Linear Combination Of Atomic Orbitals Calculations Research Articles

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Topology of the Electron Density and of Its Laplacian from Periodic LCAO Calculations on f-Electron Materials: The Case of Cesium Uranyl Chloride.

The chemistry of f-electrons in lanthanide and actinide materials is yet to be fully rationalized. Quantum-mechanical simulations can provide useful complementary insight to that obtained from experiments. The quantum theory of atoms in molecules and crystals (QTAIMAC), through thorough topological analysis of the electron density (often complemented by that of its Laplacian) constitutes a general and robust theoretical framework to analyze chemical bonding features from a computed wave function. Here, we present the extension of the Topond module (previously limited to work in terms of s-, p- and d-type basis functions only) of the Crystal program to f- and g-type basis functions within the linear combination of atomic orbitals (LCAO) approach. This allows for an effective QTAIMAC analysis of chemical bonding of lanthanide and actinide materials. The new implemented algorithms are applied to the analysis of the spatial distribution of the electron density and its Laplacian of the cesium uranyl chloride, CsUOCl, crystal. Discrepancies between the present theoretical description of chemical bonding and that obtained from a previously reconstructed electron density by experimental X-ray diffraction are illustrated and discussed.

Density functional LCAO calculations of vibrational modes and phonon density of states in the strained single-layer phosphorene

The paper presents an investigation of phosphorene under axial strain on the phonon density of states and vibrational modes. The studies were performed by means of density functional theory (DFT) within the linear combination of atomic orbitals (LCAO). The strained models were constructed using optimised supercell techniques. The vibrational mode spectra were estimated for strains applied for both the zigzag and armchair directions of phosphorene. This approach is an attractive candidate for the calculation the dynamical matrix of the system because its numerical complexity gradually increases together with the size of the analysed cell. The shift of peaks in the PDOS of black phosphorene is monotonic, and inversely proportional to the applied strain over the zigzag direction. This relation is valid for small strains (below 10%) of peaks corresponding to modes B2g and Ag2. For a strain applied over the armchair PDOS, the shifts are proportional to the strain. The peak shifts tend to become higher as the strain increases. This dependence is not monotonic, and is clearly more rapid for compressing strains. Moreover, the peaks shift slower for an armchair strain than for a zigzag strain, revealing its strong anisotropy.

Structural, magnetic and electronic properties of nickel ferrites: Experiment and LCAO calculations

Abstract Structural and magnetic response of Ni1-xCrxFe2O4 (x = 0 and 0.05) are presented using X-ray diffraction, Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR) and SQUID magnetometer. The single phase of both the compositions is confirmed using Rietveld refinement method. The absence of any impurity is further cinched using structural sensitive techniques, namely FTIR and Raman spectroscopy. Interestingly, a pinched shaped M − H behaviour is observed for the Cr doped ferrite. In addition, we have computed magnetic moment, Mulliken’s population, density of states (DOS) and Compton profiles (CPs) for NiFe2O4 using linear combination of atomic orbitals (LCAO) scheme with and without hybrid functional for exchange and correlation potentials. Further, theoretical CPs have been validated using isotropic CP measurement with 137Cs radio-isotope for NiFe2O4. Among the considered exchange-correlation potentials within LCAO, the hybrid B3LYP scheme based momentum densities give better agreement with the experimental CP. Majority- and minority-spin DOS have confirmed the insulating nature of NiFe2O4. Peculiarities of presently deduced MP data and magnetic moments are also discussed.

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

AbstractThe need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all‐electron electronic structure calculations in general—the linear combination of atomic orbitals (LCAO) method—is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform all‐electron Hartree‐Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.

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 structure of lanthanum sesquioxide: A Compton scattering study

We present the first-ever experimental and theoretical momentum densities of La2O3. The Compton line shape is measured using a 20 Ci 137Cs Compton spectrometer at an intermediate resolution with full width at half maximum of 0.34a.u. The experimental Compton profile is compared with the theoretical electron momentum densities computed using linear combination of atomic orbitals (LCAO) method with density functional theory (DFT). It is seen that the generalized gradient approximation (GGA) within DFT reconciles better with the experiment than other DFT based approximations, validating the GGA approximation for rare-earth sesquioxides. The energy bands and density of states computed using LCAO calculations show its wide band gap nature which is in tune with the available reflectivity and photo-absorption data. In addition, Mulliken׳s population and charge density are also computed and discussed.

Electronic properties and electron momentum density of monoclinic WO3

We present Compton profiles and Mulliken population (MP) data on charge re-organization of tungsten trioxide using pseudopotential approach within linear combination of atomic orbitals (LCAOs). Different exchange and correlation potentials to density functional theory (DFT) as embodied in the LCAO calculations have been validated using the first ever Compton profile measurement employing 20 Ci 137Cs source. The MP data have shown transfer of electrons from W sites which are found to be unevenly distributed among the non-equivalent six O atoms. The computed Compton profiles are found to be in reasonable agreement with the experimental data. Going beyond the LCAO calculations, energy bands, density of states (DOSs) and band gap are also reported using full potential augmented plane wave (FP-LAPW) method with DFT scheme. The FP-LAPW based partial and total DOS have also been discussed in terms of the MP data.

Optical tunability of magnetic polaron stability in single-Mn doped bulk GaAs and GaAs/AlGaAs quantum dots

Optical control of magnetic property of a magnetic polaron (MP) in Mn-doped bulk GaAs and GaAs/AlGaAs quantum dots (QDs) have been studied. We have developed basis optimization technique for the method of linear combination of atomic orbitals (LCAOs), which significantly improve the accuracy of the conventional LCAO calculation. We have demonstrated that a monochromatic, linearly polarized, intense pulsed laser field induces a collapse of the MP and an ionization of Mn-acceptor in Mn-doped GaAs materials due to a dichotomy of hole wave function. We find this optical tunability of MP stability can be adjusted by confinement introduced in GaAs QDs.

Ab initio LCAO study of the atomic, electronic and magnetic structures and the lattice dynamics of triclinic CuWO4

The electronic, structural and phonon properties of antiferromagnetic triclinic CuWO4 have been studied using the first-principles spin-polarized linear combination of atomic orbital (LCAO) calculations based on the hybrid exchange–correlation density functional (DFT)/Hartree–Fock (HF) scheme. In addition, the local atomic structure around both Cu and W atoms has been probed using extended X-ray absorption fine structure (EXAFS) spectroscopy. We show that, by using the hybrid DFT–HF functional, one can accurately and simultaneously describe the atomic structure (the unit cell parameters and the atomic fractional coordinates), the band gap and the phonon frequencies. In agreement with our EXAFS results, the LCAO calculations reproduce a strong distortion of both the CuO6 and the WO6 octahedra, which occur due to the first-order and second-order Jahn–Teller effects, respectively. We found that the HF admixture of 13–16%, which is implemented in the PBE0–13% and WCGGA–PBE-16% functionals, produces the best result for CuWO4. The calculated properties agree well with the available experimental data provided by diffraction, optical, X-ray photoelectron and Raman spectroscopies.

Spin-splitting calculation for zincblende semiconductors using an atomic bond-orbital model

We develop a 16-band atomic bond-orbital model (16ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic-orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16ABOM is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion over at the Γ point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin–orbit coupling between bonding and antibonding p-like states, evaluated by the 16ABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials.

Ab-initio study of structural and electronic properties of AlAs

The structural properties, i.e. equilibrium lattice constant, transition pressure, bulk modulus and its pressure derivatives, together with electronic properties, i.e. energy bands, Compton profile and autocorrelation function, of AlAs are presented in this work. The linear combination of atomic orbitals (LCAO) method of the CRYSTAL code was applied considering the Perdew–Burke–Ernzerhof correlation energy functional and Becke's ansatz for the exchange. The total energy of AlAs as a function of primitive cell volume has also been calculated for the zincblende (B3), nickel arsenide (B8), sodium chloride (B1) and cesium chloride (B2) phases. Structural parameters of the B3, B8, B1 and B2 phases are determined. The calculated structural parameters are found to be in good agreement with the results of previous investigations. The spherically averaged theoretical values of Compton profile are in good agreement with an earlier measurement. The LCAO calculation shows an indirect band gap of 1.85 eV, in reasonable agreement with earlier data. On the basis of the equal-valence-electron-density Compton profile, it is found that AlAs is more ionic compared to AlSb.

Pure-state noninteractingv-representability of electron densities from Kohn-Sham calculations with finite basis sets

Within the linear combination of atomic orbitals (LCAO) approximation, one can distinguish two different Kohn-Sham potentials. One is the potential available numerically in calculations, and the other is the exact potential corresponding to the LCAO density. The latter is usually not available, but can be obtained from the total density by a numerical inversion procedure or, as is done here, analytically using only one LCAO Kohn-Sham orbital. In the complete basis-set limit, the lowest-lying Kohn-Sham orbital suffices to perform the analytical inversion, and the two potentials differ by no more than a constant. The relation between these two potentials is investigated here for diatomic molecules and several atomic basis sets of increasing size and quality. The differences between the two potentials are usually qualitative (wrong behavior at nuclear cusps and far from the molecule even if Slater-type orbitals are used) and $\ensuremath{\delta}$-like features at nodal planes of the lowest-lying LCAO Kohn-Sham orbital. Such nodes occur frequently in LCAO calculations and are not physical. Whereas the behavior of the potential can be systematically improved locally by the increase of the basis sets, the occurrence of nodes is not correlated with the size of the basis set. The presence of nodes in the lowest-lying LCAO orbital can be used to monitor whether the effective potential in LCAO Kohn-Sham equations can be interpreted as the potential needed for pure-state noninteracting $v$-representability of the LCAO density. Squares of such node-containing lowest-lying LCAO Kohn-Sham orbitals are nontrivial examples of two-electron densities which are not pure-state noninteracting $v$-representable.

Evaluation of the electron momentum density of crystalline systems from ab initio linear combination of atomic orbitals calculations

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic-orbitals calculations performed in the frame of one-electron self-consistent-field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one-electron Hamiltonians, a post-Hartree-Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride.

Ab-initio determination of X-ray structure factors and the Compton profiles of CdO

X-ray structure factors and Compton profiles of CdO are presented in this work. The theoretical calculations are performed employing the first-principles linear combination of atomic orbitals (LCAO) method using the CRYSTAL code. The computations are made considering the Perdew–Burke–Ernzerhof (PBE) correlation energy functional and Becke's ansatz for the exchange. The computed X-ray structure factors for B1 structure are compared with the available experimental data. To compare the averaged theoretical Compton profile, first ever measurement on polycrystalline CdO is reported using 5Ci 241Am Compton spectrometer. The ionic model calculations have been used to estimate charge transfer in CdO. The agreement is, however, better with the LCAO calculation. The first-principles calculations of equilibrium lattice constants, bulk moduli and its pressure derivative of competing B1 and B2 phases of CdO are also reported and compared with the available results. The computed transition pressure for B1 → B2 structural phase transition is in good agreement with the experimental findings. Moreover, the electronic band structures show that B1 phase has indirect band gap of 0.43 eV in reasonable agreement with the experiments and B2 phase exhibits negative band gap of 0.9 eV.

An Orthogonalized Valence Orbital Approximation in Relativistic Full-Potential Linear-Combination-of-Atomic-Orbitals Methods

An approximation for reducing the computational cost in fully relativistic and scalar relativistic full-potential linear-combination-of-atomic-orbitals (LCAO) methods is introduced. The basic idea is the same as in the orthogonalized plane wave method; valence orbitals are orthogonalized to core orbitals and, using the orthogonalized valence orbitals as the basis functions in the generalized eigenvalue problem, the size of matrices is reduced considerably for materials with heavy atoms. This enables us to calculate their structural and electronic properties efficiently. The usefulness of the orthogonalized valence orbital approximation is shown by applying it to Au, InSb, and AmBi. In particular, it is found that the effect of spin–orbit coupling is reproduced successfully in the fully relativistic full-potential LCAO calculations within the orthogonalized valence orbital approximation.

Positron annihilation study for cadmium (electronic structure and enhancement effect)

AbstractThe three dimensional electron density in momentum space ρ(p) and in wave vector space n(k) was reconstructed for cadmium (Cd). The measurements were performed using the two dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Enhanced contributions in the spectra were observed around 5.5 mrad, discussed in terms of a Kahana-like enhancement effect. From another viewpoint, Fermi radii were analyzed in the (λM K), (ALM) and (AHK) planes, and they showed a maximum deviation of about 4% from the free electron Fermi radius. Moreover, comparisons to a radio-frequency size effect (RFSE) experiment and theoretical band structure calculations (using augmented plane wave (APW), linear combination of atomic orbital (LCAO) and linear muffin tin orbital (LMTO) methods) were examined. The results showed a qualitative agreement with both APW and LCAO calculations. However, a favorable agreement with the APW method was determined via Fermi surface dimensions. The differences of bands' occupation of n(k) between the current work and the APW method were argued in view of positron wave function in Cd.

Electron–phonon effects on the direct band gap in semiconductors: LCAO calculations

Using a perturbative treatment of the electron–phonon interaction, we have studied the effect of phonons on the direct band gap of conventional semiconductors. Our calculations are performed in the framework of the tight-binding linear combination of atomic orbitals (LCAO) approach. Within this scheme we have calculated the temperature and isotopic mass dependence of the lowest direct band gap of several semiconductors with diamond and zincblende structure. Our results reproduce the overall trend of available experimental data for the band gap as a function of temperature, as well as give correctly the mass dependence of the band gap on isotopic. A calculation of conduction band intervalley deformation potentials is also reported. Finally, calculated Debye–Waller factors are compared with X-ray and EXAFS experimental results.

Optimized Effective Potential Method and KLI Approximation for Systems with Degenerate Orbitals in the LCAO Calculations

A new formulation of the optimized effective potential (OEP) method is presented. Our OEP method is applicable to the linear combination of atomic orbital (LCAO) calculation for systems which have degenerate orbitals, in contrast to the conventional OEP method. An approximation to our OEP equation for the exchange-correlation (xc) potential, similar to the KLI approximation, is derived.

Variational calculations for the bound-unbound transition of the Yukawa potential.

We perform LCAO (linear combination of atomic orbitals) calculations for the ground state of the Yukawa potential V(r)=-(${\mathit{e}}^{2}$/r)${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{q}\mathit{r}}$ as a function of the screening parameter q. We obtain the best variational result so far for the ground-state energy ${\mathit{E}}_{0}$ as a function of q. We also obtain the critical exponents of both the probability density at the origin and the ground-state energy as functions of (q-${\mathit{q}}_{\mathit{c}}$), where ${\mathit{q}}_{\mathit{c}}$ is the critical q above which V(r) does not have a bound state. The use of the critical exponents permits the so far most precise determination of ${\mathit{q}}_{\mathit{c}}$, ${\mathit{q}}_{\mathit{c}}$=1.190 612 27\ifmmode\pm\else\textpm\fi{}0.000 000 04. We also show that it is possible to use the LCAO calculations as a tool to determine the analytical form of very precise variational wave functions. We obtain, in such a way, the wave function \ensuremath{\psi}=(${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{a}\mathit{r}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{b}\mathit{r}}$)/r+${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{b}\mathit{r}}$/(r+\ensuremath{\alpha}). This variational wave function has a bound-unbound transition at ${\mathit{q}}_{\mathit{c}}$=1.190 610 74.