Plane-wave Code Research Articles

Analytical treatment of the Yukawa screened Coulomb interaction in a plane-wave basis

The calculation of the many-electron (screened) Coulomb and exchange integrals is a very common task to perform in modern electronic structure theory. While an analytical treatment of the complete integrals is too complicated to be attempted directly, essential insight can be gained by focusing on the most significant contributions, as determined by a physical criterion. The monopole term of the screened Coulomb interaction is particularly important, since it defines the Hubbard interaction U among a set of localized electrons, which is an essential parameter for effective models of strongly correlated systems. Here, we derive an analytical solution for the matrix elements of the screened Coulomb interaction on a plane-wave basis, which is routinely used in the most common methods for electronic structure calculations. Screening is treated using a Yukawa potential, which is suitable to describe the valence electrons in the Fermi level region. For the solution of the integrals, the plane waves and the Yukawa potential are first expanded in Bessel functions of first and second kind. Then, by means of the lower and upper incomplete gamma functions, we are able to obtain closed-form integrals of a series that remains convergent for realistic parameters. Our exact solution for the radial integrals of the monopole term can find usage in plane-wave codes for electronic structure calculations, both as an output tool as well as within the computational cycle, as e.g., for many-body extensions of density-functional theory. Considering the importance of Bessel functions in solid state physics and electronic structure theory, it is also easy to foresee that our solution to the various integrals across this work may become useful to several other problems in the field.

Efficient real space formalism for hybrid density functionals.

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using abinitio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

Boosting the Modeling of Infrared and Raman Spectra of Bulk Phase Chromophores with Machine Learning.

In the field of vibrational spectroscopy simulation, hybrid approximations to Kohn-Sham density-functional theory (KS-DFT) are often considered computationally prohibitive due to the significant effort required to evaluate the exchange-correlation potential in planewave codes. In this Letter, we show that by leveraging the porting of KS-DFT on GPU and incorporating machine-learning techniques, simulating IR and Raman spectra of real-life chromophores in bulk aqueous solution becomes a routine application at this level of theory.

Contributions beyond direct random-phase approximation in the binding energy of solid ethane, ethylene, and acetylene

The random-phase approximation (RPA) includes a subset of higher than second-order correlation-energy contributions, but stays in the same complexity class as the second-order Møller–Plesset perturbation theory (MP2) in both Gaussian-orbital and plane-wave codes. This makes RPA a promising ab initio electronic structure approach for the binding energies of molecular crystals. Still, some issues stand out in practical applications of RPA. Notably, compact clusters of nonpolar molecules are poorly described, and the interaction energies strongly depend on the reference single-determinant state. Using the many-body expansion of the binding energy of a crystal, we investigate those issues and the effect of beyond-RPA corrections. We find the beneficial effect of quartic-scaling exchange and non-ring coupled-cluster doubles corrections. The nonadditive interactions in compact trimers of molecules are improved by using the self-consistent Hartree–Fock orbitals instead of the usual Kohn–Sham states, but this kind of orbital input also leads to underestimated dimer energies. Overall, a substantial improvement over the RPA with a renormalized singles approach is possible at a modest quartic-scaling cost, which encourages further research into additional RPA corrections.

Adaptive finite differencing in high accuracy electronic structure calculations

A multi-order Adaptive Finite Differencing (AFD) method is developed for the kinetic energy operator in real-space, grid-based electronic structure codes. It uses atomic pseudo orbitals produced by the corresponding pseudopotential codes to optimize the standard finite difference (SFD) operators for improved precision. Results are presented for a variety of test systems and Bravais lattice types, including the well-known Δ test for 71 elements in the periodic table, the Mott insulator NiO, and borax decahydrate, which contains covalent, ionic, and hydrogen bonds. The tests show that an 8th-order AFD operator leads to the same average Δ value as that achieved by plane-wave codes and is typically far more accurate and has a much lower computational cost than a 12th-order SFD operator. The scalability of real-space electronic calculations is demonstrated for a 2016-atom NiO cell, for which the computational time decreases nearly linearly when scaled from 18 to 144 CPU-GPU nodes.

Theoretical study of thermal stability of α″–Fe16N2 against other iron nitrides

α″–Fe16N2 has been investigated as one of promising candidates for environment-friendly magnets. While giant saturation magnetization has previously been experimentally observed in α″–Fe16N2, its magnetic anisotropy and structural stability leave room for improvement. Recent theoretical studies have considered alloying Fe16N2 with various elements to improve the magnetic properties and/or stability against decomposition. However, estimates of stability in particular are typically restricted to simple ground-state-energy comparisons, i.e. effectively taken at 0 K. For a more practical measure of stability, we therefore extend ground-state energies, obtained with the plane-wave density-functional theory code Quantum ESPRESSO, with appropriate empirical and/or statistical corrections to obtain free energies at arbitrary temperature. We then compare the stability of Fe16N2 against the neighboring phases in the Fe-N binary system, to estimate the range of temperatures at which it is stable. We compare against experimental observations of the Fe-N phase diagram.

Effect of Hubbard U on calculations of magnetic properties of α″–Fe16N2

The ordered iron nitride phase α″–Fe16N2 has been a potential candidate for rare-earth free magnets with giant saturation magnetization, but first-principles electronic-structure calculations have struggled to reproduce recent observations of high magnetic moment, while calculations of magnetocrystalline anisotropy (MCA) vary significantly. Within the framework of density-functional theory (DFT), a common extension to the usual generalized-gradient approximation (GGA) exchange-correlation (XC) functional is the inclusion of Hubbard parameters U (,J) as GGA + U. A number of previous papers have applied this method to Fe16N2, each with their own choice of Hubbard parameters. The plane-wave DFT code Quantum ESPRESSO was employed to more comprehensively study the effect of the value of Hubbard parameters U and J on the system, particularly with respect to its magnetic properties. Various approaches for setting U and J were compared, including self-consistent calculations via the linear-response method.

Correlation consistent effective core potentials for late 3d transition metals adapted for plane wave calculations.

We construct a new modification of correlation consistent effective core potentials (ccECPs) for late 3d elements Cr-Zn with Ne-core that are adapted for efficiency and low energy cut-offs in plane wave calculations. The decrease in accuracy is rather minor, so that the constructions are in the same overall accuracy class as the original ccECPs. The resulting new constructions work with energy cut-offs at or below ≈400 Ry and, thus, make calculations of large systems with transition metals feasible for plane wave codes. We also provide the basic benchmarks for atomic spectra and molecular tests of this modified option that we denote as ccECP-soft.

Cubic spline solver for generalized density functional treatments of atoms and generation of atomic datasets for use with exchange-correlation functionals including meta-GGA

Within generalized density functional theory, recent developments of functionals which depend upon the kinetic energy density, such as the r2SCAN form, show significant improvement in the computational representation of real material properties. In order to implement these forms within plane-wave codes, it is necessary to use pseudopotentials, ideally constructed with the same exchange-correlation functional as has been implemented for the projector augmented-wave (PAW) formalism in the atompaw code. This was accomplished with the help of an efficient solver for the self-consistent radial bound states of each atom, based on cubic spline interpolation. Details of the formalism are presented, and preliminary results for several simple materials are encouraging.

Magnetic correlations in single-layer NbSe2

By means of spin-resolved density functional theory calculations using both atomic orbitals and plane-wave basis codes, we study the electronic and magnetic ground state of single-layer NbSe2. We find that, for all the functionals considered, the most stable solution in this two-dimensional (2D) superconductor is the ferrimagnetic ground state with a magnetic moment of 1.09 μ B at the Nb atoms and of 0.05 μ B at the Se atoms pointing in the opposite direction. Our calculations show that the ferrimagnetic state precludes the development of charge density wave (CDW) order and their coexistence in the single-layer limit, unless graphene is considered as a substrate. The spin-resolved calculated density of states (DOS), a key fingerprint of the electronic and magnetic structure of a material, unambiguously reproduces the experimental DOS measured by scanning tunneling spectroscopy in single-layer NbSe2. Our work sets magnetism into play in this prototypical correlated 2D material, which is crucial to understand the formation mechanisms of 2D superconductivity and CDW order.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in ionic liquids.

We test a number of dispersion corrected versatile Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol-1 of benchmarks. This compares favorably with an accurate dispersion corrected hybrid, ωB97X-V. Our tests also reveal that PBE (Perdew-Burke-Ernzerhof GGA) calculations using the plane-wave projector augmented wave method and Gaussian Type Orbitals (GTOs) differ by less than 0.6 kJ mol-1 for ionic liquids, despite ions being difficult to evaluate in periodic cells - thus revealing that GTO benchmarks may be used also for plane-wave codes. Finally, the relatively high success of explicit van der Waals density functionals, compared to elemental and ionic dispersion models, suggests that improvements are required for low-cost dispersion correction models of ions.

Electrochemical Performance of Nickel Silicide Electrodes for Lithium-Ion Batteries in an Ionic-Liquid Electrolyte

Developing lithium-ion batteries (LIBs) with a high energy density, long cycle, and high safety is essential for establishing a sustainable society because LIBs are used as electric vehicle batteries and stationary batteries for utilizing renewables. Silicon (Si) has great potential as an anode active material for next-generation LIBs due to its high theoretical capacity (3580 mA h g- 1 for Li15Si4). However, Si electrodes show poor cycle stability, which is mainly caused by a large volume change in Si during the lithiation (charge) and delithiation (discharge) reactions. Additionally, Si has other disadvantages, such as high electrical resistivity and a low Li+ diffusion coefficient. We have previously investigated the lithiation and delithiation properties of pure binary silicide (M ySiz, M : transition metal) electrodes. Some electrodes maintained a high reversible capacity in an ionic-liquid electrolyte, whereas they showed a poor cycling performance in a conventional organic-liquid electrolyte. In contrast, the effect of difference in crystal phase of silicides composed of the same elements on the lithiation and delithiation properties has not yet been clarified. Herein, we synthesized various pure nickel silicide (Ni-Si) powders. and investigated their lithiation and delithiation properties in an ionic-liquid electrolyte. Ni-Si powders (NiSi2, NiSi, Ni2Si, and Ni3Si) were synthesized by a mechanical alloying (MA) method. The obtained powders were characterized by X-ray diffraction (XRD) and Raman spectroscopy. XRD patterns were identified compared with patterns in the Inorganic Crystal Structure Database (ICSD). Each silicide electrode was prepared by a gas deposition (GD) method, which does not require a binder or conductive agent. We assembled 2032-type coin cells, which consisted of the silicide electrode as the working electrode, Li metal foil as the counter electrode and a glass fiber filter as the separator. 1 mol dm- 3 (M) lithium bis(fluorosulfonyl)amide (LiFSA) in N-methyl-N-propylpyrrolidinium bis(fluorosulfonyl)amide (Py13-FSA) was used as an ionic-liquid electrolyte. A galvanostatic charge-discharge test was carried out in the potential range between 0.005 and 2.000 V vs. Li+/Li at 303 K. The current density was set at 50 mA g- 1. To discuss the charge density of each element in Li x Ni y Si z , a first-principle calculation based on density functional theory (DFT) was performed using the projector augmented wave (PAW) method as implemented in the plane wave code of the Vienna Ab initio Simulation Package (VASP). A generalized gradient approximation (GGA) was used as the term exchange correlation with a kinetic cutoff of 350 eV. Brillouin zone sampling was performed with an 8×8×8 k point mesh within a Gamma point centered mesh scheme. We synthesized various Ni-Si powders by a MA method. Comparing the XRD pattern of the prepared samples and the corresponding ICSD pattern, all peaks were assigned to pure Ni-Si phase. Additionally, there were no peaks arising from the raw materials (Ni and Si). In Raman spectra, peaks assigned to crystalline Si (c-Si) and amorphous Si (a-Si) appear at approximately 520 and 490 cm- 1, respectively. Each silicide also gives no Raman peaks of c-Si and/or a-Si which indicates that neither c-Si nor a-Si is included in the synthesized powders. Therefore, the MA treatment successfully produced a pure Ni-Si phase. Fig.1 shows the dependence of the gravimetric discharge capacity of various nickel silicide electrodes on the cycle number in 1 M LiFSA/Py13-FSA.The NiSi2 electrode exhibited the highest initial capacity of approximately 800 mA h g- 1, and the Ni3Si electrode showed the second highest capacity. The results demonstrated that there was no correlation between initial capacity and silicon content in Ni-Si. To reveal the difference in the initial capacity, we determined the charge density of each element in Li x Ni y Si z based on computational chemistry. Li and Si have positive charges in all silicides, whereas Ni has a negative charge in Li x Ni y Si z . These results indicate that Li has a high affinity with Ni in Li x Ni y Si z . In addition, it is suggested that the higher the affinity of Ni with Li is, the higher the initial capacity is. Furthermore, we investigated the distance between Li and close atoms (Ni or Si) in Li x Ni y Si z . The initial capacity increased with an increase in the distance. Therefore, both the affinity of Ni with Li and the distance between Li and neighboring atom should influence on the initial capacity. Figure 1

Open versus Interpenetrated: Switchable Supramolecular Trajectories in Mechanosynthesis of a Halogen-Bonded Borromean Network

Summary Precise control over topologically intricate molecular architectures remains an open challenge for chemists due to their inherent structural complexity. We report a simple solvent-free strategy to selectively prepare two multi-component supramolecular crystalline systems based on the halogen bond, endowed with either an unknot topology or a Borromean-type entanglement. Real-time in situ monitoring of the solvent-free mechanochemical synthesis of these three-component halogen-bonded ionic co-crystals reveals that the choice of milling conditions leads to a switch in the supramolecular reaction trajectory, resulting in the selective formation of an open halogen-bonded network or a halogen-bonded Borromean-type assembly.

In operando active learning of interatomic interaction during large-scale simulations

A well-known drawback of state-of-the-art machine-learning interatomic potentials is their poor ability to extrapolate beyond the training domain. For small-scale problems with tens to hundreds of atoms this can be solved by using active learning which is able to select atomic configurations on which a potential attempts extrapolation and add them to the ab initio-computed training set. In this sense an active learning algorithm can be viewed as an on-the-fly interpolation of an ab initio model. For large-scale problems, possibly involving tens of thousands of atoms, this is not feasible because one cannot afford even a single density functional theory (DFT) computation with such a large number of atoms.This work marks a new milestone toward fully automatic ab initio-accurate large-scale atomistic simulations. We develop an active learning algorithm that identifies local subregions of the simulation region where the potential extrapolates. Then the algorithm constructs periodic configurations out of these local, non-periodic subregions, sufficiently small to be computable with plane-wave DFT codes, in order to obtain accurate ab initio energies. We benchmark our algorithm on the problem of screw dislocation motion in bcc tungsten and show that our algorithm reaches ab initio accuracy, down to typical magnitudes of numerical noise in DFT codes. We show that our algorithm reproduces material properties such as core structure, Peierls barrier, and Peierls stress. This unleashes new capabilities for computational materials science toward applications which have currently been out of scope if approached solely by ab initio methods.

Application of k $$\cdot $$ p method on band structure of GaAs obtained through joint density-functional theory

The structural and electronic properties of zinc-blende GaAs were calculated within the framework of plane-wave density-functional theory code JDFTx by using Becke 86 in 2D and PBE exchange-correlation functionals from libXC. The standard optimized norm-conserving Vanderbilt pseudopotentials were used to calculate optimized lattice constants, band gap and spin–orbit (SO) split-off parameter. The calculated values of optimized lattice constants and direct band gap are in satisfactory agreement with other published theoretical and experimental findings. By including SO coupling, conduction bands and valence bands were studied under parabolicity to calculate effective masses. The calculated values of effective masses and SO split-off parameter are in satisfactory agreement with most recent findings. This study will be useful for more computational studies related to semiconductor spintronic devices.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

Anharmonic calculations of vibrational spectra for molecular adsorbates: A divide-and-conquer semiclassical molecular dynamics approach.

The vibrational spectroscopy of adsorbates is becoming an important investigation tool for catalysis and material science. This paper presents a semiclassical molecular dynamics method able to reproduce the vibrational energy levels of systems composed by molecules adsorbed on solid surfaces. Specifically, we extend our divide-and-conquer semiclassical method for power spectra calculations to gas-surface systems and interface it with plane-wave electronic structure codes. The Born-Oppenheimer classical dynamics underlying the semiclassical calculation is full dimensional, and our method includes not only the motion of the adsorbate but also those of the surface and the bulk. The vibrational spectroscopic peaks related to the adsorbate are accounted together with the most coupled phonon modes to obtain spectra amenable to physical interpretations. We apply the method to the adsorption of CO, NO, and H2O on the anatase-TiO2 (101) surface. We compare our semiclassical results with the single-point harmonic estimates and the classical power spectra obtained from the same trajectory employed in the semiclassical calculation. We find that CO and NO anharmonic effects of fundamental vibrations are similarly reproduced by the classical and semiclassical dynamics and that H2O adsorption is fully and properly described in its overtone and combination band relevant components only by the semiclassical approach.

First-principles study on the effects of N and Al doping on the mechanical properties and electronic structures of TiC.

First-principles calculations are carried out by DFT within the CASTEP plane wave code to investigate the mechanical properties and electronic structure of N and Al doped TiC. The results show that the co-doping of nitrogen and aluminum narrows the lattice constant and nitrogen could enhance the stability of TiC, however, aluminum makes the compound unstable. The calculated elastic constants and elastic moduli reveal that aluminum reduces the elastic constants, bulk modulus B, shear modulus G and Young's modulus E, but nitrogen can enhance them. The results of B/G and C12–C44 indicate that aluminum could significantly increase the ductility of TiC. Meanwhile, the electronic structure calculations reveal that strong p–d covalent bonds exist among C-p, N-p, Ti-d and Al-p states and Al-doping causes DOS peak transfer to a higher energy level and increases the DOS above the Fermi level. The hardness is estimated by a semi-empirical model that is based on the Mulliken overlap population and bond length. The addition of Al sharply reduces the hardness of the TiC-based alloys due to the weakest bond taking a determinative role in the hardness of materials, which is the C–Al bond in those compounds.

Assessing Relativistic Effects and Electron Correlation in the Actinide Metals Th to Pu

Density functional theory (DFT) calculations are employed to explore and assess the effects of the relativistic spin–orbit interaction and electron correlations in the actinide elements. Specifically, we address electron correlations in terms of an intra-atomic Coulomb interaction with a Hubbard U parameter (DFT + U). Contrary to recent beliefs, we show that for the ground-state properties of the light actinide elements Th to Pu, the DFT + U makes its best predictions for U = 0. Actually, our modeling suggests that the most popular DFT + U formulation leads to the wrong ground-state phase for plutonium. Instead, extending DFT and the generalized gradient approximation (GGA) with orbital–orbital interaction (orbital polarization; OP) is the most accurate approach. We believe the confusion in the literature on the subject mostly originates from incorrectly accounting for the spin–orbit (SO) interaction for the p1/2 state, which is not treated in any of the widely used pseudopotential plane-wave codes. Here, we show that for the actinides it suffices to simply discard the SO coupling for the p states for excellent accuracy. We thus describe a formalism within the projector-augmented-wave (PAW) scheme that allows for spin–orbit coupling, orbital polarization, and non-collinear magnetism, while retaining an efficient calculation of Hellmann–Feynman forces. We present results of the ground-state phases of all the light actinide metals (Th to Pu). Furthermore, we conclude that the contribution from OP is generally small, but substantial in plutonium.

Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established planewave and real-space codes. Using this implementation, we study the band structure and bending properties of X nanotubes and Xene sheets, respectively. Specifically, we first show that zigzag and armchair X nanotubes with radii in the range 1 to 5 nm are semiconducting. In particular, we find an inverse linear dependence of the bandgap with respect to the radius for all nanotubes, other than the armchair and zigzag type III carbon variants, for which we find an inverse quadratic dependence. Next, we exploit the connection between cyclic symmetry and uniform bending deformations to calculate the bending moduli of Xene sheets in both zigzag and armchair directions. We find Kirchhoff-Love type bending behavior for all sheets, with graphene and stanene possessing the largest and smallest moduli, respectively. In addition, other than graphene, the sheets demonstrate significant anisotropy, with larger bending moduli along the armchair direction. Finally, we demonstrate that the proposed approach has very good parallel scaling and is highly efficient, enabling ab initio simulations of unprecedented size for systems with a high degree of cyclic symmetry. In particular, we show that even micron-sized nanotubes can be simulated with modest computational effort.