Real-space Pseudopotential Method Research Articles

Real-space pseudopotential method for calculating magnetocrystalline anisotropy

We present a real-space pseudopotential method for calculating magnetocrystalline anisotropy within relativistic density-functional theory. The spin-orbit interaction, a fundamental origin of magnetocrystalline anisotropy, is incorporated with norm-conserving pseudopotentials expressed on a real-space grid. We demonstrate the utility of our method by calculating the magnetocrystalline anisotropy constant, ${K}_{1}$, of ${\mathrm{YCo}}_{5}$, which is a prototype compound with large ${K}_{1}$. Our calculated ${K}_{1}$ agrees with previous theoretical work. We show that our formalism also works for describing magnetocrystalline anisotropy in other transition-metal compounds, such as ${\mathrm{Mn}}_{2}\mathrm{Ga}$ and FeNi, which have modest values for ${K}_{1}$. Our real-space pseudopotential method is well suited for a parallel computing environment and is an efficacious approach to solving the relativistic Kohn-Sham equations, which include spin-orbit effects as well as noncollinear magnetism.

Real-space pseudopotential method for computing the vibrational Stark effect.

The vibrational Stark shift is an important effect in determining the electrostatic environment for molecular or condensed matter systems. However, accurate ab initio calculations of the vibrational Stark effect are a technically demanding challenge. We make use of density functional theory constructed on a real-space grid to expedite the computation of this effect. Our format is especially advantageous for the investigation of small molecules in finite fields as cluster boundary conditions eliminate spurious supercell interactions and allow for charged systems, while convergence is controlled by a single parameter, the grid spacing. The Stark tuning rate is highly sensitive to the interaction between anharmonicity in a vibrational mode and the applied field. To ensure this subtle interaction is fully captured, we apply three parallel approaches: a direct finite field, a perturbative method, and a molecular dynamics method. We illustrate this method by applying it to several small molecules containing C-O and C-N bonds and show that a consistent result can be obtained.

Structural evolution of the Pb/Si(111) interface with metal overlayer thickness

We employ a real-space pseudopotential method to compute the structural energies of a prototypical metal-semiconductor interface. Specifically, we examine a Pb(111) film overlaid on a Si(111) substrate as a function of the metal thickness. For each layer of Pb, we fully relax the atomic coordinates and determine the lowest-energy structure. Owing to the lattice mismatch between the Pb and Si crystal structures, we consider a large supercell containing up to 1505 atoms for the largest system. Systems of this size remain challenging for most current computational approaches and require algorithms specifically designed for highly parallel computational platforms. We examine the structural properties of the interface with respect to the thickness of the metal overlayer, e.g., the corrugation of the profile of the Pb overlayer. The combined influence of the Si substrate and quantum confinement results in a rich profile for a transition between a thin overlayer (less than a few monolayers), where the corrugation is strong, and the bulk region (more than a half-dozen layers), where the overlaid Pb film is atomically flat. This work proves the feasibility of handling systems with such a level of complexity.

Quantum confinement, core level shifts, and dopant segregation in P-dopedSi⟨110⟩nanowires

We examine P-doped $\text{Si}⟨110⟩$ nanowires by employing a real-space pseudopotential method. We find the defect wave function becomes more localized along the nanowire axis and the donor ionization energy increases, owing to quantum confinement. It is more difficult to dope a P atom into a $\text{Si}⟨110⟩$ nanowire than to dope Si bulk because the formation energy increases with decreasing size. By comparing the formation energy for different P positions within a nanowire, we find that if a P atom at the nanowire surface can overcome the energy barrier close to the surface, there is a tendency for the dopant to reside within the nanowire core. We calculate P core levels shift as P changes position within the nanowire and provide a means for x-ray photoelectron spectroscopy experiments to determine the location of P atoms within a Si nanowire.

Size-dependent induced magnetism in carbon-doped ZnO nanostructures

We examine the role of quantum confinement on carbon doped ZnO nanocrystals and nanowires using first-principles real-space pseudopotential method. For these nanocrystals, we find carbon dopants become magnetic under confinement. Moreover, by examining dopant-dopant interactions in ZnO nanowires, we find the ferromagnetic exchange interactions to be strongly enhanced at the nanoscale. Our work offers strong theoretical evidence for nanoscale induced magnetism and direct exchange coupling interactions arising from “nonmagnetic dopants.”

Real-space pseudopotential method for noncollinear magnetism within density functional theory

We present a real-space pseudopotential method for first principles calculations of noncollinear magnetic phenomena within density functional theory. We demonstrate the validity of the method using the test cases of the Cr 3 cluster and the Cr ( 3 × 3 ) R 3 0 ∘ monolayer. The approach retains all the typical benefits of the real-space approach, notably massive parallelization. It can be employed with arbitrary boundary conditions and can be combined with the computation of pseudopotential-based spin-orbit coupling effects.

Real-space pseudopotential method for first principles calculations of general periodic and partially periodic systems

We present a real-space method for electronic-structure calculations of systems with general full or partial periodicity. The method is based on the self-consistent solution of the Kohn-Sham equations, using first principles pseudopotentials, on a uniform three-dimensional non-Cartesian grid. Its efficacy derives from the introduction of a new generalized high-order finite-difference method that avoids the numerical evaluation of mixed derivative terms and results in a simple yet accurate finite difference operator. Our method is further extended to systems where periodicity is enforced only along some directions (e.g., surfaces), by setting up the correct electrostatic boundary conditions and by properly accounting for the ion-electron and ion-ion interactions. Our method enjoys the main advantages of real-space grid techniques over traditional plane-wave representations for density functional calculations, namely, improved scaling and easier implementation on parallel computers, as well as inherent immunity to spurious interactions brought about by artificial periodicity. We demonstrate its capabilities on bulk GaAs and Na for the fully periodic case and on a monolayer of Si-adsorbed polar nitrobenzene molecules for the partially periodic case.

Quantum confinement and strong coulombic correlation in ZnO nanocrystals

Strong coulombic correlation interaction of quantum-confined system is studied by implementing a Hubbard-type mean-field potential in real-space pseudopotential method. Effective Hubbard U potential of a nanosized material is determined by atomic correlation potential and effective dielectric constant. We apply this method with spherically shaped wurtzite ZnO nanocrystals. Inefficient screening of Coulomb interaction in nanocrystalline system leads to a significant increase of effective U parameter compared to bulk solid. As a result, quasi-particle gap of nanocrystal increases noticeably with the U potential.

Real-space pseudopotential method for spin-orbit coupling within density functional theory

We present a formalism and implementation for real-space calculations that incorporate relativistic effects, including spin-orbit coupling. We demonstrate the validity of the method using the test cases of AuH and the ${\mathrm{Au}}_{2}$ dimer. The proposed approach differs from nonrelativistic real-space calculations in the addition of nonlocal pseudopotential projectors, which are translated to small rank-1 matrix ``stencils'' operating on the discretized wave functions. This formalism retains all the usual benefits of the real-space approach, especially with respect to massive parallelization. We expect it to be readily applicable for computational studies of large systems exhibiting spin-orbit coupling effects.

Real-space pseudopotential method for electron transport properties of nanoscale junctions

We present an ab initio self-consistent method for the electronic transport of nanoscale junctions under finite bias. Our method is based on density functional theory using real-space pseudopotentials. The scattering wave function is obtained by solving a set of linear equations with a sparse coefficient matrix. Our method does not require a matrix inversion. We apply the method to a Na or Mg atom ``connected'' to two planar electrodes. Good agreement with previous work is obtained.

Ab initio calculations for the photoelectron spectra of vanadium clusters.

We report ab initio calculations for the electronic and structural properties of V(n), V(n) (-), and V(n) (+) clusters up to n=8. We performed the calculations using a real-space pseudopotential method based on the local spin density approximation for exchange and correlation. This method assumes no explicit basis. Wave functions are evaluated on a uniform grid; only one parameter, the grid spacing, is used to control convergence of the electronic properties. Charged states are easily handled in real space, in contrast to methods based on supercells where Coulombic divergences require special handling. For each size and charge state, we find the lowest energy structure. Our results for the photoelectron spectra, using the optimized structure, agree well with those obtained by experiment. We also obtain satisfactory agreement with the measured ionization potential and electron affinity, and compare our results to calculations using an explicit basis.

Real-space pseudopotential method for computing the electronic properties of periodic systems

We present a real-space method for electronic-structure calculations of periodic systems. Our method is based on the self-consistent solution of the Kohn-Sham equations on a uniform three-dimensional grid. A higher-order finite-difference method is combined with ab initio pseudopotentials. The kinetic energy operator, the nonlocal term of the ionic pseudopotential, and the Hartree and exchange-correlation potentials are set up directly on the real-space grid. The local contribution to the ionic pseudopotential is initially obtained in reciprocal space and is then transferred to the real-space grid by Fourier transform. Our method enjoys the main advantages of real-space grid techniques over traditional plane-wave representations for density-functional calculations, i.e., improved scaling and easier implementation on parallel computers. We illustrate the method by application to liquid silicon.

Application of Time-Dependent Density-Functional Theory toC6

We employ a real-space pseudopotential method todetermine the ground state structure of the carbon cluster C6via simulated annealing and the corresponding optical absorptionspectra from the adiabatic time-dependent density-functional theory(TDDFT) and the local density approximation (TDLDA). It is found thatthe ground state structure of the carbon cluster C6 belongs to amonocyclic D3h structure and the calculated spectraexhibit a variety of features that can be used for comparison againstfuture experimental investigations.

Quantum Confinement and Optical Gaps in Si Nanocrystals

Quasiparticle gaps, self-energy corrections, exciton Coulomb energies, and optical gaps in Si quantum dots are calculated from first principles using a real-space pseudopotential method. The calculations are performed on hydrogen-passivated spherical Si clusters with diameters up to 27.2 \AA{} ( $\ensuremath{\sim}800\mathrm{Si}$ and H atoms). It is shown that (i) the self-energy correction in quantum dots is enhanced substantially compared to bulk, and is not size independent as implicitly assumed in all semiempirical calculations, and (ii) quantum confinement and reduced electronic screening result in appreciable excitonic Coulomb energies. Calculated optical gaps are in very good agreement with absorption data.