Magnesium is the lightest structural alloy, yet its practical use is limited by its low ductility. Recent studies suggest ductility enhancement in dilute Mg alloys may stem from favorable solute modification of (c+a) pyramidal I/II screw dislocation core energy difference, activating (c+a) slip via a double cross-slip mechanism. This work conducts large-scale DFT calculations, reaching similar to 6,000 atoms, of (c + a) dislocation energetics in Mg and Mg-Y/Zn alloys. We find that relative solute strengthening effects on pyramidal I and II screw dislocation glide are crucial for cross-slip enhancement in Mg-Y, in contrast to prior investigations, that find solute-mediated dislocation-core energy modification as the main driver. Our predictions align with single-and poly-crystal experimental results and also capture the transition from pyramidal II to I preferred slip in Mg-Y.

Abstract Alkali salts are widely used in solution processing, yet the corresponding cations are often assumed to remain in the liquid phase. Here, we show that alkali ions introduced during the solution synthesis of SnSe are retained through particle isolation and continue to influence the material during subsequent thermal processing, where they shape the evolution of the final polycrystalline material. Different SnSe powders were prepared using Li+, Na+, and K+ precursors, as well as tetramethylammonium (TMA+) precursors as a nonalkali reference for comparison, and all samples were consolidated under identical conditions. Although all three alkali ions were found in the matrix, at grain boundaries, and in segregated nanoscale regions, they partitioned differently and resulted in distinct grain sizes, defect distributions, and therefore transport properties. Li induced the strongest grain size heterogeneity and the lowest energy barriers, Na the best overall balance between carrier concentration and mobility, and K the broadest alkali-rich grain boundary regions along with the strongest interfacial penalty to charge carrier transport. These results show that residual alkali ions are not just remnants of solution synthesis but active determinants of microstructure and thermoelectric performance in SnSe.

We present an efficient and scalable computational framework for pseudopotential Kohn-Sham density functional theory (KS-DFT) calculations using an enriched finite element (EFE) basis. The EFE basis is formed by augmenting the classical finite element (CFE) basis with compact atom-centered functions, which we term enrichment functions. The key idea is to combine the completeness of a finite element basis with the efficiency of an atom-centered basis. We orthogonalize the enrichment functions with respect to the underlying CFE basis to simultaneously improve the conditioning of the EFE basis and the efficiency of evaluating the inverse of the overlap matrix. To efficiently solve the Kohn-Sham eigenvalue problem, we employ a residual-based Chebyshev subspace iteration approach that is tolerant to approximations in the evaluation of the inverse of the overlap matrix. We demonstrate the accuracy of the framework as compared to the widely available DFT packages. For benchmark non-periodic calculations, ranging up to 39,083 electrons, the EFE basis offers a 5-7× reduction in degrees of freedom over the CFE basis. As a result of this, EFE achieves a 5-9× reduction in computational cost over the CFE basis. The EFE basis also provides a 4-5× reduction in the required memory compared to the CFE basis, thus allowing for optimal utilization of computational resources. Finally, we demonstrate that the EFE basis affords good parallel scalability. Overall, the EFE basis offers a systematically convergent, fast, scalable, resource-efficient basis for pseudopotential DFT calculations.

Noncollinear (NC) magnetism and spin-orbit coupling (SOC) are indispensable for predictive ab initio materials simulations with pronounced relativistic effects and magnetic frustration, yet they significantly increase the cost of cubic-scaling density functional theory (DFT) by introducing complex 2-component wavefunctions per electron and consequently much larger eigenproblems. We present a GPU-centric high-performance framework for NC-SOC DFT that combines: (i) algorithmic advances for solving finite-element (FE) discretized DFT equations; (ii) residual-based Chebyshev filtered subspace iteration (R-ChFSI), tolerant to inexact matrix-vector products, for the resulting sparse generalized eigenproblem; (iii) a matrix-free strategy for accelerating FE Poisson solver; (iv) R-ChFSI-enabled mixed-precision computation with block floating-point compressed MPI communication at compression ratios over 4x, preserving double-precision robustness while reducing compute and data movement costs; and (v) a communication efficient band-partitioning algorithm to improve scalability. Numerical results demonstrate improved time-to-solution and excellent scaling on exascale architectures, enabling fully relativistic pseudopotential DFT simulations of up to 100,000 electrons.

Employing the plasma enhanced atomic layer deposition method, the top heavily doped Al:HfO2 nanofilms embedded with Al-rich interlayers are fabricated with a thickness that varies between 12.8 nm and 13.6 nm, and a nominal dopant concentration of 7.7 mol%. The phase compositions and microstructures of Al:HfO2 nanofilms are characterized by grazing incidence X-ray diffraction, transmission electron microscope and Time-of-Flight secondary ion mass spectrometry. The ferroelectric properties of top heavily doped Al:HfO2 nanofilms are optimized by varying the annealing temperature and the distribution of Al-rich strips in HfO2 matrix. The largest remanent polarization is found to be 60.68 mu C/cm(2) (51.52 mu C/cm(2) corrected by positive up-negative down test) for Si-11123 Al:HfO2 nanofilm at the optimized annealing temperature of 750 degrees C, and which is comparable to those of ferroelectric HfO2 films prepared using epitaxial growth method. The large-scale density functional theory (DFT) calculation on a supercell model containing 2592 atoms for a 12 nm-thick Al:HfO2 nanofilm elucidates that the top heavily doped interlayer mimics the role of capping layer that produces lattice distortions normal to film surface. Meanwhile, other Al-rich strips could create the shearing like atomic distortions in the lateral directions of the nanofilm. A synergistic interplay between those two types of mechanical confinement leads to the prominent ferroelectric polarization in top heavily doped Al:HfO2 nanofilm. Additional ab-initio molecular dynamics simulations and dipole moment calculations with Berry phase method directly confirm the formation of ferroelectric o-phase in the mechanically confined region in both Al:HfO2-(001) and Al:HfO2-(101) nanofilms, and a low phase transition kinetic energy barrier height (similar to 7.0 kJ/mol) between t- and polar o-phase is predicted. It is also revealed that the resulting dipole moment in Al:HfO2-(101) nanofilm could exhibit a titled alignment with respect to the surface normal, giving the detectable ferroelectric polarization in experiment.

The Hohenberg-Kohn (HK) theorem -- the bedrock of density functional theory (DFT) -- establishes a universal map from the external potential to the energy. It also relates the electron density and atomic forces to the variation of the energy with the external potential. But the HK map is rarely utilized in atomistics, wherein interatomic potentials are defined using the molecular or crystal structure rather than the external potential. As a break from this tradition, we present a field theoretic atomistics framework where the external potential assumes the central quantity. We machine learn the HK energy map while satisfying the thermodynamic limit. Further, we obtain both forces and electron density from the variation of the HK energy map, that are exact relations. Our models attain good accuracy across diverse benchmarks and compete with state-of-the-art machine learned interatomic potentials. Through electron density, we predict accurate dipole and quadrupole moments, otherwise nontrivial for interatomic potentials. Our formulation paves the way for a scalable electronic structure surrogate to DFT.

The aperiodic order of quasicrystals bridges the amorphous and crystalline regime, so it has remained unclear whether quasicrystals are metastable or stable phases of matter. Density functional theory is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing size, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases, thus revealing that translational symmetry is not a necessary condition for the zero-temperature stability of inorganic solids. Although we found the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is limited by nucleation, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques broadly open the door to first-principles investigations into the structure-bonding-stability relationships of aperiodic materials.

Twisted multilayer graphene, characterized by its moire patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. While first-principles calculations are computationally prohibitive and empirical interatomic potentials often lack accuracy, machine-learning interatomic potentials (MLIPs) present a promising alternative, offering (near-)DFT accuracy at a significantly reduced computational cost. Despite their success in two-dimensional monolayer materials, MLIPs remain under-explored in twisted multilayer graphene systems. In this work, we develop an Atomic Cluster Expansion (ACE) potential for simulating twisted multilayer graphene and test it on a range of simulation tasks. We propose an approach to construct training and test datasets that incorporate all possible twist angles and local stacking, including incommensurate ones. To achieve this, we generate configurations with periodic boundary conditions suitable for DFT calculations, and then introduce an internal twist and shift within those supercell structures. We further refine the dataset through active learning filtering, guided by Bayesian uncertainty quantification. Our model is validated for accuracy and robustness through a wide range of numerical tests.

In this paper, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. This real-space approach for DFT calculations combines the efficiency of PAW formalism involving smooth electronic fields with the ability of systematically improvable higher-order finite-element basis to achieve significant computational gains. In particular, we developed efficient strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigenspace in each self-consistent field iteration. These strategies leverage the low-rank perturbation of the FE basis overlap matrix in conjunction with reduced order quadrature rules to invert the discretized PAW overlap matrix while also exploiting the sparsity of both the local and nonlocal parts of the discretized PAW Hamiltonian and overlap matrices. Further, we employ higher-order quadrature rules to accurately evaluate integrals in these matrices involving PAW-atomic data, allowing the use of coarser FE meshes for various electronic fields. Using the proposed approach, we benchmark the accuracy and performance of various representative examples involving periodic and nonperiodic systems with plane-wave-based PAW implementations. Furthermore, we also demonstrate a considerable computational advantage (similar to 5x-10x) over state-of-the-art plane-wave methods for medium to large-scale systems (similar to 6000-35 000 electrons). Finally, we show that our approach (PAW-FE) significantly reduces the degrees of freedom to achieve the desired accuracy, thereby enabling large-scale DFT simulations (>50 000 electrons) at an order of magnitude lower computational cost compared to norm-conserving pseudopotential calculations using finite-element discretization.

Are quasicrystals stable or metastable? Density functional theory (DFT) is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing sizes, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases–revealing that translational symmetry is not a necessary condition for the T = 0 K stability of inorganic solids. Although we find the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is nucleation-limited, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques here broadly open the door to first-principles investigations into the structure-bonding-stability relationships of aperiodic materials.

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes' phase evolution in terms of temperature, morphology, charge cycling and particle size.

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ∼104 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. The average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ∼ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an interoperable approach based on a multiple-program multiple-data (MPMD) paradigm, serving as an intermediary responsible for fast data exchange and interactions between the subsystems. The main goal of MiMiC is to avoid interfering with the underlying parallelization of the external programs, including the operability on hybrid architectures (e.g., CPU/GPU), and keep their setup and execution as close as possible to the original. At the moment, MiMiC offers an efficient implementation of electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) that has demonstrated unprecedented parallel scaling in simulations of large biomolecules using CPMD and GROMACS as QM and MM engines, respectively. However, as it is designed for high flexibility with general multiscale models in mind, it can be straightforwardly extended beyond QM/MM. In this article, we illustrate the software design and the features of the framework, which make it a compelling choice for multiscale simulations in the upcoming era of exascale high-performance computing.

The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO2 cluster with 3684 electrons.

A multi-scale study was carried out to quantify the effect of interstitial hydrogen concentration on plasticity in α-Fe. In this work, the influence of hydrogen on the screw dislocation glide behavior was examined across several length-scales. The insights obtained were integrated to provide an accurate continuum description for the effect of hydrogen on the dislocation based plasticity in polycrystalline α-Fe. At the outset of this work, a new FeH interatomic potential was formulated that enhanced the atomistic estimation of the variation in dislocation glide behavior in presence of hydrogen. Next, the dislocation core reconstruction observed due to the addition of hydrogen using atomistic simulations was validated with the help of large-scale DFT calculations based on the DFT-FE framework. Several atomistic simulations were carried out to comprehensively quantify the effect of hydrogen on the non-Schmid behavior exhibited during the dislocation glide in α-Fe. Finally, crystal plasticity simulations were carried out to understand the effect of hydrogen on the meso-scale deformation behavior of polycrystalline α-Fe.

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix (LRDM) based on G\^ateaux derivatives of the residual of fixed point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these G\^ateaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous SCF iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from $\sim$ 100-1100 atoms ($\sim$ 500--20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized $d$ orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20--30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed point iteration in some cases. Finally, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4$\times$ reduction in computational cost for the total ground-state calculation compared to other preconditioners.

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. We demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

We present DFT-FE 1 . 0, building on DFT-FE 0 . 6 Motamarri et al. (2020) [28], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching similar to 100, 000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation-via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency-as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT - FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our GPU acceleration, which yields similar to 20x speed-up on hybrid CPU-GPU nodes of the Summit supercomputer. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80 - 140 seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing similar to 6, 000 - 15, 000 electrons using 64 - 224 nodes of the Summit supercomputer. Program summary Program Title: DFT-FE CPC Library link to program files: https://doi.org/10.17632/c5ghfc6ctn.1 Developer's repository link: https://github com/dftfeDevelopers/dftfe Licensing provisions: LGPL v3 Programming language: C/C++ External routines/libraries: p4est (http://www.p4est.org/), deal.II (https://www.dealii.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), ELPA (https://elpa.mpcdf.mpg.de/), ScaLAPACK (http://www.netlib.org/scalapack/), Spglib (https://atztogo.github.io/spglib), ALGLIB (http://www.alglib.net/), LIBXC (http://www.tddft.org/programs/libxc/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es), NCCL (optical-https://github.com/NVIDIA/nccl). Nature of problem: Density functional theory calculations. Solution method: We employ a local real-space variational formulation of Kohn-Sham density functional theory that is applicable for both pseudopotential and all-electron calculations on periodic, semiperiodic and non-periodic geometries. Higher-order adaptive spectral finite-element basis is used to discretize the Kohn-Sham equations. Chebyshev polynomial filtered subspace iteration procedure (ChFSI) is employed to solve the nonlinear Kohn-Sham eigenvalue problem self-consistently. ChFSI in DFT-FE employs Cholesky factorization based orthonormalization, and spectrum splitting based Rayleigh-Ritz procedure in conjunction with mixed precision arithmetic. Configurational force approach is used to compute ionic forces and periodic cell stresses for geometry optimization. Additional comments including restrictions and unusual features: Exchange correlation functionals are restricted to Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), with and without spin. The pseudopotentials available are optimized norm conserving Vanderbilt (ONCV) pseudopotentials and Troullier-Martins (TM) pseudopotentials. Calculations are non-relativistic. DFT-FE handles all-electron and pseudopotential calculations in the same framework, while accommodating periodic, non-periodic and semi-periodic boundary conditions. (C) 2022 Elsevier B.V. All rights reserved.

Combining the experimental characterization with the large-scale density functional theory calculations based on finite-element discretization (DFT-FE), we address the stabilization of polar orthorhombic phases (o-HfO 2 ) in Al:HfO 2 nanofilms by means of the atomic registry distortions and lattice deformation caused by Al substitutional defects (Al Hf ) and Schottky defects (2Al Hf + V O ) in tetragonal phases (t-HfO 2 ) or monoclinic phases (m-HfO 2 ). The phase transformation directly from the t-HfO 2 into polar o-HfO 2 are also elucidated within a heterogeneous distribution of Al dopants in both t-HfO 2 bulk crystal structure and Al:HfO 2 nanofilm. It is revealed using large-scale DFT calculations that the Al substitutional defects (Al Hf ) or the Schottky defect (2Al Hf + V O ) could induce the highly extended atomic registry distortions or lattice deformation in the t- and m-HfO 2 phases, but such effects are greatly diminished in ferroelectric orthorhombic phase. By purposely engineering the multiple Al Hf defects to form dopant-rich layers in paraelectric t-HfO 2 nanofilm or bulk crystal, the induced extended lattice distortions surrounding the defect sites exhibit the shearing-like atomic displacement vector field. The large-scale DFT calculations further predicted that the shearing-like microscopic lattice distortions could directly induce the phase transformation from the t-HfO 2 into polar orthorhombic phase in both Al:HfO 2 bulk crystal and nanofilms, leading to the large remanent polarization observed in Al:HfO 2 nanofilms with the presence of Al-rich layers. The current study demonstrates that the ferroelectricity of HfO 2 bulk crystal or thin film can be optimized and tuned by delicately engineering both the distribution and concentration of Al dopants in atomic layer deposition without applying the top capping electrode, providing the extra flexibility for designing the HfO 2 based electronic devices in the future.