Plane-wave Calculations Research Articles

Improving the precision of work-function calculations within plane-wave density functional theory

Abstract Work function is a fundamental property of metals and is related to many surface-related phenomena of metals. Theoretically, it can be calculated with a metal slab supercell in density functional theory (DFT) calculations. In this paper, we discuss how the commensurability of atomic structure with the underlying fast Fourier transform (FFT) grid affects the accuracy of work function obtained from plane-wave pseudopotential DFT calculations. We show that the macroscopic average potential, which is an important property in work function calculations under the ‘bulk reference’ method, is more numerically stable when it is calculated with commensurate FFT grids than with incommensurate FFT grids. Due to the stability of the macroscopic average potential, work function calculated with commensurate FFT grids shows better convergence with respect to basis set size, vacuum length and slab thickness of a slab supercell. After we control the FFT grid commensurability issue in our work function calculations, we obtain well-converged work functions for Al, Pd, Au and Pt of (100), (110) and (111) surface orientations. For all the metals considered, the ordering of our calculated work functions of the three surface orientations agrees with experiment. Our findings reveal the importance of the FFT grid commensurability issue, which is usually neglected in practice, in obtaining accurate metal work functions, and are also meaningful to other DFT calculations which can be affected by the FFT grid commensurability issue.

PW-SMD: A Plane-Wave Implicit Solvation Model Based on Electron Density for Surface Chemistry and Crystalline Systems in Aqueous Solution.

Electron density-based implicit solvation models are a class of techniques for quantifying solvation effects and calculating free energies of solvation without an explicit representation of solvent molecules. Integral to the accuracy of solvation modeling is the proper definition of the solvation shell separating the solute molecule from the solvent environment, allowing for a physical partitioning of the free energies of solvation. Unlike state-of-the-art implicit solvation models for molecular quantum chemistry calculations, e.g., the solvation model based on solute electron density (SMD), solvation models for systems under periodic boundary conditions with plane-wave (PW) basis sets have been limited in their accuracy. Furthermore, a unified implicit solvation model with both homogeneous solution-phase and heterogeneous interfacial structures treated on equal footing is needed. In order to address this challenge, we developed a high-accuracy solvation model for periodic PW calculations that is applicable to molecular, ionic, interfacial, and bulk-phase chemistry. Our model, PW-SMD, is an extension of the SMD molecular solvation model to periodic systems in water. The free energy of solvation is partitioned into the electrostatic and cavity-dispersion-solvent structure (CDS) contributions. The electrostatic contributions of the solvation shell surrounding solute structures are parametrized based on their geometric and physical properties. In addition, the nonelectrostatic contribution to the solvation energy is accounted for by extending the CDS formalism of SMD to incorporate periodic boundary conditions. We validate the accuracy and robustness of our solvation model by comparing predicted solvation free energies against experimental data for molecular and ionic systems, carved-cluster composite energetic models of solvated reaction energies and barriers on surface systems, and deep-learning-accelerated ab initio molecular dynamics (AIMD). Our developed periodic implicit solvation model shows significantly improved accuracy compared to previous work (namely, solvation models in aqueous solution) and can be applied to simulate solvent effects in a wide range of surface and crystalline materials.

Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe2

Large-scale moiré systems are extraordinarily sensitive, with even minute atomic shifts leading to significant changes in electronic structures. Here, we investigate the lattice relaxation effect on moiré band structures in twisted bilayer MoTe2 with two approaches: (a) large-scale plane-wave basis first principle calculation down to 2.88°, (b) transfer learning structure relaxation + local-basis first principles calculation down to 1.1°. We use two types of van der Waals corrections: the D2 method of Grimme and the density-dependent energy correction, and find that the density-dependent energy correction yields a continuous evolution of bandwidth with twist angles. Based on the above results. we develop a complete continuum model with a single set of parameters for a wide range of twist angles, and perform many-body simulations at ν = −1, −2/3, −1/3.

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Strain-dependent one-dimensional confinement channels in twisted bilayer 1T′−WTe2

The low-symmetry and anistropic lattice of 1T′WTe2 is responsible for the existence of parallel one-dimensional channels in the moiré patterns of twisted bilayers. This gives the opportunity to explore moiré physics of a different nature to that widely observed in twisted bilayers of materials with hexagonal symmetries. Here, we combine plane-wave and linear-scaling density functional theory calculations to describe the electronic properties of twisted bilayer 1T′WTe2. We investigate the strain dependence of both aligned bilayer configurations across a range of stacking geometries, and of the twisted bilayer itself. For a small change in the lattice parameters of the constituent 1T′WTe2 monolayers, we find a very substantial increase in the moiré-induced striped electrostatic potential landscape in the twisted bilayer. We measure a peak-to-trough magnitude >200 meV between parallel linear channels, sufficient to induce Luttinger liquid behavior. Published by the American Physical Society 2024

Fragment Orbitals Extracted from First-Principles Plane-Wave Calculations.

Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.

Ab initio predictions of pressure-dependent structural, elastic, and thermodynamic properties of GaMF3 (M = Ca, and Sr) halide perovskites

The structural, elastic, and thermodynamic characteristics of the GaCaF3 and GaSrF3 halide perovskites have been predicted for the first time, using ab initio pseudopotential plane wave calculations. The equilibrium lattice parameters are in good agreement with previously documented results. Both compounds exhibit substantial thermodynamic and mechanical stability. The single-crystal and polycrystalline elastic properties and related properties have been examined. GaCaF3 exhibits higher hardness than GaSrF3. The temperature dependence of the lattice parameter, bulk modulus, volume thermal expansion coefficient, heat capacity, and Debye temperature, have been computed using ab initio calculations combined with the quasi-harmonic Debye model.

Determination of dissociation constants of cephalosporin antibiotics by cellmetry method

Acid dissociation constants of three cephalosporin antibiotics (cefapirin, ceftiofur, and cefotaxime) were calculated by a newly developed methodology. Plane-wave DFT calculations were performed to determine the pKa values, and by choosing the appropriate cell sizes, accurate values could be calculated. Some characteristic points were found which helped us to find correlations among the structural and physic-chemical parameters, and correlation factors were defined as well. This present study can be a base for further approaches to determining acid dissociation constants of cephalosporin molecules.Graphical

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves.

Density functional perturbation theory (DFPT) is a crucial tool for accurately describing lattice dynamics. The adaptively compressed polarizability (ACP) method reduces the computational complexity of DFPT calculations from O(N4) to O(N3) by combining the interpolative separable density fitting (ISDF) algorithm. However, the conventional QR factorization with column pivoting (QRCP) algorithm, used for selecting the interpolation points in ISDF, not only incurs a high cubic-scaling computational cost, O(N3), but also leads to suboptimal convergence. This convergence issue is particularly pronounced when considering the complex interplay between the external potential and atomic displacement in ACP-based DFPT calculations. Here, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a more efficient quadratic-scaling O(N2) alternative to the computationally intensive cubic-scaling O(N3) QRCP algorithm. We implement this efficient K-means-based ISDF algorithm to accelerate plane-wave DFPT calculations in KSSOLV, which is a MATLAB toolbox for performing Kohn-Sham density functional theory calculations within plane waves. We demonstrate that this K-means algorithm not only offers comparable accuracy to QRCP in ISDF but also achieves better convergence for ACP-based DFPT calculations. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly 2 orders of magnitude compared to QRCP in ISDF.

Massively parallel implementation of iterative eigensolvers in large-scale plane-wave density functional theory

The Kohn-sham density functional theory (DFT) is a powerful method to describe the electronic structures of molecules and solids in condensed matter physics, computational chemistry and materials science. However, large and accurate DFT calculations within plane waves process a cubic-scaling computational complexity, which is usually limited by expensive computation and communication costs. The rapid development of high performance computing (HPC) on leadership supercomputers brings new opportunities for developing plane-wave DFT calculations for large-scale systems. Here, we implement parallel iterative eigensolvers in large-scale plane-wave DFT calculations, including Davidson, locally optimal block preconditioned conjugate gradient (LOBPCG), projected preconditioned conjugate gradient (PPCG) and the Chebyshev subspace iteration (CheFSI) algorithms, and analyze the performance of these algorithms in massively parallel plane-wave computing tasks. We adopt a two-level parallelization strategy that combines the message passing interface (MPI) with open multi-processing (OpenMP) parallel programming to handle data exchange and matrix operations in the construction and diagonalization of large-scale Hamiltonian matrix within plane waves. Numerical results illustrate that these iterative eigensolvers can scale up to 42,592 processing cores with high peak performance of 30% on leadship supercomputers to study the electronic structures of bulk silicon systems containing 10,648 atoms. Program summaryProgram Title: Plane wave density functional theory (PWDFT)CPC Library link to program files:https://doi.org/10.17632/c8v2mx5vn4.1Developer's repository link:https://bitbucket.org/berkeleylab/scalesLicensing provisions: BSD 3-clauseProgramming language: C++Nature of problem: PWDFT is used for electronic structure calculations based on Kohn-Sham density functional theory. The key challenge to address is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem. MPI/OpenMP-based approaches are employed to provide multi-core acceleration for the study of the chemical and material properties of larger-scale molecules and solids.Solution method: PWDFT implements self-consistent field (SCF) iterations and direct constrained minimization algorithms with various acceleration strategies. It is written in C++ and offers parallel acceleration based on MPI/OpenMP.

Tailoring surface morphology on anatase TiO2 supported Au nanoclusters: implications for O2 activation.

Strong interaction between the support surface and metal clusters activates the adsorbed molecules at the metal cluster-support interface. Using plane-wave DFT calculations, we precisely model the interface between anatase TiO2 and small Au nanoclusters. Our study focusses on the adsorption and activation of oxygen molecules on anatase TiO2, considering the influence of oxygen vacancies and steps on the surface. We find that the plane (101) and the stepped (103) surfaces do not support O2 activation, but the presence of oxygen vacancies results in strong adsorption and O-O bond length elongation. Modifying the TiO2 surface with supported small Au n nanoclusters (n = 3-5) also significantly enhances O2 adsorption and stretches the O-O bond. We observe that manipulating the cluster orientation through discrete rotations results in improved O2 adsorption and promotes charge transfer from the surface to the molecule. We propose that the orientation of the supported cluster may be manipulated by making the cluster adsorb at the step-edge of (103) TiO2. This results in activated O2 at the cluster-support interface, with a peroxide-range bond length and a low barrier for dissociation. Our modeling demonstrates a straightforward means of exploiting the interface morphology for O2 activation under low precious metal loading, which has important implications for electrocatalytic oxidation reactions and the rational design of supported catalysts.

Tuning the magnetic properties of doped ZnS using transition metal doping: A multi-scale computational approach

Transition metal (TM)-doped dilute magnetic semiconductors (DMS) have emerged as promising materials for spintronic applications such as spin-polarized transport and information storage. However, achieving robust room-temperature ferromagnetism in DMS remains a key challenge. This work undertakes a comprehensive investigation of the effects of Ti- and Cr-doping and (Ti,Cr)-codoping on the structural, electronic, and magnetic properties of wurtzite ZnS using first-principles pseudopotential plane-wave self-consistent field calculations and Monte Carlo simulations. The first-principles DFT calculations were performed using the spin-polarized GGA+U approach to account for strong electron–electron interactions. Structural relaxations revealed expanded lattice parameters and bond lengths for the doped systems compared to pure ZnS, attributed to the larger ionic radii of the dopants. Formation energy calculations confirmed the thermodynamic stability of doping. The band structure and density of states analysis demonstrated the half-metallic nature of the doped ZnS systems with 100% spin polarization induced by strong hybridization between the TM-3d and S-3p states. This mediates robust ferromagnetic coupling, with total magnetic moments around 4-8 μB/cell depending on dopant type and concentration. To complement the zero-temperature DFT results, temperature-dependent Monte Carlo simulations using the single-spin flip Heat Bath algorithm were implemented. The modeling of magnetization, susceptibility, specific heat, and hysteresis loops enabled extracting Curie temperatures up to 427.6 K for 12.5% Cr-doped ZnS. The synergistic combination of first-principles DFT and Monte Carlo computational techniques provides significant insights into tailoring the magnetic properties of TM-doped ZnS dilute magnetic semiconductors. The tunability of structural, electronic, and magnetic characteristics through control of dopant selection and concentration demonstrates the promising potential of transition metal-doped ZnS for spintronic devices operable at room-temperature.

Using Noncovalent Interactions to Test the Precision of Projector-Augmented Wave Data Sets.

The projector-augmented wave (PAW) method is one of the approaches that are widely used to approximately treat core electrons and thus to speed up plane-wave basis set electronic structure calculations. However, PAW involves approximations, and it is thus important to understand how they affect the results. Tests of the precision of PAW data sets often use the properties of isolated atoms or atomic solids. While this is sufficient to identify problematic PAW data sets, little information has been gained to understand the origins of the errors and suggest ways to correct them. Here, we show that the interaction energies of molecular dimers are very useful not only to identify problematic PAW data sets but also to uncover the origin of the errors. Using dimers from the S22 and S66 test sets and other dimers, we find that the error in the interaction energy is composed of a short-range component with an exponential decay and a long-range electrostatic part caused by an error in the total charge density. We propose and evaluate a simple improvable scheme to correct the long-range error and find that even in its simple and readily usable form, it is able to reduce the interaction energy errors to less than half on average for hydrogen-bonded dimers.

Low thermal expansion of layered electrides predicted by density-functional theory.

Layered electrides are a unique class of materials with anionic electrons bound in interstitial regions between thin, positively charged atomic layers. While density-functional theory is the tool of choice for computational study of electrides, there has to date been no systematic comparison of density functionals or dispersion corrections for their accurate simulation. There has also been no research into the thermomechanical properties of layered electrides, with computational predictions considering only static lattices. In this work, we investigate the thermomechanical properties of five layered electrides using density-functional theory to evaluate the magnitude of thermal effects on their lattice constants and cell volumes. We also assess the accuracy of five popular dispersion corrections with both planewave and numerical atomic orbital calculations.

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.

Performance and profiling data of plane-wave calculations in quantum ESPRESSO simulation on three supercomputing centres.

This dataset reflects the parallel execution profiles of five Quantum ESPRESSO simulation (QE) versions in finding the total energy of the Cerium Oxide lattice using the self-consistent field (SCF) method. The data analysis used a strong scale setting to identify the optimal parameters and computing resources needed to complete a single SCF loop for one specific material efficiently. This analysis notably contributed to achieving the Best Performance Award at the 5th APAC HPC-AI Competition. The data comprises three sets. The first set features the parallel execution traces captured via the Extrae performance profiling tool, offering a broad view of the QE's model execution behaviour and how it used computational resources. The second set records how long QE's model ran on a single node at three HPC centres: ThaiSC TARA in Thailand, NSCC ASPIRE-1 in Singapore, and NCI Gadi in Australia. This set focuses on the impact of adjusting three parameters for K-point parallelisation. The final set presents benchmarking data generated by scaling out the QE's model across 32 nodes (1,536 CPU cores) on the NCI Gadi supercomputer. Despite its focus on a single material, the dataset serves as a roadmap for researchers to estimate required computational resources and understand scalability bottlenecks, offering general guidelines adaptable across different HPC systems.

Co-adsorption of H2+nCO+mO2 on α-Fe (110): Effect on hydrogen adsorption, dissociation and diffusion

Hydrogen enriched compressed natural gas contains CO and O2 impurities, which have a coupling effect on hydrogen adsorption, dissociation and diffusion. First principles plane wave calculations have been used to study the co-adsorption and mutual interaction of H2+nCO + mO2 on Fe (110) plane. The results show that it’s easier for pre-adsorbed nCO + mO2 to form high surface coverage compared with pre-adsorbed nCO or mO2. The CO and O2 increased H2 dissociation barrier (Edis−b), and high coverage of nCO, mO2 and nCO + mO2 increased the hydrogen dissociation activation energy (Edis). With the coverage increased, the diffusion barrier (Edif) of H atom into Fe (110) decreased from 1.01eV to 0 by nCO and increased from 1.01eV to 2.14eV by mO2. The Edif was controlled by CO under low coverage and was controlled by O2 under high coverage when nCO + mO2 pre-adsorbed: the deformation charge density and state density analysis show that in H2+nCO + mO2 system, H atom is in an electron gain state at low coverage, which is similar to H in pre-adsorbed nCO, and H is in an electron loss state at high coverage, which is similar to H in pre-adsorbed mO2.The Edif probably related to the charge interaction of Hx− and Hy+ with Fez+.The C, O and H formant peaks from density of states show the influence of C and O on hydrogen invasion in orbital energy.

Full Potential Linearized Augmented Plane Wave Calculations of Electron and Positron Energy Levels in TlBr and TlCl

Abstract Theoretical research was conducted on the energy levels of electrons and positrons in zinc-blend TlBr and TlCl using the first-principle full potential linearized augmented plane wave method based on the gradient generalized approximation GGA. The study involved the calculation of electron and positron band structures which provided predictive data on several properties such as positron mobility, positron affinity, diffusion constants, effective masses, and positronium work function.

Accuracy of a Recent Regularized Nuclear Potential.

F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [Gygi J. Chem. Theory Comput. 2023, 19, 1300-1309.]. This potential V(r) is determined by inverting the Schrödinger equation for the wave function Ansatz ϕ(r) = exp[-h(r)]/√π with h(r) = r erf(ar) + b exp(-a2r2), where a and b are parameters. Gygi fixes b by demanding ϕ to be normalized, with the value b(a) depending on the strength of the regularization controlled by a. We begin this work by re-examining the determination of b(a) and find that the original 10-decimal tabulations of Gygi are only correct to 5 decimals, leading to normalization errors in the order of 10-10. In contrast, we show that a simple 100-point radial quadrature scheme not only ensures at least 10 correct decimals of b but also leads to machine-precision level satisfaction of the normalization condition. Moreover, we extend Gygi's plane-wave study by examining the accuracy of V(r) with high-precision finite element calculations with Hartree-Fock and LDA, GGA, and meta-GGA functionals on first- to fifth-period atoms. We find that although the convergence of the total energy appears slow in the regularization parameter a, orbital energies and shapes are indeed reproduced accurately by the regularized potential even with relatively small values of a, as compared to results obtained with a point nucleus. The accuracy of the potential is furthermore studied with s-d excitation energies of Sc-Cu as well as ionization potentials of He-Kr, which are found to converge to sub-meV precision with a = 4. The findings of this work are in full support of Gygi's contribution, indicating that all-electron plane-wave calculations can be accurately performed with the regularized nuclear potential.

Low-rank approximations for accelerating plane-wave hybrid functional calculations in unrestricted and noncollinear spin density functional theory.

The adaptively compressed exchange (ACE) operator combined with interpolative separable density fitting (ISDF) decomposition has been utilized to accelerate plane-wave hybrid functional calculations for restricted Kohn-Sham density functional theory (DFT), but the neglect of spin degree of freedom has limited its application in the exploration of systems where the spin property of the electron is critical. Herein, we derive the ACE-ISDF formulation for hybrid functional calculations in both unrestricted and noncollinear spin DFT with plane waves and periodic boundary conditions. We proposed an improved ISDF algorithm for the sum of Kohn-Sham orbital pairs to further reduce the computational cost for the spin-noncollinear case. Numerical results demonstrate that these improved ACE-ISDF low-rank approximations can not only significantly reduce the computational time by two orders of magnitude compared with conventional plane-wave hybrid functional calculations but also lead to a good convergence behavior when a moderate rank parameter is set, even for complex periodic magnetic systems. By using these ACE-ISDF approximations, we investigate the electronic and magnetic properties of two-dimensional periodic ferromagnetic semiconductors consisting of triangular zigzag graphene quantum dots and transition metal atoms. Our computational results showcase that hybrid functional calculations in spin DFT can provide not only accurate electronic structures but also accurate magnetic order temperature of ferromagnetic semiconductors compared to local or semilocal functional calculations.