Large-scale Density Functional Calculations Research Articles

A Time-Dependent Random State Approach for Large-Scale Density Functional Calculations

We develop a self-consistent first-principle method based on the density functional theory. Physical quantities such as the density of states, Fermi energy and electron density are obtained using a time-dependent random state method without diagonalization. The numerical error for calculating either global or local variables always scales as , where N e is the number of electrons and S is the number of random states, leading to a sublinear computational cost with the system size. In the limit of large systems, one random state could be enough to achieve reasonable accuracy. The accuracy and scaling properties of using the method are derived analytically and verified numerically in different condensed matter systems. Our time-dependent random state approach provides a powerful strategy for large-scale density functional calculations.

Optimized Dirac Woods-Saxon basis for covariant density functional theory

The Woods-Saxon basis has achieved great success in both nonrelativistic and covariant density functional theories in recent years. Due to its nonanalytical nature, however, applications of the Woods-Saxon basis are numerically complicated and computationally time consuming. In this paper, based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we check in detail the convergence with respect to the basis space in the Dirac sea. An optimized Dirac Woods-Saxon basis is proposed, whose corresponding potential is close to the nuclear mean field. It is shown that the basis space of the optimized Dirac Woods-Saxon basis required for convergence is substantially reduced compared with the original one. In particular, it does not need to contain the bases from continuum in the Dirac sea. The application of the optimized Woods-Saxon basis would greatly reduce computing resource for large-scale density functional calculations.

Copper-doped beryllium and beryllium oxide interface: A first-principles study

Beryllium oxide (BeO) serves as a copper (Cu) diffusion barrier in designing Be ablators for inertial confinement fusion. We study the preferential site substitution of beryllium (Be) by Cu at the Be/BeO interface via large-scale density functional calculations. We first systematically study structures and properties of bulk and surface structures of Cu, Be and BeO, and two interface models are constructed with three concentrations of Cu dopants, i.e., 0.89 at.%, 0.45 at.% and 0.22 at.%. We then perform a thorough study on four different substitution sites with analysis on the atomic structures and electronic structures including the partial density of states, the bader charges, and the charge densities. We elucidate the origin of the increased substitution energy for different substitution sites, which is a result as the Cu dopants lose more electrons with the presence of more nearby O atoms and less adjacent Be atoms. The above changes of atomic structures and electronic structures explain the favorable and unfavorable substitutions of Be by Cu in the Be and BeO layers, respectively. This work provides insightful information for utilizing BeO as a valid candidate for stopping Cu diffusion.

Perspective: Methods for large-scale density functional calculations on metallic systems.

Current research challenges in areas such as energy and bioscience have created a strong need for Density Functional Theory (DFT) calculations on metallic nanostructures of hundreds to thousands of atoms to provide understanding at the atomic level in technologically important processes such as catalysis and magnetic materials. Linear-scaling DFT methods for calculations with thousands of atoms on insulators are now reaching a level of maturity. However such methods are not applicable to metals, where the continuum of states through the chemical potential and their partial occupancies provide significant hurdles which have yet to be fully overcome. Within this perspective we outline the theory of DFT calculations on metallic systems with a focus on methods for large-scale calculations, as required for the study of metallic nanoparticles. We present early approaches for electronic energy minimization in metallic systems as well as approaches which can impose partial state occupancies from a thermal distribution without access to the electronic Hamiltonian eigenvalues, such as the classes of Fermi operator expansions and integral expansions. We then focus on the significant progress which has been made in the last decade with developments which promise to better tackle the length-scale problem in metals. We discuss the challenges presented by each method, the likely future directions that could be followed and whether an accurate linear-scaling DFT method for metals is in sight.

Spontaneous appearance of a low-dimensional magnetic electron system on semiconductor nanostructures

We report on the large-scale density-functional calculations that show the emergence of the spin-polarized ground states in nanofacets self-organized on SiC (0001) surfaces. We first reveal that the nanofacet formed by bunching of single bilayer steps induces peculiar electron states localized at but extended along step edges, showing the flat-band characteristics. The electron states are of C-dangling-bond characters mixed with the back-bond character of neighboring edge Si atoms. We find that the resulting flat bands lead to the spin polarization near the step edges by H passivation of the terrace Si atoms. Interestingly, either ferromagnetic or antiferromagnetic chains appear along the step edges on the SiC nanofacet and the location of such magnetic chains can be controlled by manipulating the H passivation of atoms near the step edges. These findings open a possibility of the appearance of new magnetic functions on the covalent semiconductor surfaces without magnetic elements.

Nanostructures and Electronic Properties of a High-Efficiency Electron-Donating Polymer

The development of organic photovoltaic (OPV) solar cells has seeded a bright hope of achieving low-cost solar energy harvesting. Practical realization and successful commercialization require enhancing the efficiency of solar energy harvesting, which, in turn, relies on the core understanding of structure-property relationships in OPV materials. Here, we report the first large-scale density functional calculations of the nanoconformational and electronic properties of the thieno[3,4-b]thiophene-alt-benzodithiophene copolymer (PTB7), a high-efficiency OPV material. These first-principles results include the chain length dependence of the torsional potential, the nearest-neighbor torsional coupling, the band gap, and the electronic conjugation length. Importantly, PTB7 was found to have a torsional potential almost independent of chain length, very weak nearest-neighbor torsional coupling, a low band gap (∼1.8 eV), and a very long conjugation length (∼147 Å) compared to the other conjugated polymers like polythiophene and poly(3-alkylthiophene). These results suggest that PTB7 can be an efficient electron donor for OPV devices.

Conformations and torsional potentials of poly(3-hexylthiophene) oligomers: Density functional calculations up to the dodecamer

Fully optimized conformations of poly(3-hexylthiophene) (P3HT) oligomers up to the decamer and torsional potentials up to the dodecamer (302atoms) are investigated by large-scale density functional calculations (B3LYP/6-31+G(d,p)). Fully relaxed P3HT oligomers were investigated at a variety of conformational minima, many with skeletal structures far from planarity. The lowest energy conformations found have each hexyl group ≈74° out of plane and each backbone twist angle out of plane by ≈47°. The energies of these non-planar conformations are lower than that of the planar reference geometry by ≈30meV per monomer. Backbone torsional potentials and hexyl torsional potentials converge with oligomer length by the octamer. A wide variety of oligomer conformations are sufficiently close in energy (∼kT) that the actual conformations found in a condensed phase will be determined primarily by intermolecular interactions, and substantial conformational disorder might be expected in the heterogenous environment of practical solar devices.

Large-scale density functional calculations of the surface properties of the Wigner crystal

The surface properties of the jellium model have been investigated by large supercell computations in the density functional theory-local spin-density (DFT-LSD) approach for planar slabs with up to 1000 electrons. A wide interval of densities has been explored, extending into the stability range of the Wigner crystal. Most computations have been carried out on nominally paramagnetic samples with an equal number of spin-up and spin-down electrons. The results show that within DFT-LSD spontaneous spin polarization and charge localization start nearly simultaneously at the surface for ${r}_{s}\ensuremath{\sim}20$, then, with decreasing density, they progress toward the center of the slab. Electrons are fully localized and spin polarized at ${r}_{s}=30$. At this density the charge distribution is the superposition of disjoint charge blobs, each corresponding to one electron. The distribution of blobs displays both regularities and disorder, the first being represented by well-defined planes and simple in-plane geometries, and the latter by a variety of surface defects. The surface energy, surface dipole, electric polarisability, and magnetization pattern have been determined as a function of density. All these quantities display characteristic anomalies at the density of the localization transition. The analysis of the low-frequency electric conductivity shows that in the fluid paramagnetic regime the in-plane current preferentially flows in the central region of the slab and the two spin channels are equally conducting. In the charge localized, spin-polarized regime, conductivity is primarily a surface effect, and an apparent asymmetry is observed in the two spin currents.

Large-scale density-functional calculations on silicon divacancies

We have performed total-energy electronic-structure calculations in the density-functional theory for the divacancy in Si using our real-space finite-difference pseudopotential method. Supercell models containing up to 1000 sites as well as a cluster model containing 432 atoms are used to simulate the divacancy in an otherwise perfect crystal. We have found that the resonant bond configuration is the most stable structure, the small pairing configuration is the next, and the large pairing configuration is the least stable for negatively and positively charged as well as neutral divacancies in the supercell model. The energy differences among the three configurations are found to be the order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Considering situations of ESR measurements, we have also performed the total-energy electronic-structure calculations under uniaxial stress along the ⟨110⟩ direction. We have found that induced strains alter the energetics and the pairing configurations become most stable with increasing strains. We argue that the ground state configuration of the Si divacancy is the resonant bond configuration and the pairing configurations become stable under the uniaxial stress and are detected by the EPR measurements.

Embedding atom-jellium model for metal surface

To describe metal surfaces efficiently and accurately, an embedding atom-jellium model is proposed. Within density functional theory, we consider a multiscale scheme that combines jellium and atomistic approaches. We use the former to model layers deep inside a metal surface to reduce the computational cost and the later to maintain the accuracy required for chemical bonding. Work functions of Al(111) and Cu(111) surfaces are studied using this model with comparisons to all-atom and pure jellium models. The much closer results of the embedding atom-jellium model to the all-atom results than to the pure jellium results show a good prospect for our approach in large-scale density functional calculations.

Density functional study of the adsorption of aC60monolayer on Ag(111) and Au(111) surfaces

Large-scale density functional calculations have been applied to investigate thoroughly the energetics and electronic structure of a ${\mathrm{C}}_{60}$ monolayer adsorbed on Ag(111) and Au(111) surfaces in the $(2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ phase. Various molecular orientations and adsorption sites have been examined. We find that the most energetically preferred adsorption configuration corresponds to a hexagon of ${\mathrm{C}}_{60}$ aligned parallel to the surface and centered on an hcp site, which gives an adsorption energy of -1.5 eV and -1.2 eV on Ag(111) and Au(111) surfaces, respectively. Analysis of the electron density difference and density of states indicates that the interaction between ${\mathrm{C}}_{60}$ and the noble metal surfaces is primarily covalent, with some ionic character [a small amount of electronic charge transfer of 0.5 and 0.2 electrons per molecule from the Ag(111) and Au(111) surfaces to ${\mathrm{C}}_{60},$ respectively]. This picture is in contrast with the common notion developed from experiments that the interaction between ${\mathrm{C}}_{60}$ and noble metal surfaces is mostly ionic. We also find that the work function increases by 0.1 eV on the Ag(111) surface and decreases by 0.6 eV on the Au(111) surface upon adsorption of a ${\mathrm{C}}_{60}$ monolayer, in good agreement with the experimental data. The opposite change of the work function on the two noble metal surfaces is explained well by examining multiple surface dipole formation in the interface region.

Density functional theory determination of an axial gateway to explain the rate and endo selectivity enhancement of Diels-Alder reactions by bis(oxazoline)-Cu(II).

A novel conceptual model and unique understanding of rate and endo selectivity enhancements delivered by bis(oxazoline)-Cu(II) Lewis acid catalysts in the Diels-Alder reaction of cyclopentadiene and acrylate imide is presented. Despite previously reported kinetic and spectroscopic studies, the physical reasons for endo selectivity and rate enhancements remain poorly understood. Large-scale density functional calculations using Becke three-parameter density functional theory with the nonlocal correlation of Lee, Yang, and Parr and the 6-31G(d) basis set have been carried out for the first time to understand the geometric and energetic consequences of C(2)-substituent variation. The unique positioning of the tert-butyl C(2)-substituent with respect to the diene, referred to as the "axial gateway", maintains the electrophilicity of the catalyst by shielding the reactive metal center from nucleophilic attack. The interplay between steric and electronic factors is crucial to understanding the observed enhanced rates and endo selectivity.

Symmetry and site selectivity in molecular chemisorption: Benzene on Ni{111}

We discuss the results of large-scale density functional calculations for (7×7) benzene adsorption on the ferromagnetic substrate Ni{111}. Adsorption at the bridge site, with C–C bonds parallel to the [2̄11] direction, is found to be energetically preferred over the [1̄10]-oriented hcp site suggested by electron diffraction experiments. We discuss the roles of intermolecular forces and anisotropic molecular vibrations in accounting for this apparent discrepancy. Furthermore, our analysis of charge and spin densities clarifies the relationship between preferred adsorption sites and the symmetry of frontier molecular orbitals.

Vibrational Assignment of All 46 Fundamentals of C60 and C606-: Scaled Quantum Mechanical Results Performed in Redundant Internal Coordinates and Compared to Experiments

Traditional vibrational assignment in terms of bond stretching, angle bending, and torsion is not possible in fullerenes due to the very large number of coupled internal coordinates. Large scale density functional calculations of the vibrational properties of C60 and C606- have been carried out with Becke3LYP and BeckeLYP exchange-correlation functionals in the pursuit of obtaining a reliable set of 174 normal modes (46 fundamental frequencies) and understanding the effect of charge transfer (doping) on the vibrational modes. The calculations involve scaling of the force field in redundant internal coordinates as proposed by Pulay et al. The scaled quantum mechanical (SQM) calculations yield excellent agreement with experiment for the 14 allowed frequencies. This provides the basis for an accurate assignment of all nonallowed fundamentals and the reassignment of the observed overtone and combination bands of the high-resolution Raman (Wang et al., 1993) and IR (Martin et al. 1994) spectra. The calculated intensity ratios for the four IR active bands agree with experiment. The large IR intensity enhancements observed for C606- relative to C60 are explained by the enhancement of certain components of the atomic polar tensor that is partially due to bond equalization in the charged fullerene. This enhancement appears to be largely a molecular rather then a solid state effect.

Structure sensitivity in adsorption: CO interaction with stepped and reconstructed Pt surfaces

The structure sensitivity of CO adsorption on different flat, stepped, kinked and reconstructed Pt surfaces is studied using large-scale density-functional calculations. We find an extremely strong structure sensitivity in the adsorption energy with variations up to 1 eV (or 100%) from one structure to the next. We propose a model to explain this behavior, and use it to discuss more generally the origin of structure sensitivity in heterogeneous catalysis.