Plane-wave Results Research Articles

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates.We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

Burst events of near-inertial waves in the Beaufort Sea

Based on moored observations from the Beaufort Gyre Exploration Project, seven burst events of near-inertial waves (NIWs) during September 2017-September 2018 are investigated in this study. These NIW events are divided into two groups. Four NIW events in group I are dominated by downgoing components associated with near-inertial currents in the magnitude of about 0.1 m/s. The plane-wave fitting results indicate that these NIWs have much smaller vertical wavelengths and energy fluxes than those in the mid-latitude oceans. By performing simulations with the slab model and analyzing sea ice conditions, we find that one NIW event is directly excited by the wind in the ice-free summer of 2018. Whereas, the other three NIW events are likely induced by the ice motion. For NIWs in group II, the downgoing and upgoing components are comparable in strength. The downgoing NIWs could be directly forced by the wind; whereas the upgoing ones may be related to the eddy events.The occurrence of the NIW events caused strong shears and hence smaller Richardson number, further resulting in the elevation of the energy dissipation rate. Results of this study can improve our understanding on the NIW dynamics and their influence on the mixing in the Arctic Ocean.

The bonding of H in Zr under strain

Accurate computer simulation is important for understanding the role of irradiation-induced defects in zirconium alloys found in nuclear reactors. Of particular interest is the distribution and trapping of hydrogen, and the formation of zirconium hydride. These simulations require an accurate representation of Zr-H bonding in order to predict the behaviour of H around atomic-scale defects, dislocation lines, and dislocation loops. Here we explore the bonding of H in Zr under strain, how well it is represented by state-of-the-art Embedded Atom Method (EAM) potentials, and what physics is needed for an accurate representation in a Linear Combination of Atomic Orbitals (LCAO) Density Functional Theory (DFT) framework. For H in dilute solution under hydrostatic strain in the range -10% to +10%, solution energies and Zr-H bond lengths computed using EAM potentials are found to be in poor agreement with plane-wave DFT results. We note that the bond lengths are in a poor agreement even in equilibrium. LCAO basis sets are used to explore the importance of electron distribution around H atoms, and the transfer of electrons between H and Zr. The electron distribution around H atoms is found to be important to the explanation of the difference between octahedral and tetrahedral interstitial sites for H, with H in a tetrahedral site having very similar bonding to H in zirconium hydrides. The interatomic electron transfer has a smaller impact but is needed for maximum accuracy.

Nuclear excitation of Th229 induced by laser-driven electron recollision

Previously we proposed a new approach of exciting the $^{229}\mathrm{Th}$ nucleus using laser-driven electron recollision [Wang, Zhou, Liu, and Wang, Phys. Rev. Lett. 127, 052501 (2021)]. The current article is aimed at elaborating the method by explaining further theoretical details and presenting extended new results. The method has also been improved by adopting the electronic excitation cross sections calculated recently by Tkalya [Tkalya, Phys. Rev. Lett. 124, 242501 (2020)]. The new cross sections are obtained from Dirac distorted-wave calculations instead of from Dirac plane-wave calculations as we used previously. The distorted-wave cross sections are shown to be 5 to 6 orders of magnitude higher than the plane-wave results. With the excitation cross sections updated, the probability of isomeric excitation of $^{229}\mathrm{Th}$ from electron recollision is calculated to be on the order of ${10}^{\ensuremath{-}12}$ per nucleus per (femtosecond) laser pulse. The dependency of the excitation probability on various laser parameters is calculated and discussed, including the laser intensity, the laser wavelength, and the laser pulse duration.

Beyond two-center tight binding: Models for Mg and Zr

We describe a systematic approach to building ab initio tight-binding models and apply this to hexagonal metals Mg and Zr. Our models contain three approximations to plane-wave density functional theory (DFT): (i) we use a small basis set, (ii) we approximate self-consistency, and (iii) we approximate many-center exchange and correlation effects. We test a range of approximations for many-center exchange-correlation and self-consistency to gauge the accuracy of each in isolation. This systematic approach also allows us to combine multiple approximations in the optimal manner for our final tight-binding models. Furthermore, the breakdown of errors into those from individual approximations is expected to be a useful guide for which approximations to include in other tight-binding models. We attempt to correct any remaining errors in our models by fitting a pair potential. Our final tight-binding model for Mg shows excellent agreement with plane-wave results for a wide range of properties (e.g., errors below 10% for self-interstitial formation energies and below 3% for equilibrium volumes) and is expected to be highly transferable due to the minimal amount of fitting. Calculations with our Zr model also show good agreement with plane-wave results (e.g., errors below 2% for equilibrium volumes) except for properties where self-consistency is important, such as self-interstitial formation energies. However, for these properties we are able to generate a tight-binding model which shows excellent agreement with non-self-consistent DFT with a small basis set (i.e., many-center effects are captured accurately by our approximations). As we understand the source of remaining errors in our Zr model we are able to outline the methods required to build upon it to describe the remaining properties with greater accuracy.

Quantitative electronic stopping power from localized basis set

The electronic stopping power of a swift ion in matter can be obtained from ab initio calculations within time-dependent density functional theory. Most implementations rely today on a plane-wave plus pseudopotential approach, but at the expense of very cumbersome calculations. We show here that localized orbitals, especially with Gaussian-type orbitals, are a valuable alternative. These calculations can yield electronic stopping powers in quantitative agreement with the plane-wave results while maintaining a computational burden that is relatively low. These positive results are possible only when using Gaussian basis sets that were specially designed for the stopping power calculations. With this tool, we investigate the discrepancy between ab initio calculations and experiment at large velocity, the effect of the exchange-correlation functional, and the role of core excitations in the total stopping power. We rule out the widespread centroid path approximation as soon as the core electrons are involved in the process.

Elastic full waveform inversion using plane-wave

Elastic full waveform inversion (FWI) is used to invert multicomponent data to obtain more accurate subsurface information; however, this method has a much higher computational cost than the acoustic method. In this study, the weighted pseudo-Hessian, which gives a weighting factor based on depth, was used as a preconditioner in the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm for stable and fast convergence of elastic FWI. The multiscale approach was also applied to avoid the cycle-skipping problem. Despite fast convergence, wavefield modelling is cumbersome; thus, we performed plane-wave domain elastic FWI to reduce the amount of computation. The plane-wave domain approach requires a proper shot interval and an appropriate number of ray parameters to reduce aliasing and crosstalk noise. If these two conditions are not satisfied, artefacts may appear in the inversion results. The effects of these conditions on the plane-wave domain inversion results were investigated systematically with the Marmousi-2 model. Some artefacts appeared and the quality of inversion was slightly lower when using approximately a quarter of the number of ray parameters required for plane-wave encoding. However, the inversion result was comparable to that of the case with the satisfying condition; additionally, the inversion was more efficient. If aliasing exists in the observed data due to a large shot interval, the plane-wave domain approach can still be applied successfully, as the effect of aliasing is suppressed through the summation process of the effects by multi-ray parameters.

Paving the Way for Suitable Metasurfaces’ Measurements Under Oblique Incidence: Mono-/Bistatic and Near-/Far-Field Concerns

This paper aims at contributing to the specialized literature on the experimental characterization of metasurfaces (MTSs) reflectivity. The growing demand for angularly stable MTSs reinforces the relevance of the results under oblique incidence. Generally, reflection coefficient phase measurements are more challenging than the amplitude ones. Thus, an artificial magnetic conductor (AMC) is used to analyze the critical aspects for enlarging the angular margin that can be properly measured. The importance of the retrieving methodology along with the proposed data postprocessing is highlighted among the involved issues, according to the obtained results. The suitability of monostatic versus bistatic measurement setups for comparison with plane-wave simulation is studied. The aforementioned AMC is experimentally characterized using both setups providing relevant conclusions. The tradeoff between the manufactured prototype dimensions (to resemble the simulated infinite one) versus the required anechoic chamber size (to fulfill far-field (FF) conditions, i.e., the plane-wave incidence for the considered frequencies) is tackled. Indeed, a thorough literature revision shows that most authors do not have this key aspect into account. The relevance of the resulting error from comparisons between the near-field (NF) retrieved measurements versus plane-wave simulation results is unveiled. This is even more critical when the angular stability is analyzed, since the scattering patterns of the AMC are not conformed at NF distances, which makes the errors even greater. Consequently, noteworthy conclusions concerning the characterization of AMCs in particular and MTSs in general regarding FF or NF measurements and angular stability analysis will be presented.

Single-center approach for photodetachment and radiative electron attachment: Comparison with other theoretical approaches and with experimental photodetachment data

A single-center method for calculating photodetachment cross section for anions and radiative electron attachment cross section for neutral molecules by microreversibility is presented. It uses the integral equation method to calculate the ejected electron's continuum wave function while the single-electron bound function of the anion is described by the Dyson orbital. It is compared with related theoretical approaches and benchmarked to the experimental photodetachment cross sections of ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$, ${\mathrm{OH}}^{\ensuremath{-}}$, and ${\mathrm{CN}}^{\ensuremath{-}}$. The use of the plane-wave approximation of the ejected electron wave function combined with the Hartree-Fock frozen-core approximation of the Dyson orbital is also considered and its results are compared with those of our methods and with experiment. A good agreement between the calculated photodetachment cross sections and the experimental data is obtained for ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$ and ${\mathrm{CN}}^{\ensuremath{-}}$ when using the three methods. For ${\mathrm{OH}}^{\ensuremath{-}}$, the calculated scattering-wave electron photodetachment cross sections agree well with two most recent sets of experimental data among the three available while the plane-wave results disagree with all the experimental and theoretical data. The different approaches to calculate the Dyson orbital are also discussed as well as the convergence of the calculations with respect to the choice of the one-electron basis set. The approximation of Dyson orbitals by Kohn-Sham orbitals appears to overestimate the photodetachment cross section.

On the calculation of the stress tensor in real-space Kohn-Sham density functional theory.

We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham density functional theory calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling expression for the stress tensor that is applicable to simulations with unit cells of arbitrary symmetry, semilocal exchange-correlation functionals, and Brillouin zone integration. In particular, we rewrite the contributions arising from the self-energy and the nonlocal pseudopotential energy to make them amenable to the real-space finite-difference discretization, achieving up to three orders of magnitude improvement in the accuracy of the computed stresses. Using examples representative of static and dynamic calculations, we verify the accuracy and efficiency of the proposed formulation. In particular, we demonstrate high rates of convergence with spatial discretization, consistency between the computed energy and the stress tensor, and very good agreement with reference planewave results.

Modulational instability and localized breather in discrete Schrödinger equation with helicoidal hopping and a power-law nonlinearity

We investigate the discrete nonlinear Schrödinger model with helicoidal hopping and a power-law nonlinearity, motivated by the tunable nonlinearity in the model of DNA chain and ultra-cold atoms trapped in a helix-shaped optical trap. In the study of modulational instability, we find a successive destabilization along with increasing nonlinear-power. In particular, the critical amplitudes of second-stage instability decrease as nonlinear-power increases. Furthermore, it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. This link enable us to analytically estimate the critical parameters at which the breather solutions turn unstable, and find these parameters are dramatically influenced by the nonlinear-power. The stability properties of localized breathers perform an obvious change when the nonlinear power crosses a critical value γcr. It is reflected that at weak nonlinearity the breathers exhibit monostability, while exceeding γcr the bistability and instability will set in. The interplay between nonlinear-power and long-range hopping on the stability properties of breathers is also discussed in detail.

SQDFT: Spectral Quadrature method for large-scale parallel [formula omitted] Kohn–Sham calculations at high temperature

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature. Program summaryProgram Title: SQDFTProgram Files doi:http://dx.doi.org/10.17632/h4jnrmh9v3.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: C/C++External routines/libraries: MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/) or later.Nature of problem: Quantum mechanical calculation of static and dynamic properties of condensed matter at high temperature in the framework of Kohn–Sham Density Functional Theory (DFT).Solution method: High-order finite-difference discretization. Calculation of the electronic ground state using the self-consistent field (SCF) iteration in conjunction with Periodic Pulay extrapolation/mixing. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Solution of the Poisson equation using the Alternating Anderson–Richardson (AAR) method. Calculation of the electron density, band structure energy, electronic entropy energy, and atomic forces using the infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) approach, in which results for the infinite crystal are obtained by expressing quantities as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. NVE molecular dynamics using the leapfrog method and NVT molecular dynamics using the Verlet algorithm with the Nose–Hoover thermostat. Extrapolation of electron density between molecular dynamics steps. Parallelization via domain decomposition.Restrictions: Cubical domain. Local Density Approximation (LDA). Troullier–Martins pseudopotentials without relativistic or non-linear core corrections.

Acoustic radiation force expansions in terms of partial-wave scattering phase shifts: Extended applications

When evaluating radiation forces on spheres in sound fields, the interpretation of analytical results is greatly simplified by retaining the use of s-function notation for partial-wave coefficients imported into acoustics from quantum scattering theory. This facilitates easy interpretation of various scattering efficiency factors [L. Zhang and P. Marston, J. Acoust. Soc. Am. 140, EL178 (2016)]. This also facilitates the correction of certain plane-wave results [H. Olsen et al., J. Acoust. Soc. Am. 30, 633 (1958)] and the force parameterization for a broader class of wavefields. For situations in which dissipation is negligible, each partial-wave s-function becomes characterized by a single parameter: a phase shift. These partial-wave phase shifts are associated with scattering by plane traveling waves; the incident wavefields of interest (progressive and standing wavefields and beams) are separately parameterized. (When considering outcomes, the method of fabricating symmetric objects having a desirable set of phase shifts becomes a separate issue.) The existence of negative radiation force “islands” for beams reported in 2006 by Marston is manifested. Elementary standing and traveling wave force expressions are also recovered. This approach also manifests the utility of conservation theorems [P. Marston and L. Zhang, J. Acoust. Soc. Am. 139, 3139 (2016)]. [Work supported by ONR.]

Experimental validation of acoustic intensity bandwidth extension by phase unwrapping.

The phase and amplitude gradient estimator (PAGE) method for active acoustic intensity uses pairwise microphone transfer functions to obtain the phase gradient, which improves the calculation bandwidth over the traditional weighted quadspectral method. Additionally, for broadband sources, the PAGE theory indicates that the transfer function phase can be unwrapped to further extend the usable frequency range to beyond the spatial Nyquist frequency. Here, two experiments demonstrate intensity bandwidth extension by more than an order of magnitude using phase unwrapping. First, plane-wave tube results show accurate one-dimensional intensity calculations with the microphones separated by five wavelengths, 30 times the traditional limit. Second, two-dimensional measurements of a laboratory-scale jet with a four-microphone probe yield physically reasonable calculations at frequencies 15 times the traditional limit.

SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for extended systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within desired accuracies in DFT. We demonstrate using a wide variety of materials systems that SPARC achieves high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; exponential convergence in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consistent and display negligible ‘egg-box’ effect; accurate properties of crystals, slabs, and wires; and negligible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementations for systems consisting up to thousands of electrons, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for performing DFT simulations of extended systems. Program summaryProgram title: SPARCCatalogue identifier: AFBR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 93822No. of bytes in distributed program, including test data, etc.: 1386659Distribution format: tar.gzProgramming language: C/C++.Computer: Any system with C/C++ compiler.Operating system: Linux.RAM: Problem dependent. Ranges from 80 GB to 800 GB for a system with 2500 electrons.Classification: 7.3.External routines: PETSc 3.5.3 (http://www.mcs.anl.gov/petsc), MKL 11.2 (https://software.intel.com/en-us/intel-mkl), and MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/).Does the new version supersede the previous version?: YesNature of problem: Calculation of the static and dynamic properties of isolated and extended systems in the framework of Kohn–Sham Density Functional Theory (DFT).Solution method:High-order finite-difference discretization. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Application of Bloch-periodic and zero-Dirichlet boundary conditions on the orbitals in the direction of periodicity and vacuum, respectively. Application of periodic and Dirichlet boundary conditions on the electrostatic potential in the direction of periodicity and vacuum, respectively. Integration over the Brillouin zone for extended systems using the Monkhorst–Pack grid. Calculation of the electronic ground-state using the Chebyshev polynomial filtered self-consistent field iteration in conjunction with Anderson based extrapolation/mixing schemes. Reformulation of the non-local component of the force. Geometry optimization using the Polak–Ribiere variant of non-linear conjugate gradients with secant line search. NVE molecular dynamics using the leapfrog method. Parallelization via domain decomposition and over Brillouin zone integration.Reasons for new version:To enable the study of extended systems like crystals, slabs, and wires using SPARC.Summary of revisions:Incorporated the ability to study the static and dynamic properties of crystals, slabs, and wires.Restrictions:System size less than ∼4000 electrons. Local Density Approximation (LDA). Troullier–Martins pseudopotentials without relativistic or non-linear core corrections. Domain has to be cuboidal.Running time:Problem dependent. Timing results for selected examples provided in the paper.

SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable ‘egg-box’ effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.Program summaryProgram title: SPARCCatalogue identifier: AFBL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 47525No. of bytes in distributed program, including test data, etc.: 826436Distribution format: tar.gzProgramming language: C/C++.Computer: Any system with C/C++ compiler.Operating system: Linux.RAM: Problem dependent. Ranges from 80 GB to 800 GB for a system with 2500 electrons.Classification: 7.3.External routines: PETSc 3.5.3 (http://www.mcs.anl.gov/petsc), MKL 11.2 (https://software.intel.com/en-us/intel-mkl), and MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/).Nature of problem:Calculation of the electronic and structural ground-states for isolated clusters in the framework of Kohn–Sham Density Functional Theory (DFT).Solution method:High-order finite-difference discretization. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Calculation of the electronic ground-state using the Chebyshev polynomial filtered Self-Consistent Field (SCF) iteration in conjunction with Anderson extrapolation/mixing. Evaluation of boundary conditions for the electrostatic potential through a truncated multipole expansion. Reformulation of the non-local component of the force. Geometry optimization using the Polak–Ribiere variant of non-linear conjugate gradients with secant line search.Restrictions:System size less than ∼4000 electrons. Local Density Approximation (LDA). Troullier–Martins pseudopotentials without relativistic or non-linear core corrections.Running time:Problem dependent. Timing results for selected examples provided in the paper.

Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping

We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected Nth neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. Based on this argument, we derive analytical estimates of the critical parameters at which the fundamental on-site breather branch of solutions turns unstable. In the limit of large N, these estimates predict the emergence of an effective threshold behavior, which can be viewed as the result of a dimensional crossover to a two-dimensional square lattice.

Spectral Quadrature method for accurate [formula omitted] electronic structure calculations of metals and insulators

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. Finally, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.

First-principles investigations of elastic stability and electronic structure of cubic platinum carbide under pressure

The authors have presented a detailed investigation on the phase stabilities and electronic properties of ideal stoichiometric platinum carbide (PtC) in the rock-salt (RS) and zinc-blende (ZB) structures under high pressure. Theoretical calculations are performed using the first-principles pseudopotential density functional method, in which we employ the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof form and local density approximation (LDA) of Ceperly and Adler parameterized by Perdew and Zunger together with plane-wave basis sets for expanding the periodic electron density. Through a series of tests, such as the total energy as a function of volume, the Gibbs free energy as a function of pressure, the P-V equation of states, the elastic stabilities, and the electronic band structures of PtC with ZB and RS phases, we have confirmed that the recently synthesized compound PtC is crystallized in the ZB structure at zero pressure and that the RS structure is a high-pressure phase; the phase transition studied from the usual condition of equal enthalpies occurs at the pressures of 46.6 and 46.5 GPa for GGA and LDA calculations, respectively. Our conclusions are consistent with the theoretical prediction obtained from the full-potential linearized augmented plane-wave method, but are reversed with the DAC experimental results and other pseudopotential plane-wave theoretical results. Therefore, the experimental observation of the RS structure in PtC remains a puzzle, and our study indicates that further experimental and theoretical investigations need to be carried out to find the cause of the stability of the PtC.

Model dependence of theH2electric dipole moment

Background: Direct measurement of the electric dipole moment (EDM) of the neutron is in the future; measurement of a nuclear EDM may well come first. The deuteron is one nucleus for which exact model calculations are feasible. Purpose: We explore the model dependence of deuteron EDM calculations. Methods: Using a separable potential formulation of the Hamiltonian, we examine the sensitivity of the deuteron EDM to variation in the nucleon-nucleon interaction. We write the EDM as the sum of two terms, the first depending on the target wave function with plane-wave intermediate states, and the second depending on intermediate multiple scattering in the ${}^{3}$$P$${}_{1}$ channel, the latter being sensitive to the off-shell behavior of the ${}^{3}$$P$${}_{1}$ amplitude. Results: We compare the full calculation with the plane-wave approximation result, examine the tensor force contribution to the model results, and explore the effect of short-range repulsion found in realistic, contemporary potential models of the deuteron. Conclusions: Because one-pion exchange dominates the EDM calculation, separable potential model calculations will provide an adequate description of the $^{2}\mathrm{H}$ EDM until such time as a measurement better than $10%$ is obtained.