Localized Orbital Basis Set Research Articles

A closed local-orbital unified description of DFT and many-body effects

Density functional theory (DFT) is usually formulated in terms of the electron density as a function of position n(r). Here we discuss an alternative formulation of DFT in terms of the orbital occupation numbers {n α } associated with a local-orbital orthonormal basis set {ϕ α }. First, we discuss how the building blocks of DFT, namely the Hohenberg–Kohn theorems, the Levy–Lieb approach and the Kohn–Sham method, can be adapted for a description in terms of {n α }. In particular, the total energy is now a function of {n α }, E[{n α }], and a Kohn–Sham-like Hamiltonian is derived introducing the effects of the electron–electron interactions via effective potentials, . In a second step we consider the Hartree and exchange energies and discuss how to describe them, in the spirit of a DFT approach, in terms of the orbital occupation numbers. In this contribution special attention is paid to the description of the (intra-atomic) correlation energy and corresponding correlation potentials {V corr,α }. For this purpose, a model system is analyzed in detail, whereby an atomic Hamiltonian interacts with the environment via a simplified model; the use of this model allows us to obtain the correlation energy and potentials (in terms of {n α }) for different cases corresponding to low, intermediate and high electron correlations.

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

AbstractThis work exploits the Kohn nearsightedness principle in the algorithms arising from the anti‐Hermitian contracted Schrödinger equation. The procedure provides the implementation of approximations yielding a considerable saving of computational costs in descriptions of N‐electron molecular systems by means of that technique. We report energies, at correlated level, of linear hydrogen chains designed at different geometries, so that we can analyze the strength of the interactions between first‐, second‐, third‐, fourth‐, and so forth neighbor atoms. Using localized molecular orbital basis sets, we observe rapid decays in the values of the elements of the reduced‐density‐matrix cumulant matrices, beyond a cut‐off radius, which justify the proposed approximations. The results, in terms of energies and reduced density matrices, have been compared with those obtained from the full configuration interaction method, showing the usefulness of the nearsightedness principle in this methodology.

First-principles study of topologically protected vortices and ferroelectric domain walls in hexagonal YGaO3

Ferroelectric behavior on the meso- and macroscopic scale depends on the formation and dynamics of domains and controlling the domain patterns is imperative to device performance. While density functional theory (DFT) calculations have successfully described the basic properties of ferroelectric domain walls, the necessarily small cell sizes used for the calculations hampers DFT studies of complex domain patterns. Here, we simulate large-scale complex ferroelectric domain patterns in ferroelectric ${\mathrm{YGaO}}_{3}$ using multisite local orbitals as implemented in the DFT code conquest. The multisite local orbital basis set gives similar bulk structural and electronic properties, and atomic domain wall structures and energetics as those obtained with conventional plane-wave DFT. With this basis set model, 3600-atom cells are used to simulate topologically protected vortices. The local atomic structure at the vortex cores is subtly different from the domain walls, with a lower electronic band gap suggesting enhanced local conductance at these cores.

INFLUENCE OF PRESSURE ON STRUCTURAL, ELECTRONIC, AND OPTICAL PROPERTIES OF CHOLINE IODIDE

The influence of pressure on structural, electronic, and optical properties of choline iodide is studied within the density functional theory approach using the РВЕ gradient functional, the D3(BJ) dispersion correction, and a basis set of localized orbitals. Elastic constants, parameters of the Birch–Murnaghan equation of state, density of electronic states, and frequencies of normal longwave vibrations are calculated. It is shown that the immediate environment of the iodine atom contains 12 carbon atoms with the shortest O–H⋯I distance equal to 2.486 A. The О–H distance increases slightly together with pressure, and the I–H distance decreases while its linear modulus is an order of magnitude smaller than the bulk modulus under 97 GPa. In contrast to intramolecular vibrations, the pressure shifts of lattice vibrations exceed 10 cm–1/GPa, and their modal Gruneisen parameters are an order of magnitude larger.

A library of ab initio Raman spectra for automated identification of 2D materials

Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within third-order perturbation theory employing a localized atomic orbital basis set. The method is used to obtain the Raman spectra of 733 different monolayers selected from the Computational 2D Materials Database (C2DB). We benchmark the computational scheme against available experimental data for 15 known monolayers. Furthermore, we propose an automatic procedure for identifying a material based on an input experimental Raman spectrum and apply it to the cases of MoS2 (H-phase) and WTe2 (T{}^{prime}-phase). The Raman spectra of all materials at different excitation frequencies and polarization configurations are freely available from the C2DB. Our comprehensive and easily accessible library of ab initio Raman spectra should be valuable for both theoreticians and experimentalists in the field of 2D materials.

Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials

The simulation of charge transport in ultra-scaled electronic devices requires the knowledge of the atomic configuration and the associated potential. Such “atomistic” device simulation is most commonly handled using a tight-binding approach based on a basis-set of localized orbitals. Here, in contrast to this widely-used tight-binding approach, we formulate the problem using a highly accurate plane-wave representation of the atomic (pseudo)-potentials. We develop a new approach that separately deals with the intrinsic Hamiltonian, containing the potential due to the atomic configuration, and the extrinsic Hamiltonian, related to the external potential. We realize efficient performance by implementing a finite-element like partition-of-unity approach combining linear shape functions with Bloch-wave enhancement functions. We match the performance of previous tight-binding approaches, while retaining the benefits of a plane wave based model. We present the details of our model and its implementation in a full-fledged self-consistent ballistic quantum transport solver. We demonstrate our implementation by simulating the electronic transport and device characteristics of a graphene nanoribbon transistor containing more than 2000 atoms. We analyze the accuracy, numerical efficiency and scalability of our approach. We are able to speed up calculations by a factor of 100 compared to previous methods based on plane waves and envelope functions. Furthermore, our reduced basis-set results in a significant reduction of the required memory budget, which enables devices with thousands of atoms to be simulated on a personal computer.

Computer simulation of coal organic mass structure and its sorption properties

Structural model of C100H79O7NS coal organic mass was obtained within density functional theory in the localized orbital basis set using the B3LYP hybrid functional. The model was compared with the known experimental data for coal of different grades and its sorption properties were studied with respect to CH4, CO2 and H2O. It has been shown that macromolecule of coal organic mass has bulk structure with a pore inside it. Interaction between coal and CH4 molecules consists of typical physical adsorption with oligomer formation on the pore border, physical adsorption with elements of chemical adsorption was also observed between coal and H2O molecules. Interaction between coal and H2O molecules included both physical and chemical adsorbion.

Benchmarking the performance of plane-wave vs. localized orbital basis set methods in DFT modeling of metal surface: a case study for Fe-(110)

Reproducing electronic structure of extended metallic systems is computationally demanding with the cost efficiency of this approach heavily dependent on both the density functional and the basis function used to approximate the electronic orbitals. It is well known that the generalized gradient approximation functional (GGA) is the most suitable and reliable approach for the description of metallic systems. As for the basis functions, two approaches dominate: the linear combination of localized basis functions (LB) such as Gaussian functions and the linear combination of plane waves (PW). Both have their own advantages and disadvantages, that may impact the efficiency and accuracy of the simulations. In this work, we use the VASP and the CRYSTAL14 suites of codes that employ plane waves and localized Gaussian basis sets, respectively, to establish a benchmark on their computational efficiency for the modeling of metal surfaces. The PW basis technique requires that the entire simulation box including the vacuum space be filled with plane waves which reduces the computational efficiency and limits the vacuum space. For its part, the LB method is based on atomic localized orbitals and does not require vacuum to model surfaces. Therefore, for calculations that require relatively large vacuum thickness such as modeling of adsorption, the LB method might be superior in terms of computational expense while providing the comparable accuracy.

Ab initio study of the structure and electronic properties of magnesium and calcium nitrates and their crystal hydrates

The crystal structures and electronic properties of magnesium and calcium nitrates, magnesium nitrate hexahydrate, and calcium nitrate tetrahydrate are studied at the density functional theory level by a hybrid functional in the basis set of localized atomic orbitals using the CRYSTAL14 program code. Atomic structural parameters, atomic charges, bond populations, energy and electron spatial distributions are calculated. The mainly electrostatic nature of interactions between nitro groups and water molecules is shown. The spectrum of the density of states of crystal hydrates, in comparison with nitrates, contains additional bands due to the presence of water. In the spectra of unoccupied states a gap is observed: the anionic gap is ~6.5 eV and the cationic gap is ~8.8 eV.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

Experimental and Theoretical High-Energy-Resolution X-ray Absorption Spectroscopy: Implications for the Investigation of the Entatic State.

High-energy-resolution-fluorescence-detected X-ray absorption near-edge structure (HERFD-XANES) spectroscopy is shown to be a sensitive tool to investigate the electronic changes of copper complexes induced by geometric distortions caused by the ligand backbone as a model for the entatic state. To fully exploit the information contained in the spectra gained by the high-energy-resolution technique, (time-dependent) density functional theory calculations based on plane-wave and localized orbital basis sets are performed, which in combination allow the complete spectral range from the prepeak to the first resonances above the edge step to be covered. Thus, spectral changes upon oxidation and geometry distortion in the copper N-(1,3-dimethylimidazolidin-2-ylidene)quinolin-8-amine (DMEGqu) complexes [CuI(DMEGqu)2](PF6) and [CuII(DMEGqu)2](OTf)2·MeCN can be accessed.

Electronic and optical properties of hexathiapentacene in the gas and crystal phases

Using density functional theory (DFT) and its time-dependent (TD) extension, the electronic and optical properties of the hexathiapentacene (HTP) molecule, a derivative of pentacene (PNT) obtained by symmetric substitution of the six central H atoms with S atoms, are investigated for its gas and solid phases. For the molecular structure, all-electron calculations are performed using a Gaussian localized orbital basis set in conjunction with the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid exchange-correlation functional. Electron affinities, ionization energies, quasiparticle energy gaps, optical absorption spectra, and exciton binding energies are calculated and compared with the corresponding results for PNT, as well as with the available experimental data. The DFT and TDDFT results are also validated by performing many-body perturbation theory calculations within the $GW$ and Bethe-Salpeter equation formalisms. The functionalization with S atoms induces an increase of both ionization energies and electron affinities, a sizable reduction of the fundamental electronic gap, and a redshift of the optical absorption onset. Notably, the intensity of the first absorption peak of HTP falling in the visible region is found to be nearly tripled with respect to the pure PNT molecule. For the crystal structures, pseudopotential calculations are adopted using a plane-wave basis set together with the Perdew-Burke-Ernzerhof exchange-correlation functional empirically corrected in order to take dispersive interactions into account. The electronic excitations are also obtained within a perturbative B3LYP scheme. A comparative analysis is carried out between the ground-state and excited-state properties of crystalline HTP and PNT linking to the findings obtained for the isolated molecules.

Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulatorBi2Se3: A first-principles quantum transport study

We predict that unpolarized charge current injected into a ballistic thin film of prototypical topological insulator (TI) Bi$_2$Se$_3$ will generate a {\it noncollinear spin texture} $\mathbf{S}(\mathbf{r})$ on its surface. Furthermore, the nonequilibrium spin texture will extend into $\simeq 2$ nm thick layer below the TI surfaces due to penetration of evanescent wavefunctions from the metallic surfaces into the bulk of TI. Averaging $\mathbf{S}(\mathbf{r})$ over few \AA{} along the longitudinal direction defined by the current flow reveals large component pointing in the transverse direction. In addition, we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on TI surface. Our analysis is based on an extension of the nonequilibrium Green functions combined with density functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calculations with properly optimized local orbital basis set can precisely match putatively more accurate calculations with plane-wave basis set for the supercell of Bi$_2$Se$_3$.

In silico infrared and Raman spectroscopy under pressure: the case of CaSnO3 perovskite.

The CaSnO3 perovskite is investigated under geochemical pressure, up to 25 GPa, by means of periodic ab initio calculations performed at B3LYP level with local Gaussian-type orbital basis sets. Structural, elastic, and spectroscopic (phonon wave-numbers, infrared and Raman intensities) properties are fully characterized and discussed. The evolution of the Raman spectrum of CaSnO3 under pressure is reported to remarkably agree with a recent experimental determination [J. Kung, Y. J. Lin, and C. M. Lin, J. Chem. Phys. 135, 224507 (2011)] as regards both wave-number shifts and intensity changes. All phonon modes are symmetry-labeled and bands assigned. The single-crystal total spectrum is symmetry-decomposed into the six directional spectra related to the components of the polarizability tensor. The infrared spectrum at increasing pressure is reported for the first time and its main features discussed. All calculations are performed using the Crystal14 program, taking advantage of the new implementation of analytical infrared and Raman intensities for crystalline materials.

Ab initio modeling of wall structure and shape in perovskite-based nanotubes

A large-scale first-principles simulation of the structure and stability of SrZrO3 and BaZrO3 single- and double-wall nanotubes with different chiralities and diameters was performed using the periodic PBE0 method and the basis set of localized Gaussian-type atomic orbitals. The initial structures of nanotubes were obtained by the rolling up of slabs cut from perovskite bulk phases and consisting of two or four alternating (001) ZrO2, SrO or BaO layers. Significant structural reconstruction was found in 4-layer singe-walled and in double-walled nanotubes. If the distance between the single-wall components of double-walled nanotubes is less than approximately 5.0Å, they inclined to merge to stable polyhedron-shaped tubular objects consisting of blocks with distorted cubic perovskite structure. A comparison of the data obtained with the results of our previous works shows that the stability of perovskite nanotubes with merged walls increases in the following sequence of the parent phases: SrZrO3<BaZrO3≈SrTiO3<BaTiO3. Calculated stability correlates with a ratio RII/RIV of ionic radii of group II and IV metals.

First-principles investigation on Rydberg and resonance excitations: A case study of the firefly luciferin anion.

The optical properties of an isolated firefly luciferin anion are investigated by using first-principles calculations, employing the many-body perturbation theory to take into account the excitonic effect. The calculated photoabsorption spectra are compared with the results obtained using the time-dependent density functional theory (TDDFT) employing the localized atomic orbital (AO) basis sets and a recent experiment in vacuum. The present method well reproduces the line shape at the photon energy corresponding to the Rydberg and resonance excitations but overestimates the peak positions by about 0.5 eV. However, the TDDFT-calculated positions of some peaks are closer to those of the experiment. We also investigate the basis set dependency in describing the free electron states above vacuum level and the excitons involving the transitions to the free electron states and conclude that AO-only basis sets are inaccurate for free electron states and the use of a plane wave basis set is required.

Ab Initio Simulation of Charge Transfer at the Semiconductor Quantum Dot/TiO2 Interface in Quantum Dot‐Sensitized Solar Cells

Quantum dot‐sensitized solar cells (QDSSCs) have emerged as a promising solar architecture for next‐generation solar cells. The QDSSCs exhibit a remarkably fast electron transfer from the quantum dot (QD) donor to the TiO2 acceptor with size quantization properties of QDs that allows for the modulation of band energies to control photoresponse and photoconversion efficiency of solar cells. To understand the mechanisms that underpin this rapid charge transfer, the electronic properties of CdSe and PbSe QDs with different sizes on the TiO2 substrate are simulated using a rigorous ab initio density functional method. This method capitalizes on localized orbital basis set, which is computationally less intensive. Quite intriguingly, a remarkable set of electron bridging states between QDs and TiO2 occurring via the strong bonding between the conduction bands of QDs and TiO2 is revealed. Such bridging states account for the fast adiabatic charge transfer from the QD donor to the TiO2 acceptor, and may be a general feature for strongly coupled donor/acceptor systems. All the QDs/TiO2 systems exhibit type II band alignments, with conduction band offsets that increase with the decrease in QD size. This facilitates the charge transfer from QDs donors to TiO2 acceptors and explains the dependence of the increased charge transfer rate with the decreased QD size.

Hybrid Hartree–Fock-density functional theory study of V2O5 three phases: Comparison of bulk and layer stability, electron and phonon properties

We have performed first-principles calculations of the atomic and electronic structures and stability of three (α, β and γ) layered V2O5 phases and their free layers within the same computational approach. In computations, we have used a hybrid exchange–correlation functional within the density functional theory and a basis set of localized atomic orbitals. All the lattice parameters and the atomic positions have been totally optimized and the phonon frequencies at the Γ-point of the Brillouin zone have been obtained. The calculated relative stability of considered bulk phases decreases as α>γ>β. The calculated relative stability of layers differs from that of bulk phases and decreases as β>α⩾γ. The possibility of the folding of V2O5 layers into nanotubes is discussed.

Effects of charging and perpendicular electric field on the properties of silicene and germanene

Using first-principles density functional theory calculations, we showed that electronic and magnetic properties of bare and Ti adatom adsorbed single-layer silicene and germanene, which are charged or subjected to a perpendicular electric field, can be modified to attain new functionalities. In particular, when subjected to a perpendicular electric field, buckled atoms have the symmetry between their planes broken, opening a gap at the Dirac points. The occupation of 3d orbitals of the adsorbed Ti atom changes with charging or applied electric field, inducing significant changes in magnetic moment. We predict neutral silicene uniformly covered by Ti atoms to become a half-metal at a specific value of coverage and hence allow the transport of electrons in one spin direction, but block the opposite direction. These calculated properties, however, exhibit a dependence on the size of the vacuum spacing between periodically repeating silicene and germanene layers, if they are treated using a plane wave basis set within periodic boundary conditions. We clarified the cause of this spurious dependence and show that it can be eliminated by the use of a local orbital basis set.

Effect of molecular-orbital rotations on ground-state energies in the parametric two-electron reduced density matrix method

Different sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric two-electron reduced density matrix (2-RDM) methods [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the ground-state energies from the parametric 2-RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical Hartree-Fock calculations.