non‐Coulombic model systems such as harmonic oscillator.

Ab initio investigations of the elastic properties of chlorates and perchlorates

Elastic properties of NaClO3, KClO3, LiClO4, NaClO4, and KClO4 have been investigated from first principles by the method of linear combination of atomic orbitals in the gradient approximation of the density functional theory using CRYSTAL software. The elastic constants and moduli, hardness, Poisson’s ratio, and the anisotropy parameters have been calculated. The velocities of sound, the Debye temperature, the thermal conductivity, and the Gruneisen parameter have been estimated. It has been found that these compounds are mechanically stable, anisotropic, and ductile materials. The dependences of their elastic parameters on the atomic number of the cation have been calculated. The obtained results are in good agreement with the available experimental data.

Study on electron momentum density of zinc and cadmium molybdates: First principles calculations and Compton spectroscopy

We report first-ever Compton profiles of ZnMoO4 and CdMoO4 measured using photons of 661.65 keV emitted by 20 Ci 137Cs γ-ray source. To interpret the experimental momentum densities, we have also computed the electronic properties which include band structure, density of states (DOS), electron momentum density, Mulliken's population (MP), and anisotropy in Compton profiles using linear combination of atomic orbitals (LCAO) scheme with density functional theory. In addition, more accurate energy bands and DOS have been computed using full-potential linearized augmented plane wave method with modified Becke–Johnson potential (FP-LAPW-mBJ). The band gap values of ZnMoO4 and CdMoO4 calculated using FP-LAPW-mBJ approximation were found to be close to available experimental data. It is seen that momentum densities computed using LCAO scheme with PBEsol approximation gives a better agreement with the present measurements than other DFT approximations considered in the present work. On the basis of equal-valence-electron-density profiles, it is seen that ZnMoO4 has more covalent nature than CdMoO4 which is in tune with the present integrated DOS and Mulliken's population data.